1. The two sample t-test The carapace lengths (measure in mm) of crawfish (Palinurus vulgaris) captured in streams in Devon and Cornwall were measured. The data is given below: Carapace Length (in mm) Devon: 170,111,135,182,121,174,169,133,141,147,159,163 Cornwall: 146, 97, 102, 181, 107, 118,131,155,127,130, 129 a. Do you have reason to believe the two populations of crawfish do both have the same mean carapace length? Use the t test. b. Can you answer the question in a. using the Wilcoxon rank sum test? (See note below.) c. Compare the results obtained in a. and b. Are you surprised? The Wilcoxon Rank Sum Test - The Wilcoxon Rank Sum (WRS) test is the distribution free alternative to the t-test. It does not consider the actual value of the observations but only their relative position in the combined set of observations from the two samples, A and B. To use the WRS, you combine the observations of the two samples, order them from smallest to the largest, given rank 1 to the smallest observation (in either sample), rank 2 to the second smallest, and so on, giving rank n+m to the largest observation. The null hypothesis is that the two distributions are the same. The test statistic, WA or WB is the sum of the ranks of the observations in one of the samples. Reference Distribution For samples of similar sized with a combined number of observation in excess of 20, if H0 is true WA will have a distribution that is approximately Normal with µ = (nA)(nA+nB+1) 2 and variance σ 2 A = nAnB(nA+nB+1) 12 . Note that the variance is the
