(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 718753, 13679] NotebookOptionsPosition[ 419274, 8715] NotebookOutlinePosition[ 710839, 13443] CellTagsIndexPosition[ 710758, 13438] WindowFrame->Normal ContainsDynamic->True *) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Developing and Communicating Effective Process Control Algorithms for the \ Clinical Laboratory\ \>", "Title", CellMargins->0, CellFrameMargins->{{60, 9}, {9, 12}}, CellChangeTimes->{{3.41252692941323*^9, 3.412526931828525*^9}, { 3.412532832874496*^9, 3.412532837988109*^9}, 3.4322947707888327`*^9}, FontColor->GrayLevel[1], Background->GrayLevel[0]], Cell["George V. 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Typical instruments \ can process from 200 to 1000 samples per hour for 1 to 50 assays per sample.\ \>", "Text", CellChangeTimes->{{3.429876338522984*^9, 3.429876405898333*^9}, { 3.431959622624106*^9, 3.431959622625667*^9}}], Cell["\<\ QC has hardly changed from the days when techs could do 20 assays an hour \ manually.\ \>", "Text", CellChangeTimes->{{3.431959624551955*^9, 3.4319596474878473`*^9}}], Cell[TextData[{ "The measurement ", StyleBox["is", FontWeight->"Bold", FontSlant->"Italic"], " the \[OpenCurlyQuote]product\[CloseCurlyQuote]." }], "Text", CellChangeTimes->{{3.430564947895145*^9, 3.430564979790926*^9}}], Cell["Quality control is done using Controls", "Text", CellChangeTimes->{{3.4298765373943644`*^9, 3.4298765723161983`*^9}}], Cell["\<\ Controls are surrogates for samples, mimicing their performance, but with \ known analyte concentration.\ \>", "Text", CellChangeTimes->{{3.429876584457788*^9, 3.429876616891801*^9}}], Cell["\<\ Controls are typically run at a rate of 2% to 4%, but can be run just once a \ day.\ \>", "Text", CellChangeTimes->{{3.429876618121505*^9, 3.429876665825338*^9}}], Cell[TextData[{ "Assays have Total Allowable Error Requirements (", Cell[BoxData[ FormBox[ SubscriptBox["TE", "a"], TraditionalForm]]], "), set by the government or professional licensing agencies." }], "Text", CellChangeTimes->{{3.429876759350114*^9, 3.429876834960709*^9}, { 3.4305649426347513`*^9, 3.430564942638174*^9}}], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["The Model", "Section", CellChangeTimes->{{3.430564987544223*^9, 3.430564990654714*^9}}], Cell["\<\ Two properties affect the accuracy of the measurement: bias and imprecision. \ Both typically vary with time.\ \>", "Text", CellChangeTimes->{{3.430565093494494*^9, 3.430565133278178*^9}, { 3.430565176814193*^9, 3.430565189553055*^9}, {3.430569470436796*^9, 3.430569470438445*^9}, {3.431686581064797*^9, 3.431686581903161*^9}}], Cell[TextData[StyleBox["Bias is the difference between the mean of a large \ number of controls and target value.", "Item"]], "Text", CellChangeTimes->{{3.4305694730769377`*^9, 3.430569574060495*^9}}], Cell[BoxData[ RowBox[{"bias", " ", "=", " ", RowBox[{"\[Mu]", " ", "-", " ", "target"}]}]], "DisplayFormulaNumbered", CellChangeTimes->{{3.430569581279619*^9, 3.430569606172667*^9}}, TextAlignment->-0.5], Cell[TextData[StyleBox["Total Error (TE) is modeled by the formula:", \ "Item"]], "Text", CellChangeTimes->{{3.4305651912139*^9, 3.430565231853951*^9}}], Cell[BoxData[ RowBox[{"TE", " ", "=", " ", RowBox[{"|", "bias", "|", " ", RowBox[{"+", " ", RowBox[{ SubscriptBox["\[Sigma]", "m"], "\[Cross]", "SD"}]}]}]}]], "DisplayFormulaNumbered", CellChangeTimes->{{3.430565225866165*^9, 3.430565280663172*^9}, { 3.4305653613516397`*^9, 3.430565371163684*^9}}, TextAlignment->-0.5], Cell[TextData[{ "where ", Cell[BoxData[ FormBox[ SubscriptBox["\[Sigma]", "m"], TraditionalForm]]], "is the sigma multiplier, and determines the maximum allowable defect rate. \ " }], "Text", CellChangeTimes->{{3.430565377024206*^9, 3.430565433668951*^9}, { 3.430565494284753*^9, 3.430565513308816*^9}}], Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"defect", " ", "Rate"}], " ", "=", " ", RowBox[{"1", " ", "-", " ", RowBox[{ SubsuperscriptBox["\[Integral]", RowBox[{"-", "\[Infinity]"}], StyleBox[ SubscriptBox["\[Sigma]", "m"], FontWeight->"Bold"]], RowBox[{ FractionBox["1", SqrtBox[ RowBox[{"2", "\[Pi]"}]]], SuperscriptBox["\[ExponentialE]", FractionBox[ RowBox[{"-", SuperscriptBox["x", "2"]}], "2"]], RowBox[{"\[DifferentialD]", "x"}]}]}]}]}], FontSize->16]], "DisplayFormulaNumbered", CellChangeTimes->{{3.430565531801193*^9, 3.430565566514624*^9}, { 3.430565605290329*^9, 3.430565646730028*^9}, {3.43056587106522*^9, 3.4305659573238907`*^9}}, TextAlignment->-0.5], Cell[TextData[{ "This is just the area under the tail of the Gaussian distribution from ", Cell[BoxData[ FormBox[ SubscriptBox["\[Sigma]", "m"], TraditionalForm]]], "to ", "\[Infinity]. 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Instead control limits are established and rules set \ that determine if the QC is acceptable. The most common rule is that with 3 \ controls, the process fails if one control is beyond the limits. Sometimes, \ rules are set so that a failue occurs if 2 of 3 controls are beyond limits.\ \>", "Text", CellChangeTimes->{{3.430567138839718*^9, 3.430567310701373*^9}}], Cell[TextData[{ "Limits are set empirically. Sometimes, the limits are a simple multiple of \ the monthly control SD, and the limits are expressed by rules: ", StyleBox["1-2s", FontSlant->"Italic"], ", or ", StyleBox["1-3s", FontSlant->"Italic"], ", meaning that the process will fail if one control is beyond a limit \ computed by multiplying the monthly SD by 2, or by 3 in the second case. 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If we assume that the process SD is either constant, or changes ", StyleBox["very", FontSlant->"Italic"], " slowly, we can determine the critical bias for the assay and control. The \ critical bias is the bias when the Total Error equals the Allowable Total \ Error:" }], "Text", CellChangeTimes->{{3.430567762067562*^9, 3.430567827331283*^9}, { 3.4305678801631002`*^9, 3.4305678924030724`*^9}, {3.4305680368745003`*^9, 3.430568154610148*^9}}], Cell[BoxData[{ RowBox[{ SubscriptBox["TE", "a"], " ", "=", " ", RowBox[{"TE", " ", "=", " ", RowBox[{"|", "CriticalBias", "|", " ", RowBox[{"+", " ", RowBox[{ SubscriptBox["\[Sigma]", "m"], "\[Cross]", "SD"}]}]}]}]}], "\[IndentingNewLine]", StyleBox[ RowBox[{"CriticalBias", " ", "=", " ", RowBox[{ SubscriptBox["TE", "a"], " ", "-", " ", RowBox[{ SubscriptBox["\[Sigma]", "m"], "\[Cross]", "SD"}]}]}], FontSize->14]}], "DisplayFormulaNumbered", CellChangeTimes->{{3.430568166311986*^9, 3.4305683284418983`*^9}}, TextAlignment->-0.5], Cell["\<\ Note that the larger the SD, the smaller the Critical Bias. The ideal error \ detection curve can be goven in terms of the critical bias:\ \>", "Text", CellChangeTimes->{{3.4305683750253353`*^9, 3.430568429232768*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"criticalBias", "[", RowBox[{"tea_", ",", " ", "sm_", ",", " ", "procSD_"}], "]"}], " ", ":=", " ", RowBox[{"tea", " ", "-", " ", RowBox[{"sm", " ", "*", "procSD"}]}]}]], "DisplayFormulaNumbered", CellChangeTimes->{{3.430569120703174*^9, 3.4305691897627697`*^9}}, TextAlignment->-0.5], Cell[BoxData[ RowBox[{ RowBox[{"pEDIdeal", "[", RowBox[{"x_", ",", " ", "critBias_"}], "]"}], " ", ":=", " ", RowBox[{"\[Piecewise]", GridBox[{ { RowBox[{" ", "0", " "}], RowBox[{ RowBox[{"Abs", "[", "x", "]"}], " ", "<=", " ", "critBias"}]}, {"1", RowBox[{ RowBox[{"Abs", "[", "x", "]"}], " ", ">", " ", "critBias"}]} }]}]}]], "DisplayFormulaNumbered", CellChangeTimes->{{3.430568846275024*^9, 3.430568927936717*^9}, { 3.430568968208349*^9, 3.43056902370389*^9}}, TextAlignment->-0.5], Cell["\<\ Even though the bias and SD of the process is unknown, the process does have \ these parameters. We can determine the probability that a single control is \ with a set of limits for a given bias and SD. It is just the area under the \ Gaussian distribution with parameters bias = \[Mu] - target and \[Sigma] \ between \[PlusMinus]limit:\ \>", "Text", CellChangeTimes->{{3.430569304815692*^9, 3.430569449772929*^9}, { 3.430569626500832*^9, 3.430569680092052*^9}, 3.43057001574059*^9, { 3.430570174100127*^9, 3.430570182690588*^9}}], Cell[BoxData[ FormBox[ StyleBox[ RowBox[{ SubscriptBox["P", "s"], "=", RowBox[{ FractionBox["1", RowBox[{"\[Sigma]", " ", SqrtBox[ RowBox[{"2", " ", "\[Pi]"}]]}]], RowBox[{ SubsuperscriptBox["\[Integral]", RowBox[{"-", "lim"}], RowBox[{"+", "lim"}]], RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{"-", FractionBox[ SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "bias"}], ")"}], "2"], RowBox[{"2", " ", SuperscriptBox["\[Sigma]", "2"]}]]}]], RowBox[{"\[DifferentialD]", "x"}]}]}]}]}], FontSize->14], TraditionalForm]], "DisplayFormulaNumbered", CellMargins->{{24, Inherited}, {Inherited, Inherited}}, CellChangeTimes->{{3.420716627136118*^9, 3.4207166719660254`*^9}, { 3.420716864452269*^9, 3.420716902202675*^9}, {3.420725760279325*^9, 3.4207257868553667`*^9}, {3.420725828156679*^9, 3.42072583917418*^9}, 3.4207260364207697`*^9, {3.420726474851513*^9, 3.4207264753309193`*^9}, 3.420726520652009*^9, {3.430570193790513*^9, 3.430570204563773*^9}, { 3.431959752214324*^9, 3.431959771339034*^9}}, TextAlignment->-0.5], Cell[TextData[{ "The probability of rejection, ", Cell[BoxData[ FormBox[ SubscriptBox["P", "f"], TraditionalForm]]], ", is 1 - ", Cell[BoxData[ FormBox[ SubscriptBox["P", "s"], TraditionalForm]]], "." }], "Text", CellChangeTimes->{{3.430570261975737*^9, 3.430570320513768*^9}, { 3.4319617399380503`*^9, 3.431961743569045*^9}}], Cell["\<\ If there are more controls, then the probability of error detection is a \ simple application of binomial probability\ \>", "Text", CellChangeTimes->{{3.430570217172759*^9, 3.430570254337584*^9}, { 3.430570324673461*^9, 3.430570349209206*^9}}], Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"probability", "[", RowBox[{ "bias", ",", " ", "\[Sigma]", ",", " ", "limit", ",", " ", "n", ",", " ", "k"}], "]"}], " ", "=", RowBox[{ RowBox[{"(", "\[NoBreak]", GridBox[{ {"n"}, {"k"} }], "\[NoBreak]", ")"}], SuperscriptBox[ SubscriptBox["P", "s"], "k"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", SubscriptBox["P", "s"]}], ")"}], RowBox[{"n", "-", "k"}]]}]}], FontSize->14]], "DisplayFormulaNumbered", CellChangeTimes->{{3.430570530261702*^9, 3.430570624073053*^9}, { 3.4319616974526787`*^9, 3.431961719721098*^9}, {3.4319617615798073`*^9, 3.431961814671977*^9}}, TextAlignment->-0.5], Cell[TextData[{ "where ", Cell[BoxData[ FormBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"n"}, {"k"} }], "\[NoBreak]", ")"}], TraditionalForm]]], " is the combination of n things k at a time, n is the number of controls \ used, and k is the number of controls that have to be 'out' to signal a \ failure." }], "Text", CellChangeTimes->{{3.430570630923438*^9, 3.430570734136579*^9}, { 3.4322973475166388`*^9, 3.432297350490952*^9}}], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Exploring Acceptance Limits", "Section", CellChangeTimes->{ 3.429876275902247*^9, {3.430571058305084*^9, 3.4305710705983353`*^9}}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " 6 provides the means to explore the error detection rules. 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9, 12, 15}}, {{ Hold[$CellContext`nConsOut$$], 1, "\[OpenCurlyQuote]Out\[CloseCurlyQuote]"}, {1, 2}}, {{ Hold[$CellContext`limit$$], 0.4, "\!\(\*FractionBox[\(Limit\), SubscriptBox[\(TE\), \(a\)]]\)"}, 0.05, 2.}, {{ Hold[$CellContext`procSD$$], 0.2, "\!\(\*FractionBox[\(SD\), SubscriptBox[\(TE\), \(a\)]]\)"}, 0.1, 0.5}, {{ Hold[$CellContext`sigmMult$$], 2., "\!\(\*SubscriptBox[\(\[Sigma]\), \(m\)]\)"}, 1.65, 3.}}, Typeset`size$$ = {433., {151., 156.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`nConsTot$265753$$ = 0, $CellContext`nConsOut$265754$$ = False, $CellContext`limit$265755$$ = 0, $CellContext`procSD$265756$$ = 0, $CellContext`sigmMult$265757$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`limit$$ = 0.4, $CellContext`nConsOut$$ = 1, $CellContext`nConsTot$$ = 3, $CellContext`procSD$$ = 0.2, $CellContext`sigmMult$$ = 2.}, "ControllerVariables" :> { Hold[$CellContext`nConsTot$$, $CellContext`nConsTot$265753$$, 0], Hold[$CellContext`nConsOut$$, $CellContext`nConsOut$265754$$, False], Hold[$CellContext`limit$$, $CellContext`limit$265755$$, 0], Hold[$CellContext`procSD$$, $CellContext`procSD$265756$$, 0], Hold[$CellContext`sigmMult$$, $CellContext`sigmMult$265757$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> $CellContext`errorDetCurveTEERF[$CellContext`nConsTot$$, \ $CellContext`nConsOut$$, $CellContext`limit$$, $CellContext`procSD$$, 1., $CellContext`sigmMult$$], "Specifications" :> {{{$CellContext`nConsTot$$, 3, "Controls"}, {3, 4, 5, 6, 9, 12, 15}, ControlType -> SetterBar}, {{$CellContext`nConsOut$$, 1, "\[OpenCurlyQuote]Out\[CloseCurlyQuote]"}, {1, 2}, ControlType -> SetterBar}, {{$CellContext`limit$$, 0.4, "\!\(\*FractionBox[\(Limit\), 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Pattern[$CellContext`procSD, Blank[]]] := Module[{$CellContext`i, $CellContext`ps1}, $CellContext`ps1 = \ $CellContext`probSuc1ConERF[$CellContext`actionLimit, $CellContext`bias, \ $CellContext`procSD]; If[$CellContext`ps1 < 1.*^-6, $CellContext`ps1 = 1.*^-6]; If[$CellContext`ps1 > 0.999999, $CellContext`ps1 = 0.999999]; If[$CellContext`nConsTot >= $CellContext`nConsOut, 1 - Sum[(Binomial[$CellContext`nConsTot, $CellContext`i] ( 1 - $CellContext`ps1)^$CellContext`i) \ $CellContext`ps1^($CellContext`nConsTot - $CellContext`i), {$CellContext`i, 0, $CellContext`nConsOut - 1}], 0]], $CellContext`probSuc1ConERF[ Pattern[$CellContext`actionLimit, Blank[]], Pattern[$CellContext`bias, Blank[]], Pattern[$CellContext`procSD, Blank[]]] := (1/2) ( Erf[($CellContext`actionLimit - $CellContext`bias)/( Sqrt[2] $CellContext`procSD)] + Erf[($CellContext`actionLimit + $CellContext`bias)/( Sqrt[2] $CellContext`procSD)]), $CellContext`tenths[ Pattern[$CellContext`xmin, Blank[]], Pattern[$CellContext`xmax, 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Typeset`size$$ = {433., {204.0625, 211.9375}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`nTot$282562$$ = 0, $CellContext`nOut$282563$$ = False, $CellContext`procSD$282564$$ = 0, $CellContext`sm$282565$$ = 0, $CellContext`goal$282566$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`goal$$ = 0.95, $CellContext`nOut$$ = 1, $CellContext`nTot$$ = 3, $CellContext`procSD$$ = 0.2, $CellContext`sm$$ = 1.95}, "ControllerVariables" :> { Hold[$CellContext`nTot$$, $CellContext`nTot$282562$$, 0], Hold[$CellContext`nOut$$, $CellContext`nOut$282563$$, False], Hold[$CellContext`procSD$$, $CellContext`procSD$282564$$, 0], Hold[$CellContext`sm$$, $CellContext`sm$282565$$, 0], Hold[$CellContext`goal$$, $CellContext`goal$282566$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Quiet[ $CellContext`QCLimitsManipulate[$CellContext`nTot$$, \ $CellContext`nOut$$, 1., $CellContext`procSD$$, $CellContext`sm$$, $CellContext`goal$$]], "Specifications" :> {{{$CellContext`nTot$$, 3, "Controls"}, {3, 4, 5, 6, 9, 12, 15}, ControlType -> SetterBar}, {{$CellContext`nOut$$, 1, "\[OpenCurlyQuote]Out\[CloseCurlyQuote]"}, {1, 2}}, {{$CellContext`procSD$$, 0.2, "\!