Pensieve header: Data analysis for Maya Bar-Hillel.

In the file attached there are the results of 280 respondents, each of whom 
rated 28 variables on a 1-to-5 scale.
I’d like a Monte Carlo to assess the correlation between the means given each 
variable by two randon halves of the 280 people.

So:  divide the 280 into 2 groups of 140 each, at random.
Compute the mean rating for each of the 28 variables,
separately for each half.
Compute Pearson’s r between these mean ratings.
Repeat N times (one hundred?.
Calculate the mean r.

I suspect it will be close to 1, over and over and over again.

Initialization

SetDirectory["C:\\drorbn\\AcademicPensieve\\People\\BarHillel"]

tab=Import["Monte.xlsx"][[1]];
Dimensions[tab]

Av[l_List]:= Mean[Select[l,NumberQ]];

Comparing the first 140 with the last 140

{A=Range[140], B=Complement[Range[280], A]};
{AvA=Av/@Transpose@tab[[A]], AvB=Av/@Transpose@tab[[B]]}
basecor=Correlation[AvA, AvB]

Monte-Carlo within 1..280, 10,000 runs:

Short[cors=Sort@Table[
{A=Sort@RandomSample[Range[280],140], B=Complement[Range[280], A]};
AvA=Av/@Transpose@tab[[A]];
AvB=Av/@Transpose@tab[[B]];
Correlation[AvA, AvB],
{10000}
]]

Histogram[cors,{0.5,1,0.01}, ImageSize->640]

Mean[cors]

Count[cors,_?(#<basecor&)]/Length[cors] // N

Monte-Carlo within 1..140, 10,000 runs:

Short[cors=Sort@Table[
{A=Sort@RandomSample[Range[140],70], B=Complement[Range[140], A]};
AvA=Av/@Transpose@tab[[A]];
AvB=Av/@Transpose@tab[[B]];
Correlation[AvA, AvB],
{10000}
]]

Histogram[cors,{0.5,1,0.01}, ImageSize->640]

Mean[cors]

Count[cors,_?(#<basecor&)]/Length[cors] // N

Monte-Carlo within 141..280, 10,000 runs:

Short[cors=Sort@Table[
{A=Sort@RandomSample[Range[141,280],70], B=Complement[Range[141,280], A]};
AvA=Av/@Transpose@tab[[A]];
AvB=Av/@Transpose@tab[[B]];
Correlation[AvA, AvB],
{10000}
]]

Histogram[cors,{0.5,1,0.01}, ImageSize->640]

Mean[cors]

Count[cors,_?(#<basecor&)]/Length[cors] // N