I just read that the Ansari-Bradley test is a test of stochastic equality of two variances regardless of any distributional assumptions. If it is so flexible, why do we even need the F test?
I am confused, as for the Ansari-Bradley test it is said it is about "scale parameters", not just "variances". But whenever I go to read about the scale parameters, scaling the "width" of the distribution, there is a reference to variance.
Is somehow the F test bound to the normal distribution? Variance in general applies to any distribution, not just the normal. But I thought this may be important?
I found, when using the R statistical package, that both tests may differ a lot, sometimes the var.test() reports low p-value while the Ansari-Bradley test reports high p.value.
> a <- c(1,2,3,4,5,10,12,14,15,20,30,40,50,60,70,100) > b <- c(1.1,1.2,3,3.3,5.5,10.1,10.3,14.1,15.1,20.1,31,32,33,34,35) > ansari.test(a, b) Ansari-Bradley test data: a and b AB = 121.5, p-value = 0.4013 alternative hypothesis: true ratio of scales is not equal to 1 Warning message: In ansari.test.default(a, b) : cannot compute exact p-value with ties > var.test(a, b) F test to compare two variances data: a and b F = 4.9132, num df = 15, denom df = 14, p-value = 0.004904 alternative hypothesis: true ratio of variances is not equal to 1 95 percent confidence interval: 1.665875 14.206412 sample estimates: ratio of variances 4.9132