\(\*FractionBox[\(SD\), SubscriptBox[\(TE\), \(a\)]]\)"}, 0.099, 0.4, Appearance -> "Labeled"}, {{$CellContext`sm$$, 1.95, "\!\(\*SubscriptBox[\(\[Sigma]\), \(m\)]\)"}, 1.65, 3., Appearance -> "Labeled"}, {{$CellContext`goal$$, 0.95, "ED Goal"}, 0.5, 0.95, Appearance -> "Labeled"}}, "Options" :> {ControlPlacement -> Left}, "DefaultOptions" :> {}], ImageSizeCache->{772., {235.5625, 243.4375}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`QCLimitsManipulate[ Pattern[$CellContext`nConsTot, Blank[]], Pattern[$CellContext`nConsOut, Blank[]], Pattern[$CellContext`TotErr, Blank[]], Pattern[$CellContext`procSD, Blank[]], Pattern[$CellContext`sigmaMult, Blank[]], Pattern[$CellContext`targetProbReject, Blank[]]] := Module[{$CellContext`parameters, $CellContext`limit, \ $CellContext`critBias, $CellContext`falseAcc}, $CellContext`critBias = \ $CellContext`getBiasMax[$CellContext`TotErr, $CellContext`procSD, \ $CellContext`sigmaMult]; $CellContext`parameters = \ $CellContext`findBestAccLimitParametersERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`TotErr, $CellContext`procSD, \ $CellContext`sigmaMult, $CellContext`targetProbReject]; $CellContext`limit = Part[$CellContext`parameters, 1]; $CellContext`falseAcc = \ $CellContext`falseAccCurveTEERF[$CellContext`nConsTot, $CellContext`nConsOut, \ $CellContext`critBias, $CellContext`limit, $CellContext`procSD, \ $CellContext`TotErr]; Column[{ Row[{"\!\(\*SubscriptBox[\(TE\), \(a\)]\) set to 1.0."}], Row[{"Green : acceptance limit = \[PlusMinus]", NumberForm[ Part[$CellContext`parameters, 1], {4, 2}]}], Row[{"Orange : ideal ED, crit. bias = ", NumberForm[$CellContext`critBias, {4, 2}]}], Row[{"Red : ", NumberForm[100. Part[$CellContext`parameters, 2], {4, 2}], "% false rejection."}], Row[{"Magenta : ", NumberForm[100 $CellContext`falseAcc, {5, 3}], "% false acceptance."}], $CellContext`errorDetCurve[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`limit, $CellContext`procSD, \ $CellContext`TotErr, $CellContext`sigmaMult]}]], $CellContext`getBiasMax[ Pattern[$CellContext`TEa, Blank[]], Pattern[$CellContext`procSD, Blank[]], Pattern[$CellContext`sigmaMult, Blank[]]] := $CellContext`TEa - $CellContext`sigmaMult \ $CellContext`procSD, $CellContext`findBestAccLimitParametersERF[ Pattern[$CellContext`nConsTot, Blank[]], Pattern[$CellContext`nConsOut, Blank[]], Pattern[$CellContext`theTEa, Blank[]], Pattern[$CellContext`procSD, Blank[]], Pattern[$CellContext`sigmaMult, Blank[]], Pattern[$CellContext`targetProbReject, Blank[]]] := Module[{$CellContext`limit, $CellContext`falseRejection, \ $CellContext`critBias, $CellContext`theQCRule, $CellContext`ruleString}, \ $CellContext`limit = $CellContext`findAcceptanceLimits[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`theTEa, $CellContext`procSD, \ $CellContext`sigmaMult, $CellContext`targetProbReject]; \ $CellContext`falseRejection = \ $CellContext`falseRejectCurveTEERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`limit, $CellContext`procSD, \ $CellContext`theTEa]; $CellContext`critBias = \ $CellContext`getBiasMax[$CellContext`theTEa, $CellContext`procSD, \ $CellContext`sigmaMult]; $CellContext`theQCRule = \ $CellContext`limit/$CellContext`procSD; $CellContext`ruleString = StringJoin["Fail if ", ToString[$CellContext`nConsOut], If[$CellContext`nConsOut == 1, " con is beyond ", " cons are beyond "], ToString[$CellContext`theQCRule], " s, (N = ", ToString[$CellContext`nConsTot], ")"]; {$CellContext`limit, $CellContext`falseRejection, \ $CellContext`critBias, $CellContext`theQCRule, $CellContext`ruleString}], \ $CellContext`findAcceptanceLimits[ Pattern[$CellContext`nConsTot, Blank[]], Pattern[$CellContext`nConsOut, Blank[]], Pattern[$CellContext`TEa, Blank[]], Pattern[$CellContext`procSD, Blank[]], Pattern[$CellContext`sigmaMult, Blank[]], Pattern[$CellContext`targetProbRejection, Blank[]]] := Module[{$CellContext`slope, $CellContext`intercept, $CellContext`lim1, \ $CellContext`psd1, $CellContext`lim2, $CellContext`psd2, $CellContext`ans}, \ $CellContext`psd1 = 0.01 $CellContext`TEa; $CellContext`lim1 = \ $CellContext`findAcceptanceLimitsERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`TEa, $CellContext`psd1, \ $CellContext`sigmaMult, $CellContext`targetProbRejection]; $CellContext`psd2 = 0.15 $CellContext`TEa; $CellContext`lim2 = \ $CellContext`findAcceptanceLimitsERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`TEa, $CellContext`psd2, \ $CellContext`sigmaMult, $CellContext`targetProbRejection]; $CellContext`slope = \ ($CellContext`lim2 - $CellContext`lim1)/($CellContext`psd2 - \ $CellContext`psd1); $CellContext`intercept = $CellContext`lim1 - \ $CellContext`slope $CellContext`psd1; $CellContext`ans = $CellContext`procSD \ $CellContext`slope + $CellContext`intercept; $CellContext`ans = If[$CellContext`ans > 0, $CellContext`ans, 0]; $CellContext`ans], $CellContext`findAcceptanceLimitsERF[ Pattern[$CellContext`nConsTot, Blank[]], Pattern[$CellContext`nConsOut, Blank[]], Pattern[$CellContext`TEa, Blank[]], Pattern[$CellContext`procSD, Blank[]], Pattern[$CellContext`sigmaMult, Blank[]], Pattern[$CellContext`targetProbRejection, Blank[]]] := Module[{$CellContext`x, $CellContext`ans, $CellContext`maxBias}, \ $CellContext`maxBias = $CellContext`getBiasMax[$CellContext`TEa, \ $CellContext`procSD, $CellContext`sigmaMult]; $CellContext`ans = FindRoot[$CellContext`probErrDetectERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`x, $CellContext`maxBias, \ $CellContext`procSD] == $CellContext`targetProbRejection, {$CellContext`x, \ $CellContext`maxBias}, MaxIterations -> 25]; Part[$CellContext`ans, 1, 2]], $CellContext`probErrDetectERF[ Pattern[$CellContext`nConsTot, Blank[]], Pattern[$CellContext`nConsOut, Blank[]], Pattern[$CellContext`actionLimit, Blank[]], Pattern[$CellContext`bias, Blank[]], Pattern[$CellContext`procSD, Blank[]]] := Module[{$CellContext`i, $CellContext`ps1}, $CellContext`ps1 = \ $CellContext`probSuc1ConERF[$CellContext`actionLimit, $CellContext`bias, \ $CellContext`procSD]; If[$CellContext`ps1 < 1.*^-6, $CellContext`ps1 = 1.*^-6]; If[$CellContext`ps1 > 0.999999, $CellContext`ps1 = 0.999999]; If[$CellContext`nConsTot >= $CellContext`nConsOut, 1 - Sum[(Binomial[$CellContext`nConsTot, $CellContext`i] ( 1 - $CellContext`ps1)^$CellContext`i) \ $CellContext`ps1^($CellContext`nConsTot - $CellContext`i), {$CellContext`i, 0, $CellContext`nConsOut - 1}], 0]], $CellContext`probSuc1ConERF[ Pattern[$CellContext`actionLimit, Blank[]], Pattern[$CellContext`bias, Blank[]], Pattern[$CellContext`procSD, Blank[]]] := (1/2) ( Erf[($CellContext`actionLimit - $CellContext`bias)/( Sqrt[2] $CellContext`procSD)] + Erf[($CellContext`actionLimit + $CellContext`bias)/( Sqrt[2] $CellContext`procSD)]), $CellContext`falseRejectCurveTEERF[ Pattern[$CellContext`nConsTot, Blank[]], Pattern[$CellContext`nConsOut, Blank[]], Pattern[$CellContext`limit, Blank[]], Pattern[$CellContext`procSD, Blank[]], Pattern[$CellContext`TEa, Blank[]]] := Module[{$CellContext`ans}, Off[ MessageName[NIntegrate, "inum"]]; $CellContext`ans = NIntegrate[ $CellContext`probErrDetectERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`limit, $CellContext`x, \ $CellContext`procSD], {$CellContext`x, 0, $CellContext`TEa/ 4}]/($CellContext`TEa/4); On[ MessageName[ NIntegrate, "inum"]]; $CellContext`ans], $CellContext`falseAccCurveTEERF[ Pattern[$CellContext`nConsTot, Blank[]], Pattern[$CellContext`nConsOut, Blank[]], Pattern[$CellContext`critval, Blank[]], Pattern[$CellContext`procSD, Blank[]], Pattern[$CellContext`TEa, Blank[]]] := Module[{$CellContext`ans, $CellContext`allArea}, Off[ MessageName[NIntegrate, "inum"]]; $CellContext`allArea = 3 $CellContext`TEa - $CellContext`critval; $CellContext`ans = 1 - NIntegrate[ $CellContext`probErrDetectERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`critval, $CellContext`x, \ $CellContext`procSD], {$CellContext`x, $CellContext`limit, 3 $CellContext`TEa}]/$CellContext`allArea; On[ MessageName[ NIntegrate, "inum"]]; $CellContext`ans], $CellContext`falseAccCurveTEERF[ Pattern[$CellContext`nConsTot, Blank[]], Pattern[$CellContext`nConsOut, Blank[]], Pattern[$CellContext`critval, Blank[]], Pattern[$CellContext`limit, Blank[]], Pattern[$CellContext`procSD, Blank[]], Pattern[$CellContext`TEa, Blank[]]] := Module[{$CellContext`ans, $CellContext`allArea, \ $CellContext`upperlimit}, Off[ MessageName[ NIntegrate, "inum"]]; $CellContext`upperlimit = ($CellContext`TEa + \ $CellContext`critval)/ 2; $CellContext`allArea = $CellContext`upperlimit - \ $CellContext`critval; $CellContext`ans = 1 - NIntegrate[ $CellContext`probErrDetectERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`limit, $CellContext`x, \ $CellContext`procSD], {$CellContext`x, $CellContext`critval, \ $CellContext`upperlimit}]/$CellContext`allArea; On[ MessageName[ NIntegrate, "inum"]]; $CellContext`ans], $CellContext`errorDetCurve[ Pattern[$CellContext`nConsTot, Blank[]], Pattern[$CellContext`nConsOut, Blank[]], Pattern[$CellContext`limit, Blank[]], Pattern[$CellContext`procSD, Blank[]], Pattern[$CellContext`TEa, Blank[]], Pattern[$CellContext`sigmMult, Blank[]]] := Module[{$CellContext`fr, $CellContext`critBias, $CellContext`p1, \ $CellContext`p2, $CellContext`p3, $CellContext`p4, $CellContext`p5}, \ $CellContext`fr = $CellContext`TEa/ 4; $CellContext`critBias = \ $CellContext`getBiasMax[$CellContext`TEa, $CellContext`procSD, \ $CellContext`sigmMult]; If[$CellContext`fr > $CellContext`critBias, $CellContext`fr = \ $CellContext`critBias]; $CellContext`p1 = Plot[ $CellContext`probErrDetectERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`limit, $CellContext`x, \ $CellContext`procSD], {$CellContext`x, 0, $CellContext`fr}, Filling -> Axis, FillingStyle -> Hue[0.99], GridLines -> {$CellContext`tenths, $CellContext`tenths}, AxesOrigin -> {0, 0}, RotateLabel -> True, PlotRange -> All, Frame -> True, LabelStyle -> Directive[FontSize -> 13], ImageSize -> 433, FrameLabel -> { "\!\(\*FractionBox[\(Bias\), SubscriptBox[\(TE\), \(a\)]]\)", "Prob for Rejection", StringJoin["Rule: Fail if ", ToString[$CellContext`nConsOut], If[$CellContext`nConsOut == 1, " con is beyond ", " cons are beyond "], ToString[ NumberForm[$CellContext`limit/$CellContext`procSD, {4, 2}]], " s, (N = ", ToString[$CellContext`nConsTot], ") Acceptance Limit = \[PlusMinus]", ToString[ NumberForm[$CellContext`limit, {4, 2}]]], " "}]; $CellContext`p2 = Plot[ $CellContext`probErrDetectERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`limit, $CellContext`x, \ $CellContext`procSD], {$CellContext`x, $CellContext`fr, $CellContext`TEa}, GridLines -> {$CellContext`fiveTenths, $CellContext`tenths}, AxesOrigin -> {0, 0}, RotateLabel -> True, PlotRange -> All, Frame -> True, ImageSize -> 433]; $CellContext`p3 = Plot[ $CellContext`probErrDetectERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`limit, $CellContext`x, \ $CellContext`procSD], {$CellContext`x, $CellContext`critBias, \ $CellContext`TEa}, GridLines -> {$CellContext`fiveTenths, $CellContext`tenths}, AxesOrigin -> {0, 0}, RotateLabel -> True, PlotRange -> All, Frame -> True, ImageSize -> 433, Filling -> Top, FillingStyle -> Magenta]; $CellContext`p4 = Graphics[{Thick, Orange, Line[{{0, 0.}, {$CellContext`critBias, 0.}, {$CellContext`critBias, 1.}, {$CellContext`TEa, 1.}}]}]; $CellContext`p5 = Graphics[{Thick, Green, Line[{{$CellContext`limit, 0.5}, {$CellContext`limit, 1.}}]}]; Show[$CellContext`p1, $CellContext`p2, $CellContext`p3, \ $CellContext`p4, $CellContext`p5]], 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Line[{{3, -1}, {3, 1}}]}], $CellContext`getBiasMax[ Pattern[$CellContext`TEa, Blank[]], Pattern[$CellContext`procSD, Blank[]], Pattern[$CellContext`sigmaMult, Blank[]]] := $CellContext`TEa - $CellContext`sigmaMult \ $CellContext`procSD, $CellContext`findBestAccLimitParametersERF[ Pattern[$CellContext`nConsTot, Blank[]], Pattern[$CellContext`nConsOut, Blank[]], Pattern[$CellContext`theTEa, Blank[]], Pattern[$CellContext`procSD, Blank[]], Pattern[$CellContext`sigmaMult, Blank[]], Pattern[$CellContext`targetProbReject, Blank[]]] := Module[{$CellContext`limit, $CellContext`falseRejection, \ $CellContext`critBias, $CellContext`theQCRule, $CellContext`ruleString}, \ $CellContext`limit = $CellContext`findAcceptanceLimits[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`theTEa, $CellContext`procSD, \ $CellContext`sigmaMult, $CellContext`targetProbReject]; \ $CellContext`falseRejection = \ $CellContext`falseRejectCurveTEERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`limit, $CellContext`procSD, \ $CellContext`theTEa]; $CellContext`critBias = \ $CellContext`getBiasMax[$CellContext`theTEa, $CellContext`procSD, \ $CellContext`sigmaMult]; $CellContext`theQCRule = \ $CellContext`limit/$CellContext`procSD; $CellContext`ruleString = StringJoin["Fail if ", ToString[$CellContext`nConsOut], If[$CellContext`nConsOut == 1, " con is beyond ", " cons are beyond "], ToString[$CellContext`theQCRule], " s, (N = ", ToString[$CellContext`nConsTot], ")"]; {$CellContext`limit, $CellContext`falseRejection, \ $CellContext`critBias, $CellContext`theQCRule, $CellContext`ruleString}], \ $CellContext`findAcceptanceLimits[ Pattern[$CellContext`nConsTot, Blank[]], Pattern[$CellContext`nConsOut, Blank[]], Pattern[$CellContext`TEa, Blank[]], Pattern[$CellContext`procSD, Blank[]], Pattern[$CellContext`sigmaMult, Blank[]], Pattern[$CellContext`targetProbRejection, Blank[]]] := Module[{$CellContext`slope, $CellContext`intercept, $CellContext`lim1, \ $CellContext`psd1, $CellContext`lim2, $CellContext`psd2, $CellContext`ans}, \ $CellContext`psd1 = 0.01 $CellContext`TEa; $CellContext`lim1 = \ $CellContext`findAcceptanceLimitsERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`TEa, $CellContext`psd1, \ $CellContext`sigmaMult, $CellContext`targetProbRejection]; $CellContext`psd2 = 0.15 $CellContext`TEa; $CellContext`lim2 = \ $CellContext`findAcceptanceLimitsERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`TEa, $CellContext`psd2, \ $CellContext`sigmaMult, $CellContext`targetProbRejection]; $CellContext`slope = \ ($CellContext`lim2 - $CellContext`lim1)/($CellContext`psd2 - \ $CellContext`psd1); $CellContext`intercept = $CellContext`lim1 - \ $CellContext`slope $CellContext`psd1; $CellContext`ans = $CellContext`procSD \ $CellContext`slope + $CellContext`intercept; $CellContext`ans = If[$CellContext`ans > 0, $CellContext`ans, 0]; $CellContext`ans], $CellContext`findAcceptanceLimitsERF[ Pattern[$CellContext`nConsTot, Blank[]], Pattern[$CellContext`nConsOut, Blank[]], Pattern[$CellContext`TEa, Blank[]], Pattern[$CellContext`procSD, Blank[]], Pattern[$CellContext`sigmaMult, Blank[]], Pattern[$CellContext`targetProbRejection, Blank[]]] := Module[{$CellContext`x, $CellContext`ans, $CellContext`maxBias}, \ $CellContext`maxBias = $CellContext`getBiasMax[$CellContext`TEa, \ $CellContext`procSD, $CellContext`sigmaMult]; $CellContext`ans = FindRoot[$CellContext`probErrDetectERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`x, $CellContext`maxBias, \ $CellContext`procSD] == $CellContext`targetProbRejection, {$CellContext`x, \ $CellContext`maxBias}, MaxIterations -> 25]; Part[$CellContext`ans, 1, 2]], $CellContext`probErrDetectERF[ Pattern[$CellContext`nConsTot, Blank[]], Pattern[$CellContext`nConsOut, Blank[]], Pattern[$CellContext`actionLimit, Blank[]], Pattern[$CellContext`bias, Blank[]], Pattern[$CellContext`procSD, Blank[]]] := Module[{$CellContext`i, $CellContext`ps1}, $CellContext`ps1 = \ $CellContext`probSuc1ConERF[$CellContext`actionLimit, $CellContext`bias, \ $CellContext`procSD]; If[$CellContext`ps1 < 1.