module Statsample
module Reliability
# Analysis of a Scale. Analoge of Scale Reliability analysis on SPSS.
# Returns several statistics for complete scale and each item
# == Usage
# @x1=[1,1,1,1,2,2,2,2,3,3,3,30].to_vector(:scale)
# @x2=[1,1,1,2,2,3,3,3,3,4,4,50].to_vector(:scale)
# @x3=[2,2,1,1,1,2,2,2,3,4,5,40].to_vector(:scale)
# @x4=[1,2,3,4,4,4,4,3,4,4,5,30].to_vector(:scale)
# ds={'x1'=>@x1,'x2'=>@x2,'x3'=>@x3,'x4'=>@x4}.to_dataset
# ia=Statsample::Reliability::ScaleAnalysis.new(ds)
# puts ia.summary
class ScaleAnalysis
include Summarizable
attr_reader :ds,:mean, :sd,:valid_n, :alpha , :alpha_standarized, :variances_mean, :covariances_mean
attr_accessor :name
def initialize(ds, opts=Hash.new)
@ds=ds.dup_only_valid
@k=@ds.fields.size
@total=@ds.vector_sum
@item_mean=@ds.vector_mean.mean
@mean=@total.mean
@median=@total.median
@skew=@total.skew
@kurtosis=@total.kurtosis
@sd = @total.sd
@variance=@total.variance
@valid_n = @total.size
opts_default={:name=>"Reliability Analisis"}
@opts=opts_default.merge(opts)
@name=@opts[:name]
# Mean for covariances and variances
@variances=@ds.fields.map {|f| @ds[f].variance}.to_scale
@variances_mean=@variances.mean
@covariances_mean=(@variance-@variances.sum).quo(@k**2-@k)
begin
@alpha = Statsample::Reliability.cronbach_alpha(ds)
@alpha_standarized = Statsample::Reliability.cronbach_alpha_standarized(ds)
rescue => e
raise DatasetException.new(@ds,e), "Error calculating alpha"
end
end
# Returns a hash with structure
def item_characteristic_curve
i=0
out={}
total={}
@ds.each do |row|
tot=@total[i]
@ds.fields.each do |f|
out[f]||= {}
total[f]||={}
out[f][tot]||= 0
total[f][tot]||=0
out[f][tot]+= row[f]
total[f][tot]+=1
end
i+=1
end
total.each do |f,var|
var.each do |tot,v|
out[f][tot]=out[f][tot].to_f / total[f][tot]
end
end
out
end
def gnuplot_item_characteristic_curve(directory, base="crd",options={})
require 'gnuplot'
crd=item_characteristic_curve
@ds.fields.each do |f|
x=[]
y=[]
Gnuplot.open do |gp|
Gnuplot::Plot.new( gp ) do |plot|
crd[f].sort.each do |tot,prop|
x.push(tot)
y.push((prop*100).to_i.to_f/100)
end
plot.data << Gnuplot::DataSet.new( [x, y] ) do |ds|
ds.with = "linespoints"
ds.notitle
end
end
end
end
end
def svggraph_item_characteristic_curve(directory, base="icc",options={})
require 'statsample/graph/svggraph'
crd=ItemCharacteristicCurve.new(@ds)
@ds.fields.each do |f|
factors=@ds[f].factors.sort
options={
:height=>500,
:width=>800,
:key=>true
}.update(options)
graph = ::SVG::Graph::Plot.new(options)
factors.each do |factor|
factor=factor.to_s
dataset=[]
crd.curve_field(f, factor).each do |tot,prop|
dataset.push(tot)
dataset.push((prop*100).to_i.to_f/100)
end
graph.add_data({
:title=>"#{factor}",
:data=>dataset
})
end
File.open(directory+"/"+base+"_#{f}.svg","w") {|fp|
fp.puts(graph.burn())
}
end
end
def item_total_correlation
@ds.fields.inject({}) do |a,v|
vector=@ds[v].clone
ds2=@ds.clone
ds2.delete_vector(v)
total=ds2.vector_sum
a[v]=Statsample::Bivariate.pearson(vector,total)
a
end
end
def item_statistics
@ds.fields.inject({}) do |a,v|
a[v]={:mean=>@ds[v].mean,:sds=>@ds[v].sds}
a
end
end
# Returns a dataset with cases ordered by score
# and variables ordered by difficulty
def item_difficulty_analysis
dif={}
@ds.fields.each{|f| dif[f]=@ds[f].mean }
dif_sort=dif.sort{|a,b| -(a[1]<=>b[1])}
scores_sort={}
scores=@ds.vector_mean
scores.each_index{|i| scores_sort[i]=scores[i] }
scores_sort=scores_sort.sort{|a,b| a[1]<=>b[1]}
ds_new=Statsample::Dataset.new(['case','score'] + dif_sort.collect{|a,b| a})
scores_sort.each do |i,score|
row=[i, score]
case_row=@ds.case_as_hash(i)
dif_sort.each{|variable,dif_value| row.push(case_row[variable]) }
ds_new.add_case_array(row)
end
ds_new.update_valid_data
ds_new
end
def stats_if_deleted
@ds.fields.inject({}) do |a,v|
ds2=@ds.clone
ds2.delete_vector(v)
total=ds2.vector_sum
a[v]={}
a[v][:mean]=total.mean
a[v][:sds]=total.sds
a[v][:variance_sample]=total.variance_sample
a[v][:alpha]=Statsample::Reliability.cronbach_alpha(ds2)
a
end
end
def report_building(builder) #:nodoc:
builder.section(:name=>@name) do |s|
s.table(:name=>_("Summary for %s") % @name) do |t|
t.row [_("Items"), @ds.fields.size]
t.row [_("Valid cases"), @valid_n]
t.row [_("Sum mean"), @mean]
t.row [_("Sum sd"), @sd]
t.row [_("Sum variance"), @variance]
t.row [_("Sum median"), @median]
t.hr
t.row [_("Item mean"), @item_mean]
t.row [_("Skewness"), "%0.4f" % @skew]
t.row [_("Kurtosis"), "%0.4f" % @kurtosis]
t.hr
t.row [_("Cronbach's alpha"), "%0.4f" % @alpha]
t.row [_("Standarized Cronbach's alpha"), "%0.4f" % @alpha_standarized]
t.row [_("Variances mean"), "%g" % @variances_mean]
t.row [_("Covariances mean") , "%g" % @covariances_mean]
end
s.text _("items for obtain alpha(0.8) : %d" % Statsample::Reliability::n_for_desired_alpha(0.8, @variances_mean,@covariances_mean))
s.text _("items for obtain alpha(0.9) : %d" % Statsample::Reliability::n_for_desired_alpha(0.9, @variances_mean,@covariances_mean))
itc=item_total_correlation
sid=stats_if_deleted
is=item_statistics
s.table(:name=>_("Items report for %s") % @name, :header=>["item","mean","sd", "mean if deleted", "var if deleted", "sd if deleted"," item-total correl.", "alpha if deleted"]) do |t|
@ds.fields.each do |f|
t.row(["#{@ds[f].name}(#{f})", sprintf("%0.5f",is[f][:mean]), sprintf("%0.5f",is[f][:sds]), sprintf("%0.5f",sid[f][:mean]), sprintf("%0.5f",sid[f][:variance_sample]), sprintf("%0.5f",sid[f][:sds]), sprintf("%0.5f",itc[f]), sprintf("%0.5f",sid[f][:alpha])])
end # end each
end # table
end # section
end # def
end # class
end # module
end # module