The f-tests

# input data y1=c(45,87,123,120,70) y2=c(51,71,42,37,51,78,51,49,56,47,58)

# test ratio of sample variances n1=length(y1) # assume no missing points n2=length(y2) v1=var(y1) # assume no missing points v2=var(y2) f=v1/v2 # observed variance ratio p=pf(f,n1-1,n2-1) # test f p=.5-abs(p-.5) # when p > 0.5 then p = 1-p p*2 # 2-tailed P-value # log transform and repeat F-test v1=var(log(y1)) # assume y is +ve v2=var(log(y2)) f=v1/v2 p=pf(f,n1-1,n2-1) p=.5-abs(p-.5) # when p > 0.5 then p = 1-p p*2 # 2-tailed P-value

> # test ratio of sample variances > p*2 # 2-tailed P-value [1] 0.00810827 > # log transform and repeat F-test > p*2 # 2-tailed P-value [1] 0.0769091