*^-6, $CellContext`ps1 = 1.*^-6]; If[$CellContext`ps1 > 0.999999, $CellContext`ps1 = 0.999999]; If[$CellContext`nConsTot >= $CellContext`nConsOut, 1 - Sum[(Binomial[$CellContext`nConsTot, $CellContext`i] ( 1 - $CellContext`ps1)^$CellContext`i) \ $CellContext`ps1^($CellContext`nConsTot - $CellContext`i), {$CellContext`i, 0, $CellContext`nConsOut - 1}], 0]], $CellContext`probSuc1ConERF[ Pattern[$CellContext`actionLimit, Blank[]], Pattern[$CellContext`bias, Blank[]], Pattern[$CellContext`procSD, Blank[]]] := (1/2) ( Erf[($CellContext`actionLimit - $CellContext`bias)/( Sqrt[2] $CellContext`procSD)] + Erf[($CellContext`actionLimit + $CellContext`bias)/( Sqrt[2] $CellContext`procSD)]), $CellContext`falseRejectCurveTEERF[ Pattern[$CellContext`nConsTot, Blank[]], Pattern[$CellContext`nConsOut, Blank[]], Pattern[$CellContext`limit, Blank[]], Pattern[$CellContext`procSD, Blank[]], Pattern[$CellContext`TEa, Blank[]]] := Module[{$CellContext`ans}, Off[ MessageName[NIntegrate, "inum"]]; $CellContext`ans = NIntegrate[ $CellContext`probErrDetectERF[$CellContext`nConsTot, \ $CellContext`nConsOut, $CellContext`limit, $CellContext`x, \ $CellContext`procSD], {$CellContext`x, 0, $CellContext`TEa/ 4}]/($CellContext`TEa/4); On[ MessageName[NIntegrate, "inum"]]; $CellContext`ans]}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.431173999778454*^9, 3.4311740485772047`*^9, 3.431174309751395*^9, 3.4312612352912273`*^9, 3.4319601906049843`*^9, 3.4322956899867992`*^9, 3.432299518009049*^9, 3.432299583421977*^9}] }, {2}]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Grades", "Section", CellChangeTimes->{ 3.429876275902247*^9, {3.430571154542738*^9, 3.43057115612593*^9}}], Cell[TextData[{ "Rather than just seeing if the computed Total Error (", Cell[BoxData[ FormBox[ SubscriptBox["TE", "calc"], TraditionalForm]]], ") is greater than the Allowable Total Error (", Cell[BoxData[ FormBox[ SubscriptBox["TE", "a"], TraditionalForm]]], "), the ratio is used:" }], "Text", CellChangeTimes->{{3.431258424934655*^9, 3.431258504899487*^9}, { 3.431258539623431*^9, 3.4312585425434723`*^9}}], Cell[BoxData[ StyleBox[ RowBox[{ StyleBox["r", FontSlant->"Italic"], " ", "=", " ", FractionBox[ SubscriptBox["TE", "calc"], SubscriptBox["TE", "a"]]}], FontSize->16]], "DisplayFormulaNumbered", CellChangeTimes->{{3.431258511191004*^9, 3.4312585530116673`*^9}}, TextAlignment->-0.5], Cell[TextData[{ "If ", StyleBox["r", FontSlant->"Italic"], " is much less than 1, the process performance is much better than the \ requirements demand. A ratio of 1.0 indicates that the process is \ \[OpenCurlyQuote]just\[CloseCurlyQuote] acceptble, and a ratio much greater \ than one indicates a substantial process failure.\nUsing this information, a \ grade can be computed. Conceptually, a simple grade equation may be the \ following:" }], "Text", CellChangeTimes->{{3.43125857019016*^9, 3.431258745058176*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"Grade", " ", "=", " ", RowBox[{"100", " ", "-", " ", RowBox[{"30", " ", "\[Cross]", FractionBox[ SubscriptBox["TE", "calc"], SubscriptBox["TE", "a"]]}]}]}], FontSize->16]], "DisplayFormulaNumbered", CellChangeTimes->{{3.431258749343028*^9, 3.431258786126297*^9}}, TextAlignment->-0.5], Cell["\<\ Clearly, a grade provides much more information about the process. \ \>", "Text", CellChangeTimes->{{3.43125893619901*^9, 3.4312589685614357`*^9}}], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Grade Computation", "Section", CellChangeTimes->{ 3.429876275902247*^9, {3.4316844140175056`*^9, 3.431684426672056*^9}, { 3.431960508075122*^9, 3.431960510205509*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"gradeVariationExplorer", "[", RowBox[{ RowBox[{"pt", "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], ",", " ", RowBox[{"pt", "\[LeftDoubleBracket]", "2", "\[RightDoubleBracket]"}], ",", " ", "TEa", ",", " ", "sigMult", ",", "maxBias", ",", " ", "nCons"}], " ", "]"}], ",", " ", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"nCons", ",", " ", "6", ",", " ", "\"\\""}], "}"}], ",", RowBox[{"{", RowBox[{ "3", ",", " ", "6", ",", " ", "9", ",", "12", ",", " ", "16", ",", " ", "20"}], "}"}], ",", " ", RowBox[{"ControlType", " ", "\[Rule]", " ", "SetterBar"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "sigMult", ",", " ", "2.5", ",", " ", "\"\<\!\(\*SubscriptBox[\(\[Sigma]\), \(m\)]\)\>\""}], "}"}], ",", " ", "1.65", ",", " ", "3.0", ",", " ", RowBox[{"Appearance", " ", "\[Rule]", " ", "\"\\""}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "TEa", ",", " ", "8.0", ",", " ", "\"\<\!\(\*SubscriptBox[\(TE\), \(a\)]\)\>\""}], "}"}], ",", " ", "1", ",", " ", "9.5", ",", " ", RowBox[{"Appearance", " ", "\[Rule]", " ", "\"\\""}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "maxBias", ",", " ", "0.85", ",", " ", "\"\<\!\(\*SubscriptBox[\(Bias\), \(max\)]\)\>\""}], "}"}], ",", " ", "0.25", ",", " ", "1.0", ",", " ", RowBox[{"Appearance", " ", "\[Rule]", " ", "\"\\""}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"pt", " ", ",", " ", RowBox[{"{", RowBox[{"2", ",", "1.5"}], "}"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "10"}], ",", " ", "0.05"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"10", ",", "6"}], "}"}], ",", " ", "Locator"}], "}"}], ",", RowBox[{"ControlPlacement", " ", "\[Rule]", " ", "Left"}], ",", " ", RowBox[{"SaveDefinitions", " ", "\[Rule]", " ", "True"}]}], "]"}]], "Input",\ CellChangeTimes->{{3.431683753282145*^9, 3.43168378247233*^9}, { 3.4316842186210318`*^9, 3.431684301492628*^9}, {3.432295726719438*^9, 3.432295740983841*^9}, {3.432300101526545*^9, 3.432300102189748*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`maxBias$$ = 0.85, $CellContext`nCons$$ = 9, $CellContext`pt$$ = {-2.49, 1.3900000000000001`}, $CellContext`sigMult$$ = 2.5, $CellContext`TEa$$ = 8., Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`nCons$$], 6, "Controls"}, {3, 6, 9, 12, 16, 20}}, {{ Hold[$CellContext`sigMult$$], 2.5, "\!\(\*SubscriptBox[\(\[Sigma]\), \(m\)]\)"}, 1.65, 3.}, {{ Hold[$CellContext`TEa$$], 8., "\!\(\*SubscriptBox[\(TE\), \(a\)]\)"}, 1, 9.5}, {{ Hold[$CellContext`maxBias$$], 0.85, "\!\(\*SubscriptBox[\(Bias\), \(max\)]\)"}, 0.25, 1.}, {{ Hold[$CellContext`pt$$], {2, 1.5}}, {-10, 0.05}, {10, 6}}}, Typeset`size$$ = {433., {285.0625, 292.9375}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`nCons$292325$$ = 0, $CellContext`sigMult$292326$$ = 0, $CellContext`TEa$292327$$ = 0, $CellContext`maxBias$292328$$ = 0, $CellContext`pt$292329$$ = {0, 0}}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`maxBias$$ = 0.85, $CellContext`nCons$$ = 6, $CellContext`pt$$ = {2, 1.5}, $CellContext`sigMult$$ = 2.5, $CellContext`TEa$$ = 8.}, "ControllerVariables" :> { Hold[$CellContext`nCons$$, $CellContext`nCons$292325$$, 0], Hold[$CellContext`sigMult$$, $CellContext`sigMult$292326$$, 0], Hold[$CellContext`TEa$$, $CellContext`TEa$292327$$, 0], Hold[$CellContext`maxBias$$, $CellContext`maxBias$292328$$, 0], Hold[$CellContext`pt$$, $CellContext`pt$292329$$, {0, 0}]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> $CellContext`gradeVariationExplorer[ Part[$CellContext`pt$$, 1], Part[$CellContext`pt$$, 2], $CellContext`TEa$$, $CellContext`sigMult$$, \ $CellContext`maxBias$$, $CellContext`nCons$$], "Specifications" :> {{{$CellContext`nCons$$, 6, "Controls"}, {3, 6, 9, 12, 16, 20}, ControlType -> SetterBar}, {{$CellContext`sigMult$$, 2.5, "\!\(\*SubscriptBox[\(\[Sigma]\), \(m\)]\)"}, 1.65, 3., Appearance -> "Labeled"}, {{$CellContext`TEa$$, 8., "\!\(\*SubscriptBox[\(TE\), \(a\)]\)"}, 1, 9.5, Appearance -> "Labeled"}, {{$CellContext`maxBias$$, 0.85, "\!\(\*SubscriptBox[\(Bias\), \(max\)]\)"}, 0.25, 1., Appearance -> "Labeled"}, {{$CellContext`pt$$, {2, 1.5}}, {-10, 0.05}, {10, 6}, ControlType -> Locator}}, "Options" :> {ControlPlacement -> Left}, "DefaultOptions" :> {}], ImageSizeCache->{772., {316.5625, 324.4375}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`gradeVariationExplorer[ Pattern[$CellContext`nomBias, Blank[]], Pattern[$CellContext`nomSD, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`maxBias, Blank[]], Pattern[$CellContext`nCons, Blank[]]] := Module[{$CellContext`nomGrade, $CellContext`gradeMean, \ $CellContext`gradeSD, $CellContext`gradesList, $CellContext`pointsList, \ $CellContext`p1, $CellContext`p2}, {$CellContext`nomGrade, \ $CellContext`gradeMean, $CellContext`gradeSD, $CellContext`gradesList, \ $CellContext`pointsList} = \ $CellContext`gradeTestForPlotSimple[$CellContext`nCons, $CellContext`nomBias, \ $CellContext`nomSD, $CellContext`sm, $CellContext`tea, $CellContext`maxBias, 1000]; $CellContext`p1 = \ $CellContext`gradePlotBkgd[$CellContext`sm, $CellContext`tea, \ $CellContext`maxBias]; $CellContext`p2 = ListPlot[$CellContext`pointsList, PlotRange -> {{-10, 10}, {0, 6}, All}]; Column[{ Row[{"Grade = ", NumberForm[ $CellContext`conGrade2[$CellContext`nomBias, \ $CellContext`nomSD, $CellContext`sm, $CellContext`tea, $CellContext`maxBias], \ {3, 1}], " Bias: ", NumberForm[$CellContext`nomBias, {4, 2}], " SD: ", NumberForm[$CellContext`nomSD, {4, 2}]}], Row[{"CI based on 1000 trials."}], Row[{"Grade 95% CI = \[PlusMinus]", NumberForm[2 $CellContext`gradeSD, {4, 2}], " (", NumberForm[$CellContext`nomGrade - 2 $CellContext`gradeSD, {4, 1}], " - ", NumberForm[$CellContext`nomGrade + 2 $CellContext`gradeSD, {4, 1}], ")"}], Show[$CellContext`p1, $CellContext`p2], $CellContext`gradeDistGraph[$CellContext`gradeMean, \ $CellContext`gradeSD, $CellContext`gradesList]}]], \ $CellContext`gradeVariationExplorer[ Pattern[$CellContext`nomBias, Blank[]], Pattern[$CellContext`nomSD, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`maxBias, Blank[]], Pattern[$CellContext`nCons, Blank[]], Pattern[$CellContext`gradeCalcType, Blank[]]] := Module[{$CellContext`nomGrade, $CellContext`gradeMean, \ $CellContext`gradeSD, $CellContext`gradesList, $CellContext`pointsList, \ $CellContext`p1, $CellContext`p2}, {$CellContext`nomGrade, \ $CellContext`gradeMean, $CellContext`gradeSD, $CellContext`gradesList, \ $CellContext`pointsList} = $CellContext`gradeTestForPlot[$CellContext`nCons, \ $CellContext`nomBias, $CellContext`nomSD, $CellContext`sm, $CellContext`tea, \ $CellContext`maxBias, 1000, $CellContext`gradeCalcType]; If[$CellContext`gradeCalcType == 1, $CellContext`p1 = \ $CellContext`newGradePlotBkgd[$CellContext`sm, $CellContext`tea, \ $CellContext`maxBias], $CellContext`p1 = \ $CellContext`tradGradePlotBkgd[$CellContext`sm, $CellContext`tea, \ $CellContext`maxBias]]; $CellContext`p2 = ListPlot[$CellContext`pointsList, PlotRange -> {{-10, 10}, {0, 6}, All}]; Column[{ Row[{"New Grade = ", NumberForm[ $CellContext`conGrade[$CellContext`nomBias, \ $CellContext`nomSD, $CellContext`sm, $CellContext`tea, $CellContext`maxBias], \ {3, 1}], " 'Traditional' Grade = ", NumberForm[ $CellContext`conGrade2[$CellContext`nomBias, \ $CellContext`nomSD, $CellContext`sm, $CellContext`tea, $CellContext`maxBias], \ {3, 1}]}], Row[{"nominal Bias = ", NumberForm[$CellContext`nomBias, {4, 2}], " nominal SD = ", NumberForm[$CellContext`nomSD, {4, 2}]}], Row[{" Confidence interval based on 1000 trials."