Demonstration of confidence intervals

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Demonstration of confidence intervals

Postby trubador » Tue Oct 20, 2015 1:26 pm

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!npop = 1000 'size of the population
wfcreate u !npop 'create an unstructured workfile
!mu = 5 'population mean
!sig = 0.5 'population standard deviation
series ypop = !mu + !sig*@rnorm 'hypothetical population

!nrep = 100 'number of draws
!nsamp = 50 'sample size
!alpha = 0.05 'significance level
%insmpl = @pagesmpl 'population range
%outsmpl = "1 "+@str(!nsamp) 'sample range

'Series objects are bound by the frequency of the workfile
if !nrep>!npop then
  @uiprompt("Number of draws should be less than the population size!")
  !nrep = 100

smpl 1 !nrep 'adjust the page sample
series meanval 'create a series to hold the mean of each sample
series lbound 'create a series to hold the lower bounds of the confidence intervals
series ubound 'create a series to hold the upper bounds of the confidence intervals
group confidence 'create a group to store the confidence intervals
confidence.add ubound lbound meanval 'add series to the group object
%false="" 'create a blank string

'Loop for drawing samples
for !i=1 to !nrep
 ypop.resample(outsmpl=%outsmpl,insmpl=%insmpl,permute,suffix=ysamp) 'sampling
 meanval(!i) = @mean(ysamp) 'mean values
 lbound(!i) = @mean(ysamp) - @qnorm(1-!alpha/2)*@stdev(ysamp)/@sqrt(!nsamp) 'lower bound
 ubound(!i) = @mean(ysamp) + @qnorm(1-!alpha/2)*@stdev(ysamp)/@sqrt(!nsamp) 'upper bound
   if !mu>ubound(!i) or !mu<lbound(!i,2) then
    %false=%false+" "+@str(!i) 'false positives (type I errors)
 statusline !i of !nrep 'monitor the progress

%confchart = @getnextname("confchart") 'name the chart
!rotate=0 '=1 to rotate the chart
if !rotate=1 then
  freeze({%confchart}) confidence.errbar(rotate) 'generate the chart
  {%confchart}.draw(line,bottom,color(red),width(1)) 5 'draw the population mean
  for !j=1 to @wcount(%false)
    !s = @val(@word(%false,!j))
    {%confchart}.draw(shade,left,rgb(230,184,183)) !s 'highlight false positives
  freeze({%confchart}) confidence.errbar
  {%confchart}.draw(line,left,color(red),width(1)) 5
  for !j=1 to @wcount(%false)
    !s = @val(@word(%false,!j))
    {%confchart}.draw(shade,bottom,rgb(230,184,183)) !s

%header = "# samples = "+@str(!nrep)+" | # rejects = "+@str(@wcount(%false))+" | sample size = "+@str(!nsamp)+" | moments of sampling distribution = ("+@str(@mean(meanval),"f.2")+","+@str(@stdevp(meanval),"f.3")+")"
{%confchart}.addtext(t) {%header}
{%confchart}.setupdate(m) 'enables the slider bar
show {%confchart} 'display the chart

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