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MathGroup Archive 1999

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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. 
>


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