}], Row[{"Grade 95% Confidence Interval = \[PlusMinus]", NumberForm[2 $CellContext`gradeSD, {4, 2}], " range: (", NumberForm[$CellContext`nomGrade - 2 $CellContext`gradeSD, {4, 1}], " - ", NumberForm[$CellContext`nomGrade + 2 $CellContext`gradeSD, {4, 1}], ")"}], Show[$CellContext`p1, $CellContext`p2], $CellContext`gradeDistGraph[$CellContext`gradeMean, \ $CellContext`gradeSD, $CellContext`gradesList]}]], $CellContext`nomGrade = 94.30739731828638, $CellContext`pointsList = CompressedData[" 1:eJwVl2k8lG8bhi2Jki1FaCFUUlGpaHFOIYlkSUT/UihRikhEqbRISVESQrZE pCJLQlKy7/s6MwxmMKuxe+f99HyZeeY3931d53kcSuevWjgJ8PHxDQny8f3/ ufXwlN8O0xEQ2dPRPw/UYXypXOHQyBgSlbYwVa/VITuJ2fL95AwyXUR2pZ7q hN1j2uZz26ah6xGxYBhEherkPcsba2cwjgaP9a1zKP/FJ2fiVYmlXvOymseG UXxPv5nTPgffgtMVNE8yZPsKMgTmB2HaW6wSyntPf9BcxdKiSQhSG/IPfx1B ehqt+Ojzftj9d3i97S86Psie8N0nUIWuBmH1lC8DiE+P0jX+ycAhE4vqI6l1 CC2+fSQ1dAa+bh8lRJynUN3l/fabwTzedbBzvvu1w2n6XV78KTps1hz/0/gi H2t+6XtVs5qLGhsfPxo9Poq0pi9SmZX98L+Z/7B6ZT9qr2XpXn9GR9GPA8Rl FmNIk6feTP4bhTcdz5oyCoYgUlpwgRbPhdQ9q2/BemS8fFEkeKyFhVJGpfDK 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Line[{{3, -1}, {3, 1}}]}], $CellContext`gradeTestForPlotSimple[ Pattern[$CellContext`ncontrols, Blank[]], Pattern[$CellContext`testMean, Blank[]], Pattern[$CellContext`testSD, Blank[]], Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`maxBias, Blank[]], Pattern[$CellContext`nTrials, Blank[]]] := Module[{$CellContext`trueGrade, $CellContext`rawList, \ $CellContext`trialsList, $CellContext`pointsList, $CellContext`gradeMean, \ $CellContext`gradeSD}, $CellContext`trueGrade = \ $CellContext`conGrade2[$CellContext`testMean, $CellContext`testSD, \ $CellContext`sm, $CellContext`tea, $CellContext`maxBias]; \ $CellContext`rawList = Table[ $CellContext`testFuncSimple[$CellContext`ncontrols, \ $CellContext`testMean, $CellContext`testSD, $CellContext`sm, \ $CellContext`tea, $CellContext`maxBias], {$CellContext`nTrials}]; \ $CellContext`trialsList = Part[$CellContext`rawList, All, 1]; $CellContext`pointsList = Part[$CellContext`rawList, All, 2]; $CellContext`gradeMean = Mean[$CellContext`trialsList]; $CellContext`gradeSD = StandardDeviation[$CellContext`trialsList]; \ {$CellContext`trueGrade, $CellContext`gradeMean, $CellContext`gradeSD, \ $CellContext`trialsList, $CellContext`pointsList}], $CellContext`conGrade2[ Pattern[$CellContext`bias, Blank[]], Pattern[$CellContext`sd, Blank[]], Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`maxBias, Blank[]]] := Module[{$CellContext`x1, $CellContext`y1, $CellContext`m, \ $CellContext`biasCutoff, $CellContext`r, $CellContext`grade, \ $CellContext`absBias}, $CellContext`biasCutoff = $CellContext`maxBias \ $CellContext`tea; $CellContext`absBias = Abs[$CellContext`bias]; $CellContext`m = 1.; If[$CellContext`absBias == 0., {$CellContext`x1 = 0.; $CellContext`y1 = $CellContext`tea/$CellContext`sm}, \ {$CellContext`m = $CellContext`sd/$CellContext`absBias; $CellContext`x1 = \ $CellContext`tea/($CellContext`sm $CellContext`m + 1); $CellContext`y1 = $CellContext`tea \ ($CellContext`m/($CellContext`sm $CellContext`m + 1))}]; If[$CellContext`x1 > $CellContext`biasCutoff, {$CellContext`x1 = \ $CellContext`biasCutoff; $CellContext`y1 = $CellContext`m \ $CellContext`biasCutoff}]; $CellContext`r = ($CellContext`absBias + \ $CellContext`sd)/(Abs[$CellContext`x1] + Abs[$CellContext`y1]); $CellContext`grade = 104. - 34. $CellContext`r; If[$CellContext`grade > 100., $CellContext`grade = 100.]; If[$CellContext`grade < 0., $CellContext`grade = 0.]; $CellContext`grade], $CellContext`testFuncSimple[ Pattern[$CellContext`ntrials, Blank[]], Pattern[$CellContext`testMean, Blank[]], Pattern[$CellContext`testSD, Blank[]], Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`maxBias, Blank[]]] := Module[{$CellContext`myList, $CellContext`compMean, \ $CellContext`compSD, $CellContext`grade}, $CellContext`myList = RandomReal[ NormalDistribution[$CellContext`testMean, $CellContext`testSD], \ $CellContext`ntrials]; $CellContext`compMean = Mean[$CellContext`myList]; $CellContext`compSD = StandardDeviation[$CellContext`myList]; $CellContext`grade = \ $CellContext`conGrade2[$CellContext`compMean, $CellContext`compSD, \ $CellContext`sm, $CellContext`tea, $CellContext`maxBias]; \ {$CellContext`grade, {$CellContext`compMean, $CellContext`compSD}}], \ $CellContext`gradePlotBkgd[ Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`maxBias, Blank[]]] := Module[{$CellContext`p1, $CellContext`myPoly}, $CellContext`myPoly = Polygon[{{(-$CellContext`tea) $CellContext`maxBias, 0}, {(-$CellContext`tea) $CellContext`maxBias, \ ($CellContext`tea (1 - $CellContext`maxBias))/$CellContext`sm}, { 0, $CellContext`tea/$CellContext`sm}, {$CellContext`tea \ $CellContext`maxBias, ($CellContext`tea ( 1 - $CellContext`maxBias))/$CellContext`sm}, \ {$CellContext`tea $CellContext`maxBias, 0}, {(-$CellContext`tea) $CellContext`maxBias, 0}}]; Graphics[{ EdgeForm[ Directive[ Thickness[0.01], Red]], Directive[Green, Opacity[0.7]], $CellContext`myPoly}, PlotRange -> {{-10.1, 10.1}, {0, 6}}, GridLines -> Automatic, Frame -> True, LabelStyle -> Directive[FontSize -> 14], FrameLabel -> {{"S.D.", ""}, {"bias", ""}}, ImageSize -> {433, 300}, AspectRatio -> Full]], $CellContext`gradeDistGraph[ Pattern[$CellContext`\[Mu], Blank[]], Pattern[$CellContext`\[Sigma], Blank[]], Pattern[$CellContext`theData, Blank[List]]] := Module[{$CellContext`curve, $CellContext`hist, $CellContext`scale, \ $CellContext`maxBin}, $CellContext`maxBin = Max[ BinCounts[$CellContext`theData, {0, 100, 1}]]; $CellContext`scale = \ $CellContext`maxBin/$CellContext`gauss[$CellContext`\[Mu], \ $CellContext`\[Mu], $CellContext`\[Sigma]]; $CellContext`curve = Plot[$CellContext`scale $CellContext`gauss[$CellContext`x, \ $CellContext`\[Mu], $CellContext`\[Sigma]], {$CellContext`x, 0, 100}, PlotStyle -> Thick, PlotRange -> {{0, 100}, All}]; $CellContext`hist = Histograms`Histogram[$CellContext`theData, Histograms`HistogramRange -> {0, 100}, Histograms`HistogramCategories -> 100, GridLines -> Automatic]; Show[$CellContext`hist, $CellContext`curve, PlotRange -> All, ImageSize -> {433, 200}, AspectRatio -> 3/10, Frame -> True, FrameLabel -> {{"frequency", " "}, { "grade", "Distribution of computed grades"}}]], $CellContext`gauss[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`\[Mu], Blank[]], Pattern[$CellContext`\[Sigma], Blank[]]] := Exp[-((($CellContext`x - $CellContext`\[Mu])/$CellContext`\[Sigma])^2/ 2)]/($CellContext`\[Sigma] Sqrt[2 Pi]), Histograms`Histogram[ PatternTest[ Pattern[Histograms`Private`list, Blank[]], VectorQ], PatternTest[ Pattern[Histograms`Private`opts, BlankNullSequence[]], OptionQ]] := With[{Histograms`Private`res = Histograms`Private`histogram[ N[Histograms`Private`list], Histograms`Private`opts]}, Condition[ Histograms`Private`res, Histograms`Private`res =!= $Failed]], Options[Histograms`Histogram] := { Histograms`ApproximateIntervals -> Automatic, BarCharts`BarEdges -> True, BarCharts`BarEdgeStyle -> GrayLevel[0], BarCharts`BarOrientation -> Vertical, BarCharts`BarStyle -> Automatic, Histograms`FrequencyData -> False, Histograms`HistogramCategories -> Automatic, Histograms`HistogramRange -> Automatic, Histograms`HistogramScale -> Automatic, AlignmentPoint -> Center, AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesLabel -> None, AxesOrigin -> Automatic, AxesStyle -> {}, Background -> None, BaselinePosition -> Automatic, BaseStyle -> {}, ColorOutput -> Automatic, ContentSelectable -> Automatic, Epilog -> {}, Frame -> False, FrameLabel -> None, FrameStyle -> {}, FrameTicks -> Automatic, FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, ImageMargins -> 0., ImagePadding -> All, ImageSize -> Automatic, LabelStyle -> {}, Method -> Automatic, PlotLabel -> None, PlotRange -> All, PlotRangeClipping -> True, PlotRangePadding -> Automatic, PlotRegion -> Automatic, PreserveImageOptions -> Automatic, Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, TicksStyle -> {}, DisplayFunction :> $DisplayFunction, FormatType :> TraditionalForm}, TagSet[Histograms`Histogram, MessageName[Histograms`Histogram, "fdfail"], "When FrequencyData -> True and HistogramCategories -> cutoffs, the \ length of the cutoffs vector should be exactly one more than the length of \ the frequency data."], TagSet[Histograms`Histogram, MessageName[Histograms`Histogram, "fdhc"], "Warning: `` is not a valid setting for HistogramCategories when \ FrequencyData -> True. When the data represents frequencies, \ HistogramCategories should specify Automatic or a list of cutoffs. Taking \ HistogramCategories -> Automatic."], TagSet[Histograms`Histogram, MessageName[Histograms`Histogram, "hcat"], "`` is not a valid histogram categories specification. Taking \ HistogramCategories->Automatic."], TagSet[Histograms`Histogram, MessageName[Histograms`Histogram, "ltail"], "Warning: `1` points from the left tail of the data, strictly less \ than `2`, are not included in histogram."], TagSet[Histograms`Histogram, MessageName[Histograms`Histogram, "ltail1"], "Warning: One point from the left tail of the data, strictly less \ than `1`, is not included in histogram."], TagSet[Histograms`Histogram, MessageName[Histograms`Histogram, "noapprox"], "ApproximateIntervals -> `` is a not a valid setting when \ HistogramCategories->{c1, c2, ..., cm}. Taking ApproximateIntervals -> \ False."], TagSet[Histograms`Histogram, MessageName[Histograms`Histogram, "range"], "Warning: `` is not a valid setting for HistogramRange. Taking \ HistogramRange -> Automatic."], TagSet[Histograms`Histogram, MessageName[Histograms`Histogram, "rcount"], "Frequency count of data in categories failed."], TagSet[Histograms`Histogram, MessageName[Histograms`Histogram, "realvec"], "The first argument to Histogram is expected to be a vector of real \ values."], TagSet[Histograms`Histogram, MessageName[Histograms`Histogram, "rtail"], "Warning: `1` points from the right tail of the data, greater than or \ equal to `2`, are not included in histogram."], TagSet[Histograms`Histogram, MessageName[Histograms`Histogram, "rtail1"], "Warning: One point from the right tail of the data, greater than or \ equal to `1`, is not included in histogram."], TagSet[Histograms`Histogram, MessageName[Histograms`Histogram, "ticks"], "`` is not a valid tick specification. Taking Ticks->Automatic."], TagSet[Histograms`Histogram, MessageName[Histograms`Histogram, "usage"], "\!\(\*RowBox[{\"Histogram\", \"[\", RowBox[{\"{\", \ RowBox[{SubscriptBox[StyleBox[\"x\", \"TI\"], StyleBox[\"1\", \"TR\"]], \ \",\", SubscriptBox[StyleBox[\"x\", \"TI\"], StyleBox[\"2\", \"TR\"]], \",\", \ StyleBox[\"\[Ellipsis]\", \"TI\"]}], \"}\"}], \"]\"}]\) generates a histogram \ of the univariate data \!\(\*RowBox[{\"{\", RowBox[{SubscriptBox[StyleBox[\"x\ \", \"TI\"], StyleBox[\"1\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"x\", \ \"TI\"], StyleBox[\"2\", \"TR\"]], \",\", StyleBox[\"\[Ellipsis]\", \ \"TR\"]}], \"}\"}]\).\n\!\(\*RowBox[{\"Histogram\", \"[\", \ RowBox[{RowBox[{\"{\", RowBox[{SubscriptBox[StyleBox[\"f\", \"TI\"], \ StyleBox[\"1\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"f\", \"TI\"], \ StyleBox[\"2\", \"TR\"]], \",\", StyleBox[\"\[Ellipsis]\", \"TR\"]}], \ \"}\"}], \",\", RowBox[{\"FrequencyData\", \"->\", \"True\"}]}], \"]\"}]\) \ generates a histogram of the univariate frequency data \!\(\*RowBox[{\"{\", \ RowBox[{SubscriptBox[StyleBox[\"f\", \"TI\"], StyleBox[\"1\", \"TR\"]], \ \",\", SubscriptBox[StyleBox[\"f\", \"TI\"], StyleBox[\"2\", \"TR\"]], \",\", \ StyleBox[\"\[Ellipsis]\", \"TR\"]}], \"}\"}]\), where \ \!\(\*SubscriptBox[StyleBox[\"f\", \"TI\"], StyleBox[\"i\", \"TI\"]]\) is the \ frequency with which the original data occurs in category \ \!\(\*StyleBox[\"i\", \"TI\"]\)."], Histograms`Private`histogram[ Pattern[Histograms`Private`list, Blank[]], Pattern[Histograms`Private`opts, BlankNullSequence[]]] := Module[{Histograms`Private`approximate, Histograms`Private`bedges, Histograms`Private`bedgestyle, Histograms`Private`borien, Histograms`Private`bstyle, Histograms`Private`fdata, Histograms`Private`hcat, Histograms`Private`range, Histograms`Private`scale, Histograms`Private`ticks, Histograms`Private`padding, Histograms`Private`countdata, Histograms`Private`numberOfBins, Histograms`Private`dmin, Histograms`Private`dmax, Histograms`Private`datamin, Histograms`Private`datamax, Histograms`Private`cutoffs, Histograms`Private`fixedbins = False, Histograms`Private`binmin, Histograms`Private`binmax, Histograms`Private`totalcount, Histograms`Private`leftTailCount, Histograms`Private`rightTailCount, Histograms`Private`binwidths, Histograms`Private`bincenters, Histograms`Private`autoticks, Histograms`Private`autolength, Histograms`Private`caxisticks, Histograms`Private`phwdata, Histograms`Private`orig, Histograms`Private`rng, Histograms`Private`gropts, Histograms`Private`groptslist, Histograms`Private`area}, If[ Not[ TrueQ[ Element[Histograms`Private`list, Reals]]], Message[ MessageName[Histograms`Histogram, "realvec"]]; Return[$Failed]]; { Histograms`Private`approximate, Histograms`Private`bedges, Histograms`Private`bedgestyle, Histograms`Private`borien, Histograms`Private`bstyle, Histograms`Private`fdata, Histograms`Private`hcat, Histograms`Private`range, Histograms`Private`scale, Histograms`Private`ticks, Histograms`Private`padding} = ReplaceAll[{ Histograms`ApproximateIntervals, BarCharts`BarEdges, BarCharts`BarEdgeStyle, BarCharts`BarOrientation, BarCharts`BarStyle, Histograms`FrequencyData, Histograms`HistogramCategories, Histograms`HistogramRange, Histograms`HistogramScale, Ticks, PlotRangePadding}, Flatten[{Histograms`Private`opts, Options[Histograms`Histogram]}]]; If[ And[ TrueQ[Histograms`Private`fdata], VectorQ[Histograms`Private`hcat], Length[Histograms`Private`list] + 1 != Length[Histograms`Private`hcat]], Message[ MessageName[Histograms`Histogram, "fdfail"]]; Return[$Failed]]; If[ And[Histograms`Private`range =!= Automatic, Not[ MatchQ[Histograms`Private`range, { Alternatives[ PatternTest[ Blank[], NumberQ], Automatic], Alternatives[ PatternTest[ Blank[], NumberQ], Automatic]}]]], Histograms`Private`range = Automatic]; If[ TrueQ[Histograms`Private`fdata], Histograms`Private`countdata = Histograms`Private`list; Histograms`Private`numberOfBins = Length[Histograms`Private`countdata]; If[ Not[ Or[Histograms`Private`hcat === Automatic, BarCharts`Private`monotoneIncreasingVectorQ[ Histograms`Private`hcat]]], Message[ MessageName[Histograms`Histogram, "fdhc"], Histograms`Private`hcat]; Histograms`Private`hcat = Automatic]; { Histograms`Private`datamin, Histograms`Private`datamax} = Histograms`Private`findRange[Histograms`Private`range, If[ Histograms`Private`hcat === Automatic, { 0, Histograms`Private`numberOfBins}, { Min[Histograms`Private`hcat], Max[Histograms`Private`hcat]}]]; If[Histograms`Private`hcat === Automatic, Histograms`Private`cutoffs = Histograms`Private`datamin + ((Histograms`Private`datamax - Histograms`Private`datamin) Range[0, Histograms`Private`numberOfBins])/ Histograms`Private`numberOfBins, Histograms`Private`cutoffs = Histograms`Private`findCutoffs1[ Histograms`Private`hcat, Histograms`Private`datamin, Histograms`Private`datamax, Histograms`Private`countdata]; Histograms`Private`numberOfBins = Length[Histograms`Private`cutoffs] - 1]; { Histograms`Private`binmin, Histograms`Private`binmax} = { First[Histograms`Private`cutoffs], Last[Histograms`Private`cutoffs]}, { Histograms`Private`dmin, Histograms`Private`dmax} = { Min[Histograms`Private`list], Max[Histograms`Private`list]}; { Histograms`Private`datamin, Histograms`Private`datamax} = Histograms`Private`findRange[ Histograms`Private`range, { Histograms`Private`dmin, Histograms`Private`dmax}]; If[ And[ Histograms`Private`datamin <= Histograms`Private`dmin, Histograms`Private`datamax >= Histograms`Private`dmax], Histograms`Private`totalcount = Length[Histograms`Private`list], Histograms`Private`totalcount = With[{Histograms`Private`d1 = Histograms`Private`datamin, Histograms`Private`d2 = Histograms`Private`datamax}, Compile[{{Histograms`Private`l, Blank[Real], 1}}, Module[{Histograms`Private`count = 0, Histograms`Private`n}, Do[ If[ Histograms`Private`d1 <= Part[Histograms`Private`l, Histograms`Private`n] <= Histograms`Private`d2, Increment[Histograms`Private`count]], { Histograms`Private`n, Length[Histograms`Private`l]}]; Histograms`Private`count]][Histograms`Private`list]]]; Histograms`Private`cutoffs = Histograms`Private`findCutoffs2[ Histograms`Private`hcat, Histograms`Private`datamin, Histograms`Private`datamax, Histograms`Private`totalcount, Histograms`Private`approximate]; If[Head[Histograms`Private`cutoffs] === BarCharts`Private`binrange, Histograms`Private`fixedbins = Histograms`Private`cutoffs; Histograms`Private`cutoffs = Part[Histograms`Private`cutoffs, 1] + Part[Histograms`Private`cutoffs, 3] Range[0, Round[(Part[Histograms`Private`cutoffs, 2] - Part[ Histograms`Private`cutoffs, 1])/Part[ Histograms`Private`cutoffs, 3]]]]; Histograms`Private`numberOfBins = Length[Histograms`Private`cutoffs] - 1; { Histograms`Private`binmin, Histograms`Private`binmax} = { First[Histograms`Private`cutoffs], Last[Histograms`Private`cutoffs]}; Histograms`Private`countdata = If[Head[Histograms`Private`fixedbins] === BarCharts`Private`binrange, BarCharts`Private`bincounts[ Histograms`Private`list, Histograms`Private`fixedbins], BinCounts[Histograms`Private`list, { Join[{-Infinity}, Histograms`Private`cutoffs, {Infinity}]}]]; If[ Not[ ListQ[Histograms`Private`countdata]], Message[ MessageName[Histograms`Histogram, "rcount"]]; Return[$Failed]]; If[ And[ Or[ Histograms`Private`range === Automatic, First[Histograms`Private`range] === Automatic], First[Histograms`Private`countdata] > 0], If[First[Histograms`Private`countdata] === 1, Message[ MessageName[Histograms`Histogram, "ltail1"], Histograms`Private`binmin], Message[ MessageName[Histograms`Histogram, "ltail"], First[Histograms`Private`countdata], Histograms`Private`binmin]]]; If[ And[ Or[ Histograms`Private`range === Automatic, Last[Histograms`Private`range] === Automatic], Last[Histograms`Private`countdata] > 0], If[Last[Histograms`Private`countdata] === 1, Message[ MessageName[Histograms`Histogram, "rtail1"], Histograms`Private`binmax], Message[ MessageName[Histograms`Histogram, "rtail"], Last[Histograms`Private`countdata], Histograms`Private`binmax]]]; If[ Not[ ListQ[Histograms`Private`padding]], Histograms`Private`padding = { Histograms`Private`padding, Histograms`Private`padding}]; Histograms`Private`padding = ReplaceAll[Histograms`Private`padding, Automatic -> Scaled[0.02]]; Histograms`Private`countdata = Take[Histograms`Private`countdata, {2, -2}]]; Histograms`Private`binwidths = Drop[Histograms`Private`cutoffs, 1] - Drop[ Histograms`Private`cutoffs, -1]; If[ Or[ TrueQ[Histograms`Private`scale], And[Histograms`Private`scale === Automatic, Not[ Or[Histograms`Private`hcat === Automatic, IntegerQ[Histograms`Private`hcat], 0.0001 > Abs[ Max[Histograms`Private`binwidths]/Min[ Histograms`Private`binwidths] - 1]]]]], Histograms`Private`countdata = Histograms`Private`countdata/Histograms`Private`binwidths]; Histograms`Private`bincenters = Drop[ FoldList[ Plus, Histograms`Private`binmin, Histograms`Private`binwidths], -1] + (1 Histograms`Private`binwidths)/2; Histograms`Private`autoticks = Histograms`Private`LinearScale[ Histograms`Private`binmin, Histograms`Private`binmax, 7]; Histograms`Private`autolength = Length[Histograms`Private`autoticks]; If[ MatchQ[Histograms`Private`ticks, Alternatives[ Automatic, Histograms`IntervalCenters, Histograms`IntervalBoundaries]], Histograms`Private`ticks = {Histograms`Private`ticks, Automatic}]; If[Histograms`Private`ticks === None, Histograms`Private`ticks = {None, None}]; If[ Not[ And[ ListQ[Histograms`Private`ticks], Length[Histograms`Private`ticks] == 2, Histograms`Private`ticksCheckQ[Histograms`Private`ticks]]], Message[ MessageName[Histograms`Histogram, "ticks"], Histograms`Private`ticks]; Histograms`Private`ticks = {Automatic, Automatic}]; Histograms`Private`caxisticks = Switch[ Part[Histograms`Private`ticks, 1], PatternTest[ Blank[], ListQ], Map[Histograms`Private`neatTick, Part[Histograms`Private`ticks, 1]], Histograms`IntervalBoundaries, Histograms`Private`trim[ Map[Histograms`Private`neatTick, Histograms`Private`cutoffs], Histograms`Private`autolength], Histograms`IntervalCenters, Histograms`Private`trim[ Map[Histograms`Private`neatTick, Histograms`Private`bincenters], Histograms`Private`autolength], None, None, Blank[], Histograms`Private`autoticks]; Histograms`Private`ticks = {Histograms`Private`caxisticks, Part[Histograms`Private`ticks, 2]}; Histograms`Private`phwdata = Transpose[{ Histograms`Private`bincenters, Histograms`Private`countdata, Histograms`Private`binwidths}]; Histograms`Private`orig = { First[Histograms`Private`cutoffs], 0}; Histograms`Private`rng = {{ First[Histograms`Private`cutoffs], Last[Histograms`Private`cutoffs]}, All}; If[Histograms`Private`borien === Horizontal, Histograms`Private`ticks = Reverse[Histograms`Private`ticks]; Histograms`Private`orig = Reverse[Histograms`Private`orig]; Histograms`Private`rng = Reverse[Histograms`Private`rng]]; Histograms`Private`gropts = FilterRules[{Histograms`Private`opts, Options[Histograms`Histogram]}, Options[Graphics]]; Histograms`Private`groptslist = DeleteCases[{Histograms`Private`gropts}, Blank[][Ticks, Blank[]]]; If[ And[ NumberQ[Histograms`Private`scale], FreeQ[Histograms`Private`scale, Complex], Histograms`Private`scale > 0], Histograms`Private`area = Total[ Part[Histograms`Private`phwdata, All, 2]]; Histograms`Private`phwdata = Map[{ Part[#, 1], (Part[#, 2] Histograms`Private`scale)/( Histograms`Private`area Part[#, 3]), Part[#, 3]}& , Histograms`Private`phwdata]]; If[Histograms`Private`bstyle === Automatic, Histograms`Private`bstyle = RGBColor[ 0.7771114671549554, 0.7981689173723965, 0.92304875257496]]; BarCharts`GeneralizedBarChart[ Histograms`Private`phwdata, AxesOrigin -> Histograms`Private`orig, BarCharts`BarEdges -> Histograms`Private`bedges, BarCharts`BarEdgeStyle -> Histograms`Private`bedgestyle, BarCharts`BarOrientation -> Histograms`Private`borien, BarCharts`BarStyle -> Histograms`Private`bstyle, PlotRange -> Histograms`Private`rng, Ticks -> Histograms`Private`ticks, PlotRangePadding -> Histograms`Private`padding, Apply[Sequence, Histograms`Private`groptslist]]], TagSet[Histograms`ApproximateIntervals, MessageName[Histograms`ApproximateIntervals, "usage"], "ApproximateIntervals is an option of histogram functions that \ specifies whether the HistogramCategories or HistogramRange settings should \ be adjusted so that the interval boundaries are described by simple \ numbers."], TagSet[BarCharts`BarEdges, MessageName[BarCharts`BarEdges, "usage"], "BarEdges is an option for bar charts that determines whether edges \ are to be drawn around the bars."], TagSet[BarCharts`BarEdgeStyle, MessageName[BarCharts`BarEdgeStyle, "usage"], "BarEdgeStyle is an option for bar charts that determines the style \ for the edges."], TagSet[BarCharts`BarOrientation, MessageName[BarCharts`BarOrientation, "usage"], "BarOrientation is an option for BarChart that determines whether the \ bars are oriented vertically or horizontally."], TagSet[BarCharts`BarStyle, MessageName[BarCharts`BarStyle, "usage"], "BarStyle is an option for bar charts that determines the default \ style for the bars. "], TagSet[Histograms`FrequencyData, MessageName[Histograms`FrequencyData, "usage"], "FrequencyData is an option of histogram functions that specifies \ whether the data argument represents the original data or the frequencies \ with which the original data fall in the respective categories."], TagSet[Histograms`HistogramCategories, MessageName[Histograms`HistogramCategories, "usage"], "HistogramCategories is an option of histogram functions that \ specifies the categories in the histogram."], TagSet[Histograms`HistogramRange, MessageName[Histograms`HistogramRange, "usage"], "HistogramRange is an option of histogram functions that specifies \ the lower and upper limits of the points to be included in the histogram."], TagSet[Histograms`HistogramScale, MessageName[Histograms`HistogramScale, "usage"], "HistogramScale is an option of histogram functions that specifies \ the way in which the bar heights are to be scaled."], BarCharts`Private`monotoneIncreasingVectorQ[ Pattern[BarCharts`Private`x, Blank[]]] := Module[{BarCharts`Private`positions}, BarCharts`Private`positions = If[ VectorQ[BarCharts`Private`x], BarCharts`Private`x, Map[If[ ListQ[#], First[#], #]& , BarCharts`Private`x]]; And[ VectorQ[BarCharts`Private`positions, NumberQ], FreeQ[BarCharts`Private`positions, Complex], Apply[Less, BarCharts`Private`positions]]], Histograms`Private`findRange[ Pattern[Histograms`Private`range, Blank[]], { Pattern[Histograms`Private`imin, Blank[]], Pattern[Histograms`Private`imax, Blank[]]}] := Module[{Histograms`Private`min = Histograms`Private`imin, Histograms`Private`max = Histograms`Private`imax}, AddTo[Histograms`Private`max, 10 $MachineEpsilon]; Switch[Histograms`Private`range, Alternatives[Automatic, {Automatic, Automatic}], { Histograms`Private`min, Histograms`Private`max}, Condition[{ PatternTest[ Pattern[Histograms`Private`l, Blank[]], NumberQ], PatternTest[ Pattern[Histograms`Private`u, Blank[]], NumberQ]}, And[ FreeQ[{Histograms`Private`l, Histograms`Private`u}, Complex], Histograms`Private`l < Histograms`Private`u]], Histograms`Private`range, Condition[{ PatternTest[ Pattern[Histograms`Private`l, Blank[]], NumberQ], Automatic}, And[ FreeQ[Histograms`Private`l, Complex], Histograms`Private`l < Histograms`Private`max]], { Part[Histograms`Private`range, 1], Histograms`Private`max}, Condition[{Automatic, PatternTest[ Pattern[Histograms`Private`u, Blank[]], NumberQ]}, And[ FreeQ[Histograms`Private`u, Complex], Histograms`Private`min < Histograms`Private`u]], {Histograms`Private`min, Part[Histograms`Private`range, 2]}, Blank[], Message[ MessageName[Histograms`Histogram, "range"], Histograms`Private`range]; { Histograms`Private`min, Histograms`Private`max}]], Histograms`Private`findRange[ Pattern[Histograms`Private`range, Blank[]], Pattern[Histograms`Private`list, Blank[]]] := Module[{Histograms`Private`min, Histograms`Private`max}, { Histograms`Private`min, Histograms`Private`max} = { Min[Histograms`Private`list], Max[Histograms`Private`list]}; AddTo[Histograms`Private`max, 10 $MachineEpsilon]; Switch[Histograms`Private`range, Alternatives[Automatic, {Automatic, Automatic}], { Histograms`Private`min, Histograms`Private`max}, Condition[{ PatternTest[ Pattern[Histograms`Private`l, Blank[]], NumberQ], PatternTest[ Pattern[Histograms`Private`u, Blank[]], NumberQ]}, And[ FreeQ[{Histograms`Private`l, Histograms`Private`u}, Complex], Histograms`Private`l < Histograms`Private`u]], Histograms`Private`range, Condition[{ PatternTest[ Pattern[Histograms`Private`l, Blank[]], NumberQ], Automatic}, And[ FreeQ[Histograms`Private`l, Complex], Histograms`Private`l < Histograms`Private`max]], { Part[Histograms`Private`range, 1], Histograms`Private`max}, Condition[{Automatic, PatternTest[ Pattern[Histograms`Private`u, Blank[]], NumberQ]}, And[ FreeQ[Histograms`Private`u, Complex], Histograms`Private`min < Histograms`Private`u]], {Histograms`Private`min, Part[Histograms`Private`range, 2]}, Blank[], Message[ MessageName[Histograms`Histogram, "range"], Histograms`Private`range]; { Histograms`Private`min, Histograms`Private`max}]], Histograms`Private`findCutoffs1[ Pattern[Histograms`Private`hcat, Blank[]], Pattern[Histograms`Private`datamin, Blank[]], Pattern[Histograms`Private`datamax, Blank[]], Pattern[Histograms`Private`data, Blank[]]] := Module[{Histograms`Private`countdata = Histograms`Private`data, Histograms`Private`cutoffs = Histograms`Private`hcat, Histograms`Private`n}, If[Histograms`Private`datamin >= First[Histograms`Private`cutoffs], While[ Not[ Inequality[ Part[Histograms`Private`cutoffs, 1], LessEqual, Histograms`Private`datamin, Less, Part[Histograms`Private`cutoffs, 2]]], Histograms`Private`countdata = Drop[Histograms`Private`countdata, 1]; Histograms`Private`cutoffs = Drop[Histograms`Private`cutoffs, 1]]]; If[Histograms`Private`datamax < Last[Histograms`Private`cutoffs], While[ Not[ Histograms`Private`n = Length[Histograms`Private`cutoffs]; Inequality[ Part[Histograms`Private`cutoffs, Histograms`Private`n - 1], LessEqual, Histograms`Private`datamax, Less, Part[Histograms`Private`cutoffs, Histograms`Private`n]]], Histograms`Private`countdata = Drop[Histograms`Private`countdata, -1]; Histograms`Private`cutoffs = Drop[Histograms`Private`cutoffs, -1]]]; Histograms`Private`cutoffs], Histograms`Private`findCutoffs2[ Pattern[Histograms`Private`hcat, Blank[]], Pattern[Histograms`Private`datamin, Blank[]], Pattern[Histograms`Private`datamax, Blank[]], Pattern[Histograms`Private`totalcount, Blank[]], Pattern[Histograms`Private`approximate, Blank[]]] := Module[{Histograms`Private`numberOfBins, Histograms`Private`cutoffs, Histograms`Private`binmin, Histograms`Private`binmax, Histograms`Private`bindelta}, If[ BarCharts`Private`monotoneIncreasingVectorQ[ Histograms`Private`hcat], If[ Not[ Or[ Histograms`Private`approximate === Automatic, Histograms`Private`approximate === False]], Message[ MessageName[Histograms`Histogram, "noapprox"], Histograms`Private`approximate]]; Histograms`Private`cutoffs = Histograms`Private`hcat; If[Histograms`Private`datamin >= First[Histograms`Private`cutoffs], While[ Not[ Inequality[ Part[Histograms`Private`cutoffs, 1], LessEqual, Histograms`Private`datamin, Less, Part[Histograms`Private`cutoffs, 2]]], Histograms`Private`cutoffs = Drop[Histograms`Private`cutoffs, 1]]]; If[Histograms`Private`datamax < Last[Histograms`Private`cutoffs], While[ Not[ Histograms`Private`n = Length[Histograms`Private`cutoffs]; Inequality[ Part[Histograms`Private`cutoffs, Histograms`Private`n - 1], LessEqual, Histograms`Private`datamax, Less, Part[Histograms`Private`cutoffs, Histograms`Private`n]]], Histograms`Private`cutoffs = Drop[Histograms`Private`cutoffs, -1]]], If[ Histograms`Private`PositiveIntegerQ[Histograms`Private`hcat], Histograms`Private`numberOfBins = Histograms`Private`hcat, Histograms`Private`numberOfBins = Sqrt[Histograms`Private`totalcount]]; If[ Or[Histograms`Private`approximate === Automatic, TrueQ[ Histograms`Private`approximate]], { Histograms`Private`binmin, Histograms`Private`binmax, Histograms`Private`bindelta} = Histograms`Private`approximateIntervals[ Histograms`Private`datamin, Histograms`Private`datamax, Histograms`Private`numberOfBins]; Histograms`Private`numberOfBins = Round[(Histograms`Private`binmax - Histograms`Private`binmin)/ Histograms`Private`bindelta], Histograms`Private`numberOfBins = Round[Histograms`Private`numberOfBins]; { Histograms`Private`binmin, Histograms`Private`binmax, Histograms`Private`bindelta} = { Histograms`Private`datamin, Histograms`Private`datamax, (Histograms`Private`datamax - Histograms`Private`datamin)/ Histograms`Private`numberOfBins}]; Histograms`Private`cutoffs = BarCharts`Private`binrange[ Histograms`Private`binmin, Histograms`Private`binmax, Histograms`Private`bindelta]; Null]; Histograms`Private`cutoffs], Histograms`Private`PositiveIntegerQ[ PatternTest[ Pattern[Histograms`Private`a, Blank[Integer]], Positive]] := True, Histograms`Private`PositiveIntegerQ[ Blank[]] := False, Histograms`Private`approximateIntervals[ Pattern[Histograms`Private`min, Blank[]], Pattern[Histograms`Private`max, Blank[]], Pattern[Histograms`Private`numOfInt, Blank[]]] := Module[{Histograms`Private`nmin = N[Histograms`Private`min], Histograms`Private`nmax = N[Histograms`Private`max], Histograms`Private`spacing, Histograms`Private`t, Histograms`Private`nicebins, Histograms`Private`first, Histograms`Private`last, Histograms`Private`delta}, If[Histograms`Private`numOfInt === 1, Histograms`Private`spacing = (If[# == 0., 1, #]& )[ Histograms`Private`max - Histograms`Private`min]; Return[{Histograms`Private`min - 0.2 Histograms`Private`spacing, Histograms`Private`max + 0.2 Histograms`Private`spacing, 1.5 Histograms`Private`spacing}]]; If[Abs[(Histograms`Private`max - Histograms`Private`min)/( Histograms`Private`spacing = (If[# == 0., 1, #]& )[ Max[ Abs[{Histograms`Private`min, Histograms`Private`max}]]])] < 10^(-5), Histograms`Private`spacing = 0.2 Histograms`Private`spacing; Return[{Histograms`Private`min - 1.5 Histograms`Private`spacing, Histograms`Private`min + 1.5 Histograms`Private`spacing, Histograms`Private`spacing}]]; Histograms`Private`spacing = Histograms`Private`TickSpacing[ Histograms`Private`nmax - Histograms`Private`nmin, Histograms`Private`numOfInt, {1, 2, 2.5, 5, 10}, Nearest]; Histograms`Private`t = Range[Ceiling[ Histograms`Private`nmin/Histograms`Private`spacing - 0.05] Histograms`Private`spacing, Histograms`Private`max, Histograms`Private`spacing]; If[Length[Histograms`Private`t] == 1, Histograms`Private`t = Join[Histograms`Private`t, Histograms`Private`t + Histograms`Private`spacing]]; Histograms`Private`nicebins = Map[{#, If[Round[#] == #, Round[#], #]}& , Histograms`Private`t]; { Histograms`Private`first, Histograms`Private`last} = { Part[ First[Histograms`Private`nicebins], 1], Part[ Last[Histograms`Private`nicebins], 1]}; Histograms`Private`delta = Part[Histograms`Private`nicebins, 2, 1] - Histograms`Private`first; While[ Or[ Histograms`Private`min < Histograms`Private`first, Histograms`Private`max >= Histograms`Private`last], If[ Histograms`Private`min < Histograms`Private`first, Histograms`Private`nicebins = Join[ Map[{#, If[Round[#] == #, Round[#], #]}& , { Histograms`Private`first - Histograms`Private`delta}], Histograms`Private`nicebins]]; If[Histograms`Private`max >= Histograms`Private`last, Histograms`Private`nicebins = Join[Histograms`Private`nicebins, Map[{#, If[Round[#] == #, Round[#], #]}& , { Histograms`Private`last + Histograms`Private`delta}]]]; { Histograms`Private`first, Histograms`Private`last} = { Part[ First[Histograms`Private`nicebins], 1], Part[ Last[Histograms`Private`nicebins], 1]}]; { Histograms`Private`first, Histograms`Private`last, Histograms`Private`delta}], Histograms`Private`TickSpacing[ Pattern[Histograms`Private`dx, Blank[]], Pattern[Histograms`Private`n, Blank[]], Pattern[Histograms`Private`prefs, Blank[List]], Optional[ Pattern[Histograms`Private`method, Blank[]], GreaterEqual]] := Module[{Histograms`Private`dist = N[Histograms`Private`dx/Histograms`Private`n], Histograms`Private`scale, Histograms`Private`prefsdelta, Histograms`Private`min, Histograms`Private`pos}, Histograms`Private`scale = 10.^Floor[ Log[10., Histograms`Private`dist]]; DivideBy[Histograms`Private`dist, Histograms`Private`scale]; If[Histograms`Private`dist < 1, TimesBy[Histograms`Private`dist, 10]; DivideBy[Histograms`Private`scale, 10]]; If[Histograms`Private`dist >= 10, DivideBy[Histograms`Private`dist, 10]; TimesBy[Histograms`Private`scale, 10]]; Histograms`Private`scale Switch[Histograms`Private`method, GreaterEqual, First[ Select[ Histograms`Private`prefs, Histograms`Private`dist <= #& ]], LessEqual, First[ Select[ Reverse[Histograms`Private`prefs], Histograms`Private`dist >= #& ]], Nearest, Histograms`Private`prefsdelta = Map[Abs[# - Histograms`Private`dist]& , Histograms`Private`prefs]; Histograms`Private`min = Min[Histograms`Private`prefsdelta]; Histograms`Private`pos = Part[ Position[ Histograms`Private`prefsdelta, Histograms`Private`min], 1, 1]; Part[Histograms`Private`prefs, Histograms`Private`pos]]], BarCharts`Private`bincounts[ Pattern[BarCharts`Private`dat, Blank[]], BarCharts`Private`binrange[ Pattern[BarCharts`Private`min, Blank[]], Pattern[BarCharts`Private`max, Blank[]], Pattern[BarCharts`Private`incr, Blank[]]]] := BarCharts`Private`bincountfunc[ BarCharts`Private`dat, BarCharts`Private`min, BarCharts`Private`max, BarCharts`Private`incr], BarCharts`Private`bincountfunc = CompiledFunction[{{ Blank[Real], 1}, Blank[Real], Blank[Real], Blank[Real]}, {{3, 1, 0}, {3, 0, 0}, {3, 0, 1}, {3, 0, 2}, {2, 1, 1}}, {2, 10, 5, 0, 3}, {{1, 5}, {24, 0, 3}, {18, 1, 3, 4}, {7, 1, 0}, {94, 260, 2, 0, 0, 3, 0, 2, 3, 0, 3}, {21, 4, 3, 4}, {93, 47, 3, 0, 4, 2, 0, 0}, {24, 0, 4}, {94, 257, 3, 0, 4, 3, 1, 0, 3, 1, 1}, {7, 1, 1}, {94, 260, 2, 0, 1, 3, 0, 2, 3, 0, 4}, {94, 273, 3, 0, 4, 3, 1, 1, 3, 1, 2}, {93, 48, 3, 1, 2, 2, 1, 1}, {7, 2, 1}, {94, 257, 2, 0, 1, 2, 1, 1, 2, 1, 2}, {7, 0, 1}, {7, 2, 2}, {17, 0, 2, 5}, {7, 0, 7}, {64, 5, 2, 1}, {7, 0, 8}, {11, 8, 2}, {4, 3}, {7, 0, 8}, {65, 7, 8, 1}, {5, 2, 5, -2}, {44, 0, 6}, {7, 0, 7}, {4, 30}, {70, 2, 0, 7, 0, 8}, {11, 8, 1}, {7, 1, 8}, {36, 1, 8, 0}, {3, 0, 8}, {7, 1, 8}, {7, 1, 2}, {70, 1, 0, 2, 0, 5}, {7, 1, 2}, {17, 5, 2, 5}, {71, 1, 0, 8, 0, 5}, {4, 18}, {7, 1, 8}, {17, 0, 8, 2}, {36, 2, 1, 1}, {3, 1, 10}, {7, 2, 2}, {17, 0, 2, 8}, {7, 2, 2}, {17, 0, 2, 9}, {70, 1, 0, 9, 0, 2}, { 7, 1, 9}, {17, 2, 9, 2}, {71, 1, 0, 8, 0, 2}, {4, 5}, {70, 1, 0, 1, 0, 8}, {7, 1, 9}, {17, 8, 9, 8}, {71, 1, 0, 1, 0, 8}, {5, 7, 6, -29}, {2}}, Function[{ BarCharts`Private`dat, BarCharts`Private`min, BarCharts`Private`max, BarCharts`Private`incr}, Module[{BarCharts`Private`nbin = Round[(BarCharts`Private`max - BarCharts`Private`min)/ BarCharts`Private`incr], BarCharts`Private`vals = Floor[(BarCharts`Private`dat - BarCharts`Private`min)/ BarCharts`Private`incr] + 2, BarCharts`Private`bins, BarCharts`Private`thisval = 0}, BarCharts`Private`bins = Table[0, {BarCharts`Private`nbin + 2}]; Do[BarCharts`Private`thisval = Part[BarCharts`Private`vals, BarCharts`Private`i]; Which[BarCharts`Private`thisval < 1, AddTo[ Part[BarCharts`Private`bins, 1], 1], BarCharts`Private`thisval > BarCharts`Private`nbin + 1, AddTo[ Part[BarCharts`Private`bins, BarCharts`Private`nbin + 2], 1], True, AddTo[ Part[BarCharts`Private`bins, BarCharts`Private`thisval], 1]], {BarCharts`Private`i, Length[BarCharts`Private`dat]}]; BarCharts`Private`bins]], Evaluate], Histograms`Private`LinearScale[ Pattern[Histograms`Private`min, Blank[]], Pattern[Histograms`Private`max, Blank[]], Optional[ Pattern[Histograms`Private`n, Blank[Integer]], 8]] := Module[{Histograms`Private`spacing, Histograms`Private`t, Histograms`Private`nmin = N[Histograms`Private`min], Histograms`Private`nmax = N[Histograms`Private`max]}, Condition[ Histograms`Private`spacing = Histograms`Private`TickSpacing[ Histograms`Private`nmax - Histograms`Private`nmin, Histograms`Private`n, {1, 2, 2.5, 5, 10}]; Histograms`Private`t = N[Histograms`Private`spacing Range[ Ceiling[ Histograms`Private`nmin/Histograms`Private`spacing - 0.05], Floor[ Histograms`Private`max/Histograms`Private`spacing + 0.05]]]; Map[{#, If[Round[#] == #, Round[#], #]}& , Histograms`Private`t], Histograms`Private`nmin <= Histograms`Private`nmax]], TagSet[Histograms`IntervalCenters, MessageName[Histograms`IntervalCenters, "usage"], "IntervalCenters is a possible value for the Ticks option of \ histogram functions. For example, Histogram[data, Ticks -> IntervalCenters] \ Automatic}], or Histogram[data, Ticks -> IntervalCenters], places the ticks \ of the category axis at the interval centers, and sets the ticks of the \ frequency axis automatically."], TagSet[Histograms`IntervalBoundaries, MessageName[Histograms`IntervalBoundaries, "usage"], "IntervalBoundaries is a possible value for the Ticks option of \ histogram functions. For example, Histogram[data, Ticks -> \ {IntervalBoundaries, Automatic}], or Histogram[data, Ticks -> \ IntervalBoundaries] places the ticks of the category axis at the interval \ boundaries, and sets the ticks of the frequency axis automatically."], Histograms`Private`ticksCheckQ[{ Pattern[Histograms`Private`x, Blank[]], Pattern[Histograms`Private`y, Blank[]], Pattern[Histograms`Private`z, Blank[]]}] := And[ Or[ Histograms`Private`x === None, Histograms`Private`x === Automatic, Histograms`Private`monotoneIncreasingVectorQ[Histograms`Private`x], Histograms`Private`x === Histograms`IntervalBoundaries, Histograms`Private`x === Histograms`IntervalCenters], Or[ Histograms`Private`y === None, Histograms`Private`y === Automatic, Histograms`Private`monotoneIncreasingVectorQ[Histograms`Private`y], Histograms`Private`y === Histograms`IntervalBoundaries, Histograms`Private`y === Histograms`IntervalCenters], Or[ Histograms`Private`z === None, Histograms`Private`z === Automatic, Histograms`Private`monotoneIncreasingVectorQ[ Histograms`Private`z]]], Histograms`Private`monotoneIncreasingVectorQ[ Pattern[Histograms`Private`x, Blank[]]] := Module[{Histograms`Private`positions}, Histograms`Private`positions = If[ VectorQ[Histograms`Private`x], Histograms`Private`x, Map[If[ ListQ[#], First[#], #]& , Histograms`Private`x]]; And[ VectorQ[Histograms`Private`positions, NumberQ], FreeQ[Histograms`Private`positions, Complex], Apply[Less, Histograms`Private`positions]]], Histograms`Private`neatTick[ Pattern[Histograms`Private`t, Blank[]]] := If[ TrueQ[Round[Histograms`Private`t] == Histograms`Private`t], Round[Histograms`Private`t], If[Head[Histograms`Private`t] === Rational, N[Histograms`Private`t], Histograms`Private`t]], Histograms`Private`trim[ Pattern[Histograms`Private`tlist, Blank[]], Pattern[Histograms`Private`n, Blank[]]] := Module[{Histograms`Private`l = Length[Histograms`Private`tlist], Histograms`Private`delta, Histograms`Private`k, Histograms`Private`result = {}}, Histograms`Private`delta = Round[Histograms`Private`l/Histograms`Private`n]; If[ Or[ Histograms`Private`l <= Histograms`Private`n, Histograms`Private`delta == 1], Histograms`Private`tlist, If[ EvenQ[Histograms`Private`l], Histograms`Private`k = 1; While[Histograms`Private`k <= Histograms`Private`l, If[Mod[Histograms`Private`k - 1, Histograms`Private`delta] == 0, AppendTo[Histograms`Private`result, Part[Histograms`Private`tlist, Histograms`Private`k]], AppendTo[Histograms`Private`result, { Part[Histograms`Private`tlist, Histograms`Private`k], ""}]]; Increment[Histograms`Private`k]], Histograms`Private`k = (Histograms`Private`l + 1)/2; While[Histograms`Private`k <= Histograms`Private`l, If[Mod[Histograms`Private`k - (Histograms`Private`l + 1)/2 + Histograms`Private`delta, Histograms`Private`delta] == 0, AppendTo[Histograms`Private`result, Part[Histograms`Private`tlist, Histograms`Private`k]], AppendTo[Histograms`Private`result, { Part[Histograms`Private`tlist, Histograms`Private`k], ""}]]; AddTo[ Histograms`Private`k, Histograms`Private`delta]]; Histograms`Private`k = (Histograms`Private`l + 1)/2 - Histograms`Private`delta; While[Histograms`Private`k >= 1, If[Mod[Histograms`Private`k - ((Histograms`Private`l + 1)/2 - Histograms`Private`delta), Histograms`Private`delta] == 0, PrependTo[Histograms`Private`result, Part[Histograms`Private`tlist, Histograms`Private`k]], PrependTo[Histograms`Private`result, { Part[Histograms`Private`tlist, Histograms`Private`k], ""}]]; SubtractFrom[ Histograms`Private`k, Histograms`Private`delta]]]; Histograms`Private`result]], BarCharts`GeneralizedBarChart[ Pattern[BarCharts`Private`idata, Repeated[{ Repeated[{ PatternTest[ Blank[], BarCharts`Private`numberQ], PatternTest[ Blank[], BarCharts`Private`numberQ], PatternTest[ Blank[], BarCharts`Private`numberQ]}]}]], PatternTest[ Pattern[BarCharts`Private`opts, BlankNullSequence[]], OptionQ]] := BarCharts`GeneralizedBarChart[{BarCharts`Private`idata}, BarCharts`Private`opts], BarCharts`GeneralizedBarChart[ Pattern[BarCharts`Private`idata, { Repeated[{ Repeated[{ PatternTest[ Blank[], BarCharts`Private`numberQ], PatternTest[ Blank[], BarCharts`Private`numberQ], PatternTest[ Blank[], BarCharts`Private`numberQ]}]}]}], PatternTest[ Pattern[BarCharts`Private`opts, BlankNullSequence[]], OptionQ]] := Module[{BarCharts`Private`data = BarCharts`Private`idata, BarCharts`Private`bsty, BarCharts`Private`val, BarCharts`Private`vpos, BarCharts`Private`unob, BarCharts`Private`edge, BarCharts`Private`esty, BarCharts`Private`bsf, BarCharts`Private`orient, BarCharts`Private`ln = Length[BarCharts`Private`idata], BarCharts`Private`lns = Map[Length, BarCharts`Private`idata], BarCharts`Private`bars, BarCharts`Private`disp, BarCharts`Private`pr, BarCharts`Private`origopts}, { BarCharts`Private`bsty, BarCharts`Private`val, BarCharts`Private`edge, BarCharts`Private`esty, BarCharts`Private`orient, BarCharts`Private`pr} = ReplaceAll[{ BarCharts`BarStyle, BarCharts`BarValues, BarCharts`BarEdges, BarCharts`BarEdgeStyle, BarCharts`BarOrientation, PlotRange}, Flatten[{BarCharts`Private`opts, Options[BarCharts`GeneralizedBarChart]}]]; BarCharts`Private`origopts = FilterRules[ Flatten[{BarCharts`Private`opts, Options[BarCharts`GeneralizedBarChart]}], {DisplayFunction}]; BarCharts`Private`gopts = FilterRules[{BarCharts`Private`opts, Options[BarCharts`GeneralizedBarChart]}, Options[Graphics]]; If[ And[ BarCharts`Private`bsty =!= Automatic, BarCharts`Private`bsty =!= None, Head[BarCharts`Private`bsty] =!