% A sample of 11 Classical Neanderthal European skull capacities
% gave the sample variance of 11175, n2=4 middle eastern
% skulls produced the sample variance of 741.
% Assuming the measurements are normally distributed
%test the hypothesis that the population variances are the same
%against the two sided alternative. Use alpha=0.05.
s12 = 11175; s22=741;
n1=11; n2=4;
f = s12/s22 %test statistics
% since s12 > s22 -> f > 1 and critical
%region is the upper tail of F-distribution with
%n1-1, n2-1 degrees of freedom
crit = finv(0.95, n1-1, n2-1) %8.7855 critical val
% compare this critical point with f
pval = 2*min(fcdf(f, n1-1, n2 -1), 1-fcdf(f, n1-1, n2 -1))
%0.0469 p-value
%
%
%------------------
% suppose that we took statistics ff=s22/s12 instead of
% f=s12/s22.
ff=1/f %0.0663 s22/s12
pval = 2*min(fcdf(ff, n2-1, n1-1), 1-fcdf(ff, n2-1, n1-1) ) %p value
%
critnew = finv(0.05, n2-1, n1-1) %critical pt
critold = 1/critnew % test for consistency
% this reciprocal should be equal to critical point for
% f=1/ff.