Re: Results Scaling
- To: mathgroup at smc.vnet.net
- Subject: [mg19617] Re: [mg19580] Results Scaling
- From: BobHanlon at aol.com
- Date: Sun, 5 Sep 1999 16:57:40 -0400
- Sender: owner-wri-mathgroup at wolfram.com
Anthony, One approach is to use T-Scores which are normalized to a mean of 50 and a standard deviation of 10. A T-Score readily gives the deviation from the mean in standard deviations. For example, a T-Score of 65 is 1.5 standard deviations above the mean. Bob Hanlon ____________________ Needs["Statistics`ContinuousDistributions`"] Needs["Statistics`DataManipulation`"]; Needs["Graphics`Graphics`"]; Needs["Utilities`FilterOptions`"]; Options[plotContDistData] = {nbrBins -> 12}; plotContDistData::usage = "plotContDistData[dist, data] overlays the PDF for the specified \ continuous distribution over a bar chart of the data list."; plotContDistData[dist_, data_List, opts___?OptionQ] := Module[{mu, sigma, xmin, xmax, pltPDF, x, nbrVal = Length[data], step, k, pltData, nBins, pltOpts}, nBins = (nbrBins /. Flatten[{opts}]) /. Options[plotContDistData]; pltOpts = FilterOptions[Plot, opts]; mu = N[Mean[dist]]; sigma = N[StandardDeviation[dist]]; xmin = Max[mu - 3sigma, Domain[dist][[1, 1]]]; xmax = Min[mu + 3sigma, Domain[dist][[1, 2]]]; pltPDF = Plot[PDF[dist, x], {x, xmin, xmax}, PlotStyle -> AbsoluteThickness[2], DisplayFunction -> Identity, Evaluate[pltOpts]]; step = (xmax - xmin)/nBins; pltData = GeneralizedBarChart[ Transpose[{Table[xmin + step(k - 1/2), {k, nBins}], BinCounts[data, {xmin, xmax, step}]/(step*nbrVal), Table[step, {nBins}]}], DisplayFunction -> Identity, Evaluate[pltOpts]]; Show[{pltData, pltPDF}, DisplayFunction -> $DisplayFunction]]; dist = NormalDistribution[70, 5]; scores = RandomArray[dist, 200]; {mu = Mean[scores], sigma = StandardDeviation[scores]} {70.1659, 4.61972} plotContDistData[dist, scores]; The T-Scores are normalized to a mean of 50 and a standard deviation of 10. normalizedScores = 50 + 10(scores - mu)/sigma; {Mean[normalizedScores], StandardDeviation[normalizedScores]} {50., 10.} plotContDistData[NormalDistribution[50, 10], normalizedScores]; In a message dated 9/4/99 4:45:09 AM, antonyip at ihug.co.nz writes: >I am currently developing a student results entry application. >One of features of this application is to allow user to statistical scale >students results. >I am just wondering if any body here have similar experience before. >I really want to know the statistical algorithm that can be used to scale >student results. >