= List, Not[ MatchQ[BarCharts`Private`bsty, Alternatives[ Hue, RGBColor, GrayLevel, CMYKColor, Opacity, Directive][ BlankSequence[]]]]], BarCharts`Private`bsty = Apply[Join, Map[BarCharts`Private`bsty[ Part[#, 2]]& , BarCharts`Private`data, {2}]], BarCharts`Private`bsty = BarCharts`Private`barcoloring[ BarCharts`Private`bsty, BarCharts`Private`ln, BarCharts`Private`lns]]; If[ TrueQ[BarCharts`Private`edge], If[ BarCharts`Private`ln === 1, BarCharts`Private`esty = BarCharts`Private`CycleValues[BarCharts`Private`esty, Length[ First[BarCharts`Private`data]]], BarCharts`Private`esty = Apply[Join, MapThread[Table[#, {#2}]& , { BarCharts`Private`CycleValues[ BarCharts`Private`esty, BarCharts`Private`ln], BarCharts`Private`lns}]]], BarCharts`Private`esty = None]; If[ Not[ MemberQ[{Horizontal, Vertical}, BarCharts`Private`orient]], Message[ MessageName[BarCharts`GeneralizedBarChart, "badorient"], BarCharts`Private`orient]; BarCharts`Private`orient = Vertical]; BarCharts`Private`val = TrueQ[BarCharts`Private`val]; BarCharts`Private`vpos = 0.05; BarCharts`Private`data = Flatten[BarCharts`Private`data, 1]; BarCharts`Private`bars = Map[ BarCharts`Private`barcoords[BarCharts`Private`orient], BarCharts`Private`data]; If[BarCharts`Private`val, Show[ BarCharts`Private`RectanglePlot[ BarCharts`Private`bars, BarCharts`Private`RectangleStyle -> BarCharts`Private`bsty, BarCharts`Private`EdgeStyle -> BarCharts`Private`esty, DisplayFunction -> Identity], Graphics[ Map[ BarCharts`Private`varcoords[ BarCharts`Private`orient, BarCharts`Private`vpos, #& ], BarCharts`Private`data]], If[ BarCharts`Private`pr === Automatic, PlotRange -> All, PlotRange -> BarCharts`Private`pr], BarCharts`Private`origopts, BarCharts`Private`gopts], BarCharts`Private`RectanglePlot[ BarCharts`Private`bars, BarCharts`Private`RectangleStyle -> BarCharts`Private`bsty, BarCharts`Private`EdgeStyle -> BarCharts`Private`esty, BarCharts`Private`ObscuredFront -> BarCharts`Private`unob, BarCharts`Private`gopts]]], BarCharts`GeneralizedBarChart[{}, Pattern[BarCharts`Private`opts, BlankNullSequence[]]] := Show[ Graphics[{}, FilterRules[{BarCharts`Private`opts, Options[BarCharts`GeneralizedBarChart]}, Options[Graphics]]]], Options[BarCharts`GeneralizedBarChart] := { AlignmentPoint -> Center, AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesLabel -> None, AxesOrigin -> Automatic, AxesStyle -> {}, Background -> None, BarCharts`BarEdges -> True, BarCharts`BarEdgeStyle -> Opacity[0.5], BarCharts`BarOrientation -> Vertical, BarCharts`BarStyle -> Automatic, BarCharts`BarValues -> False, BaselinePosition -> Automatic, BaseStyle -> {}, ColorOutput -> Automatic, ContentSelectable -> Automatic, Epilog -> {}, Frame -> False, FrameLabel -> None, FrameStyle -> {}, FrameTicks -> Automatic, FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, ImageMargins -> 0., ImagePadding -> All, ImageSize -> Automatic, LabelStyle -> {}, Method -> Automatic, PlotLabel -> None, PlotRange -> All, PlotRangeClipping -> True, PlotRangePadding -> Automatic, PlotRegion -> Automatic, PreserveImageOptions -> Automatic, Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, TicksStyle -> {}, DisplayFunction :> $DisplayFunction, FormatType :> TraditionalForm}, TagSet[BarCharts`GeneralizedBarChart, MessageName[BarCharts`GeneralizedBarChart, "badorient"], "The value given for BarOrientation is invalid; please use Horizontal \ or Vertical. The chart will be generated with Vertical."], TagSet[BarCharts`GeneralizedBarChart, MessageName[BarCharts`GeneralizedBarChart, "usage"], "\!\(\*RowBox[{\"GeneralizedBarChart\", \"[\", RowBox[{\"{\", \ RowBox[{RowBox[{\"{\", RowBox[{SubscriptBox[StyleBox[\"pos\", \"TI\"], \ StyleBox[\"1\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"height\", \"TI\"], \ StyleBox[\"1\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"width\", \"TI\"], \ StyleBox[\"1\", \"TR\"]]}], \"}\"}], \",\", RowBox[{\"{\", \ RowBox[{SubscriptBox[StyleBox[\"pos\", \"TI\"], StyleBox[\"2\", \"TR\"]], \",\ \", SubscriptBox[StyleBox[\"height\", \"TI\"], StyleBox[\"2\", \"TR\"]], \ \",\", SubscriptBox[StyleBox[\"width\", \"TI\"], StyleBox[\"2\", \"TR\"]]}], \ \"}\"}], \",\", RowBox[{StyleBox[\"\[Ellipsis]\", \"TR\"], RowBox[{\"}\", \"]\ \"}]}]}]}]}]\) generates a bar chart with the bars at the given positions, \ and with given heights and widths.\n\!\(\*RowBox[{\"GeneralizedBarChart\", \ \"[\", RowBox[{\"{\", RowBox[{SubscriptBox[StyleBox[\"list\", \"TI\"], \ StyleBox[\"1\", \"TR\"]], \",\", SubscriptBox[StyleBox[\"list\", \"TI\"], \ StyleBox[\"2\", \"TR\"]], \",\", StyleBox[\"\[Ellipsis]\", \"TR\"]}], \ StyleBox[\"}\", \"TR\"]}], \"]\"}]\) generates a bar chart from lists of \ data."], BarCharts`Private`numberQ[ Pattern[BarCharts`Private`x, Blank[]]] := NumberQ[ N[BarCharts`Private`x]], TagSet[BarCharts`BarValues, MessageName[BarCharts`BarValues, "usage"], "BarValues is an option for BarChart and GeneralizedBarChart that \ allows the length of the bar to be displayed above each bar."], BarCharts`Private`gopts = { AxesOrigin -> {0, 0}, PlotRange -> {{0, 101}, All}, Ticks -> {{{0., 0}, {20., 20}, {40., 40}, {60., 60}, {80., 80}, { 100., 100}}, Automatic}, PlotRangePadding -> { Scaled[0.02], Scaled[0.02]}, GridLines -> Automatic, AlignmentPoint -> Center, AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesLabel -> None, AxesOrigin -> Automatic, AxesStyle -> {}, Background -> None, BaselinePosition -> Automatic, BaseStyle -> {}, ColorOutput -> Automatic, ContentSelectable -> Automatic, Epilog -> {}, Frame -> False, FrameLabel -> None, FrameStyle -> {}, FrameTicks -> Automatic, FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, ImageMargins -> 0., ImagePadding -> All, ImageSize -> Automatic, LabelStyle -> {}, Method -> Automatic, PlotLabel -> None, PlotRange -> All, PlotRangeClipping -> True, PlotRangePadding -> Automatic, PlotRegion -> Automatic, PreserveImageOptions -> Automatic, Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, TicksStyle -> {}, DisplayFunction :> $DisplayFunction, FormatType :> TraditionalForm, AlignmentPoint -> Center, AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesLabel -> None, AxesOrigin -> Automatic, AxesStyle -> {}, Background -> None, BaselinePosition -> Automatic, BaseStyle -> {}, ColorOutput -> Automatic, ContentSelectable -> Automatic, Epilog -> {}, Frame -> False, FrameLabel -> None, FrameStyle -> {}, FrameTicks -> Automatic, FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, ImageMargins -> 0., ImagePadding -> All, ImageSize -> Automatic, LabelStyle -> {}, Method -> Automatic, PlotLabel -> None, PlotRange -> All, PlotRangeClipping -> True, PlotRangePadding -> Automatic, PlotRegion -> Automatic, PreserveImageOptions -> Automatic, Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, TicksStyle -> {}, DisplayFunction :> $DisplayFunction, FormatType :> TraditionalForm}, $DisplayFunction = Identity, BarCharts`Private`barcoloring[Automatic, 1, Blank[]] := { Hue[0.67, 0.45, 0.65]}, BarCharts`Private`barcoloring[Automatic, Pattern[BarCharts`Private`ln, Blank[]], Pattern[BarCharts`Private`lns, Blank[]]] := Apply[Join, MapThread[Table[#, {#2}]& , { Table[ Hue[ FractionalPart[ 0.67 + (2. (BarCharts`Private`i - 1))/GoldenRatio], 0.45, 0.65], {BarCharts`Private`i, 1, BarCharts`Private`ln}], BarCharts`Private`lns}]], BarCharts`Private`barcoloring[ Pattern[BarCharts`Private`bsty, Blank[]], 1, Pattern[BarCharts`Private`lns, Blank[]]] := BarCharts`Private`CycleValues[BarCharts`Private`bsty, First[BarCharts`Private`lns]], BarCharts`Private`barcoloring[ Pattern[BarCharts`Private`bsty, Blank[]], Pattern[BarCharts`Private`ln, Blank[]], Pattern[BarCharts`Private`lns, Blank[]]] := Apply[Join, MapThread[Table[#, {#2}]& , { BarCharts`Private`CycleValues[ BarCharts`Private`bsty, BarCharts`Private`ln], BarCharts`Private`lns}]], BarCharts`Private`CycleValues[{}, Blank[]] := {}, BarCharts`Private`CycleValues[ Pattern[BarCharts`Private`list, Blank[List]], Pattern[BarCharts`Private`n, Blank[Integer]]] := Module[{BarCharts`Private`hold = BarCharts`Private`list}, While[Length[BarCharts`Private`hold] < BarCharts`Private`n, BarCharts`Private`hold = Join[BarCharts`Private`hold, BarCharts`Private`hold]]; ReplaceAll[ Take[BarCharts`Private`hold, BarCharts`Private`n], None -> {}]], BarCharts`Private`CycleValues[ Pattern[BarCharts`Private`item, Blank[]], Pattern[BarCharts`Private`n, Blank[]]] := BarCharts`Private`CycleValues[{BarCharts`Private`item}, BarCharts`Private`n], BarCharts`Private`barcoords[Horizontal][{ Pattern[BarCharts`Private`pos, Blank[]], Pattern[BarCharts`Private`len, Blank[]], Pattern[BarCharts`Private`wid, Blank[]]}] := {{ 0, BarCharts`Private`pos - BarCharts`Private`wid/2}, { BarCharts`Private`len, BarCharts`Private`pos + BarCharts`Private`wid/2}}, BarCharts`Private`barcoords[Vertical][{ Pattern[BarCharts`Private`pos, Blank[]], Pattern[BarCharts`Private`len, Blank[]], Pattern[BarCharts`Private`wid, Blank[]]}] := {{ BarCharts`Private`pos - BarCharts`Private`wid/2, 0}, { BarCharts`Private`pos + BarCharts`Private`wid/2, BarCharts`Private`len}}, BarCharts`Private`RectanglePlot[ Pattern[BarCharts`Private`boxes, { Repeated[{{ PatternTest[ Blank[], BarCharts`Private`numberQ], PatternTest[ Blank[], BarCharts`Private`numberQ]}, { PatternTest[ Blank[], BarCharts`Private`numberQ], PatternTest[ Blank[], BarCharts`Private`numberQ]}}]}], PatternTest[ Pattern[BarCharts`Private`opts, BlankNullSequence[]], OptionQ]] := Module[{BarCharts`Private`ln = Length[BarCharts`Private`boxes], BarCharts`Private`bstyle, BarCharts`Private`estyle, BarCharts`Private`gopts, BarCharts`Private`sort}, { BarCharts`Private`bstyle, BarCharts`Private`estyle, BarCharts`Private`sort} = ReplaceAll[{ BarCharts`Private`RectangleStyle, BarCharts`Private`EdgeStyle, BarCharts`Private`ObscuredFront}, Flatten[{BarCharts`Private`opts, Options[BarCharts`Private`RectanglePlot]}]]; BarCharts`Private`gopts = FilterRules[{BarCharts`Private`opts, Options[BarCharts`Private`RectanglePlot]}, Options[Graphics]]; If[BarCharts`Private`bstyle === Automatic, BarCharts`Private`bstyle = Map[Hue, (0.6 Range[0, BarCharts`Private`ln - 1])/( BarCharts`Private`ln - 1)]]; If[BarCharts`Private`bstyle === {}, BarCharts`Private`bstyle = {{}}]; If[BarCharts`Private`bstyle === None, BarCharts`Private`bstyle = {{}}]; If[BarCharts`Private`estyle === Automatic, BarCharts`Private`estyle = { GrayLevel[0]}]; If[BarCharts`Private`estyle === {}, BarCharts`Private`estyle = {{}}]; If[BarCharts`Private`estyle === None, BarCharts`Private`estyle = {{}}]; BarCharts`Private`bstyle = BarCharts`Private`CycleValues[ BarCharts`Private`bstyle, BarCharts`Private`ln]; BarCharts`Private`estyle = BarCharts`Private`CycleValues[ BarCharts`Private`estyle, BarCharts`Private`ln]; BarCharts`Private`recs = Table[{ Part[BarCharts`Private`bstyle, BarCharts`Private`i], EdgeForm[ Part[BarCharts`Private`estyle, BarCharts`Private`i]], Apply[Rectangle, Part[BarCharts`Private`boxes, BarCharts`Private`i]]}, { BarCharts`Private`i, Length[BarCharts`Private`boxes]}]; Show[ Graphics[BarCharts`Private`recs], BarCharts`Private`gopts]], BarCharts`Private`RectanglePlot[ Pattern[BarCharts`Private`boxes, { Repeated[{ PatternTest[ Blank[], BarCharts`Private`numberQ], PatternTest[ Blank[], BarCharts`Private`numberQ]}]}], Pattern[BarCharts`Private`opts, BlankNullSequence[]]] := BarCharts`Private`RectanglePlot[ Map[{#, # + 1}& , BarCharts`Private`boxes], BarCharts`Private`opts], Options[BarCharts`Private`RectanglePlot] := { BarCharts`Private`RectangleStyle -> Automatic, BarCharts`Private`EdgeStyle -> Automatic, BarCharts`Private`ObscuredFront -> False, AlignmentPoint -> Center, AspectRatio -> GoldenRatio^(-1), Axes -> False, AxesLabel -> None, AxesOrigin -> Automatic, AxesStyle -> {}, Background -> None, BaselinePosition -> Automatic, BaseStyle -> {}, ColorOutput -> Automatic, ContentSelectable -> Automatic, Epilog -> {}, Frame -> False, FrameLabel -> None, FrameStyle -> {}, FrameTicks -> Automatic, FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, ImageMargins -> 0., ImagePadding -> All, ImageSize -> Automatic, LabelStyle -> {}, Method -> Automatic, PlotLabel -> None, PlotRange -> All, PlotRangeClipping -> True, PlotRangePadding -> Automatic, PlotRegion -> Automatic, PreserveImageOptions -> Automatic, Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, TicksStyle -> {}, DisplayFunction :> $DisplayFunction, FormatType :> TraditionalForm}, BarCharts`Private`recs = {{ RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{0, 0}, {1, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{1, 0}, {2, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{2, 0}, {3, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{3, 0}, {4, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{4, 0}, {5, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{5, 0}, {6, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{6, 0}, {7, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{7, 0}, {8, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{8, 0}, {9, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{9, 0}, {10, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{10, 0}, {11, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{11, 0}, {12, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{12, 0}, {13, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{13, 0}, {14, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{14, 0}, {15, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{15, 0}, {16, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{16, 0}, {17, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{17, 0}, {18, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{18, 0}, {19, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{19, 0}, {20, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{20, 0}, {21, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{21, 0}, {22, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{22, 0}, {23, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{23, 0}, {24, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{24, 0}, {25, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{25, 0}, {26, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{26, 0}, {27, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{27, 0}, {28, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{28, 0}, {29, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{29, 0}, {30, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{30, 0}, {31, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{31, 0}, {32, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{32, 0}, {33, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{33, 0}, {34, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{34, 0}, {35, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{35, 0}, {36, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{36, 0}, {37, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{37, 0}, {38, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{38, 0}, {39, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{39, 0}, {40, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{40, 0}, {41, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{41, 0}, {42, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{42, 0}, {43, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{43, 0}, {44, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{44, 0}, {45, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{45, 0}, {46, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{46, 0}, {47, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{47, 0}, {48, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{48, 0}, {49, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{49, 0}, {50, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{50, 0}, {51, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{51, 0}, {52, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{52, 0}, {53, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{53, 0}, {54, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{54, 0}, {55, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{55, 0}, {56, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{56, 0}, {57, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{57, 0}, {58, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{58, 0}, {59, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{59, 0}, {60, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{60, 0}, {61, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{61, 0}, {62, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{62, 0}, {63, 2}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{63, 0}, {64, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{64, 0}, {65, 2}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{65, 0}, {66, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{66, 0}, {67, 3}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{67, 0}, {68, 9}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{68, 0}, {69, 4}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{69, 0}, {70, 10}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{70, 0}, {71, 17}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{71, 0}, {72, 27}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{72, 0}, {73, 27}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{73, 0}, {74, 30}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{74, 0}, {75, 39}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{75, 0}, {76, 45}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{76, 0}, {77, 67}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{77, 0}, {78, 54}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{78, 0}, {79, 55}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{79, 0}, {80, 68}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{80, 0}, {81, 67}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{81, 0}, {82, 67}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{82, 0}, {83, 68}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{83, 0}, {84, 62}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{84, 0}, {85, 59}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{85, 0}, {86, 42}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{86, 0}, {87, 52}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{87, 0}, {88, 44}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{88, 0}, {89, 32}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{89, 0}, {90, 18}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{90, 0}, {91, 16}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{91, 0}, {92, 7}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{92, 0}, {93, 5}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{93, 0}, {94, 2}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{94, 0}, {95, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{95, 0}, {96, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{96, 0}, {97, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{97, 0}, {98, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{98, 0}, {99, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{99, 0}, {100, 0}]}, { RGBColor[0.7771114671549554, 0.7981689173723965, 0.92304875257496], EdgeForm[ GrayLevel[0]], Rectangle[{100, 0}, {101, 0}]}}, BarCharts`Private`varcoords[Horizontal, Pattern[BarCharts`Private`offset, Blank[]], Pattern[BarCharts`Private`format, Blank[]]][{ Pattern[BarCharts`Private`pos, Blank[]], Pattern[BarCharts`Private`len, Blank[]], Pattern[BarCharts`Private`wid, Blank[]]}] := Text[ BarCharts`Private`format[BarCharts`Private`len], Scaled[{ReplaceAll[ Sign[BarCharts`Private`len], 0 -> 1] BarCharts`Private`offset, 0}, {BarCharts`Private`len, BarCharts`Private`pos}]], BarCharts`Private`varcoords[Vertical, Pattern[BarCharts`Private`offset, Blank[]], Pattern[BarCharts`Private`format, Blank[]]][{ Pattern[BarCharts`Private`pos, Blank[]], Pattern[BarCharts`Private`len, Blank[]], Pattern[BarCharts`Private`wid, Blank[]]}] := Text[ BarCharts`Private`format[BarCharts`Private`len], Scaled[{0, ReplaceAll[ Sign[BarCharts`Private`len], 0 -> 1] BarCharts`Private`offset}, { BarCharts`Private`pos, BarCharts`Private`len}]], $CellContext`gradeTestForPlot[ Pattern[$CellContext`ncontrols, Blank[]], Pattern[$CellContext`testMean, Blank[]], Pattern[$CellContext`testSD, Blank[]], Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`maxBias, Blank[]], Pattern[$CellContext`nTrials, Blank[]]] := Module[{$CellContext`trueGrade, $CellContext`rawList, \ $CellContext`trialsList, $CellContext`pointsList, $CellContext`gradeMean, \ $CellContext`gradeSD}, $CellContext`trueGrade = \ $CellContext`conGrade[$CellContext`testMean, $CellContext`testSD, \ $CellContext`sm, $CellContext`tea, $CellContext`maxBias]; \ $CellContext`rawList = Table[ $CellContext`testFunc[$CellContext`ncontrols, \ $CellContext`testMean, $CellContext`testSD, $CellContext`sm, \ $CellContext`tea, $CellContext`maxBias], {$CellContext`nTrials}]; \ $CellContext`trialsList = Part[$CellContext`rawList, All, 1]; $CellContext`pointsList = Part[$CellContext`rawList, All, 2]; $CellContext`gradeMean = Mean[$CellContext`trialsList]; $CellContext`gradeSD = StandardDeviation[$CellContext`trialsList]; \ {$CellContext`trueGrade, $CellContext`gradeMean, $CellContext`gradeSD, \ $CellContext`trialsList, $CellContext`pointsList}], \ $CellContext`gradeTestForPlot[ Pattern[$CellContext`ncontrols, Blank[]], Pattern[$CellContext`testMean, Blank[]], Pattern[$CellContext`testSD, Blank[]], Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`maxBias, Blank[]], Pattern[$CellContext`nTrials, Blank[]], Pattern[$CellContext`gradeCalType, Blank[]]] := Module[{$CellContext`trueGrade, $CellContext`rawList, \ $CellContext`trialsList, $CellContext`pointsList, $CellContext`gradeMean, \ $CellContext`gradeSD}, If[$CellContext`gradeCalType == 1, $CellContext`trueGrade = \ $CellContext`conGrade[$CellContext`testMean, $CellContext`testSD, \ $CellContext`sm, $CellContext`tea, $CellContext`maxBias], \ $CellContext`trueGrade = $CellContext`conGrade2[$CellContext`testMean, \ $CellContext`testSD, $CellContext`sm, $CellContext`tea, \ $CellContext`maxBias]]; $CellContext`rawList = Table[ $CellContext`testFunc[$CellContext`ncontrols, \ $CellContext`testMean, $CellContext`testSD, $CellContext`sm, \ $CellContext`tea, $CellContext`maxBias, $CellContext`gradeCalType], \ {$CellContext`nTrials}]; $CellContext`trialsList = Part[$CellContext`rawList, All, 1]; $CellContext`pointsList = Part[$CellContext`rawList, All, 2]; $CellContext`gradeMean = Mean[$CellContext`trialsList]; $CellContext`gradeSD = StandardDeviation[$CellContext`trialsList]; \ {$CellContext`trueGrade, $CellContext`gradeMean, $CellContext`gradeSD, \ $CellContext`trialsList, $CellContext`pointsList}], $CellContext`conGrade[ Pattern[$CellContext`bias, Blank[]], Pattern[$CellContext`sd, Blank[]], Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`maxBias, Blank[]]] := Module[{$CellContext`grade}, $CellContext`grade = 104. - 34. ( Sqrt[($CellContext`bias/$CellContext`maxBias)^2 + \ ($CellContext`sm $CellContext`sd)^2]/$CellContext`tea); If[$CellContext`grade > 100., $CellContext`grade = 100.]; If[$CellContext`grade < 0., $CellContext`grade = 0.]; $CellContext`grade], $CellContext`testFunc[ Pattern[$CellContext`ntrials, Blank[]], Pattern[$CellContext`testMean, Blank[]], Pattern[$CellContext`testSD, Blank[]], Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`maxBias, Blank[]]] := Module[{$CellContext`myList, $CellContext`compMean, \ $CellContext`compSD, $CellContext`grade}, $CellContext`myList = RandomReal[ NormalDistribution[$CellContext`testMean, $CellContext`testSD], \ $CellContext`ntrials]; $CellContext`compMean = Mean[$CellContext`myList]; $CellContext`compSD = StandardDeviation[$CellContext`myList]; $CellContext`grade = \ $CellContext`conGrade[$CellContext`compMean, $CellContext`compSD, \ $CellContext`sm, $CellContext`tea, $CellContext`maxBias]; \ {$CellContext`grade, {$CellContext`compMean, $CellContext`compSD}}], \ $CellContext`testFunc[ Pattern[$CellContext`ntrials, Blank[]], Pattern[$CellContext`testMean, Blank[]], Pattern[$CellContext`testSD, Blank[]], Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`maxBias, Blank[]], Pattern[$CellContext`gradeCalType, Blank[$CellContext`Bool]]] := Module[{$CellContext`myList, $CellContext`compMean, \ $CellContext`compSD, $CellContext`grade}, $CellContext`myList = RandomReal[ NormalDistribution[$CellContext`testMean, $CellContext`testSD], \ $CellContext`ntrials]; $CellContext`compMean = Mean[$CellContext`myList]; $CellContext`compSD = StandardDeviation[$CellContext`myList]; If[$CellContext`gradeCalType, $CellContext`grade = \ $CellContext`conGrade[$CellContext`compMean, $CellContext`compSD, \ $CellContext`sm, $CellContext`tea, $CellContext`maxBias], $CellContext`grade = \ $CellContext`conGrade2[$CellContext`compMean, $CellContext`compSD, \ $CellContext`sm, $CellContext`tea, $CellContext`maxBias]]; \ {$CellContext`grade, {$CellContext`compMean, $CellContext`compSD}}], \ $CellContext`testFunc[ Pattern[$CellContext`ntrials, Blank[]], Pattern[$CellContext`testMean, Blank[]], Pattern[$CellContext`testSD, Blank[]], Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`maxBias, Blank[]], Pattern[$CellContext`gradeCalType, Blank[]]] := Module[{$CellContext`myList, $CellContext`compMean, \ $CellContext`compSD, $CellContext`grade}, $CellContext`myList = RandomReal[ NormalDistribution[$CellContext`testMean, $CellContext`testSD], \ $CellContext`ntrials]; $CellContext`compMean = Mean[$CellContext`myList]; $CellContext`compSD = StandardDeviation[$CellContext`myList]; If[$CellContext`gradeCalType == 1, $CellContext`grade = \ $CellContext`conGrade[$CellContext`compMean, $CellContext`compSD, \ $CellContext`sm, $CellContext`tea, $CellContext`maxBias], $CellContext`grade = \ $CellContext`conGrade2[$CellContext`compMean, $CellContext`compSD, \ $CellContext`sm, $CellContext`tea, $CellContext`maxBias]]; \ {$CellContext`grade, {$CellContext`compMean, $CellContext`compSD}}], \ $CellContext`newGradePlotBkgd[ Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`maxBias, Blank[]]] := Plot[ $CellContext`grade70[$CellContext`x, $CellContext`sm, \ $CellContext`tea, $CellContext`maxBias], {$CellContext`x, -10, 10}, PlotRange -> {{-10.1, 10.1}, {0, 6}}, GridLines -> Automatic, ImageSize -> {500, 300}, Filling -> Axis, FillingStyle -> Directive[Green, Opacity[0.7]], Frame -> True, LabelStyle -> Directive[FontSize -> 14], FrameLabel -> {{"S.D.", ""}, {"bias", ""}}, PlotStyle -> { Thickness[0.01], Red}, Epilog -> { Tooltip[ Line[{{(-$CellContext`tea) $CellContext`maxBias, 0}, {(-$CellContext`tea) $CellContext`maxBias, \ ($CellContext`tea (1 - $CellContext`maxBias))/$CellContext`sm}, { 0, $CellContext`tea/$CellContext`sm}, {$CellContext`tea \ $CellContext`maxBias, ($CellContext`tea ( 1 - $CellContext`maxBias))/$CellContext`sm}, \ {$CellContext`tea $CellContext`maxBias, 0}}], "Alternate grade 70 line"]}], $CellContext`grade70[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`maxBias, Blank[]]] := (1/$CellContext`sm) Sqrt[$CellContext`tea^2 - ($CellContext`x/$CellContext`maxBias)^2], \ $CellContext`tradGradePlotBkgd[ Pattern[$CellContext`sm, Blank[]], Pattern[$CellContext`tea, Blank[]], Pattern[$CellContext`maxBias, Blank[]]] := Module[{$CellContext`p1, $CellContext`p2, $CellContext`myPoly}, \ $CellContext`myPoly = Polygon[{{(-$CellContext`tea) $CellContext`maxBias, 0}, {(-$CellContext`tea) $CellContext`maxBias, \ ($CellContext`tea (1 - $CellContext`maxBias))/$CellContext`sm}, { 0, $CellContext`tea/$CellContext`sm}, {$CellContext`tea \ $CellContext`maxBias, ($CellContext`tea ( 1 - $CellContext`maxBias))/$CellContext`sm}, \ {$CellContext`tea $CellContext`maxBias, 0}, {(-$CellContext`tea) $CellContext`maxBias, 0}}]; $CellContext`p1 = Graphics[{ EdgeForm[ Directive[ Thickness[0.01], Red]], Directive[Green, Opacity[0.7]], $CellContext`myPoly}, PlotRange -> {{-10.1, 10.1}, {0, 6}}, GridLines -> Automatic, Frame -> True, LabelStyle -> Directive[FontSize -> 14], FrameLabel -> {{"S.D.", ""}, {"bias", ""}}, ImagePadding -> All]; $CellContext`p2 = Plot[ $CellContext`grade70[$CellContext`x, $CellContext`sm, \ $CellContext`tea, $CellContext`maxBias], {$CellContext`x, -10, 10}, PlotRange -> {{-10.1, 10.1}, {0, 6}}, GridLines -> Automatic, ImageSize -> {500, 300}, Frame -> True, LabelStyle -> Directive[FontSize -> 14], FrameLabel -> {{"S.D.", ""}, {"bias", ""}}]; Show[$CellContext`p2, $CellContext`p1, ImageSize -> {500, 300}]]}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{ 3.431683714604232*^9, 3.4316837566084337`*^9, 3.431684272496826*^9, 3.431684309374065*^9, {3.43229572847334*^9, 3.432295742670891*^9}, 3.4323001048054867`*^9, 3.432300326787225*^9}] }, {2}]], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"], ButtonFrame->"None"], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"], ButtonFrame->"None"] }], "PreviousNext"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Lessons Learned: Design", "Section", CellChangeTimes->{ 3.429876275902247*^9, {3.43168463816182*^9, 3.431684653126843*^9}}], Cell["\<\ Using Mathematica, I was able to design a system so that process evaluation \ was clear and intuitive. Combined with an analysis of patient results, it is \ easy to tell the difference between a good process and a poor one.\ \>", "Text", CellChangeTimes->{{3.431685004801293*^9, 3.431685032653389*^9}, { 3.431685195230761*^9, 3.4316852531888943`*^9}, {3.4319602687354193`*^9, 3.4319603889420547`*^9}}], Cell["\<\ Using grades has proven to be a powerful means of expression, and has been \ used for other types of analysis: patient analysis, calibration analysis.It \ is far superior to pass/fail whenever the underlying model is continuous.\ \>", "Text", CellChangeTimes->{{3.431685004801293*^9, 3.431685032653389*^9}, { 3.431685195230761*^9, 3.4316852531888943`*^9}, {3.4319602687354193`*^9, 3.4319603889420547`*^9}}], Cell[CellGroupData[{ Cell["Good Process", "Subsection", CellChangeTimes->{{3.431685255803203*^9, 3.431685258277443*^9}}], Cell[GraphicsData["CompressedBitmap", "\<\ eJzsvQe8XcV1L7y1yzm3SLrqFFEEEr2Dwbg+J59L4u/Feclz4i89jv1iJ/EX 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