Nonparamentric Stats –Distribution free tests –e.g., rank tests Sign test –H 0 : Median = 100 H a : Median > 100 if median = 100, then half above, half below 100 let S = # of x greater than 100 Is total # of + or - way more than expected? –let + be “success”, - “failure” –binomial –this case:  = 0.5 –compare binomial probability to 

–Example 12.2 sign test 10 water samples median > 5.0 ppm expect S = 5 if median = 5.0 find S = 7 binomial n = 10,  = 0.5 –what is P(S>=7) –table (or Excel): P = >  »do not reject

Two-sample tests –Wilcoxon rank sum test –Example 12.3 visual acuity of deaf vs. hearing Table 12.3 critical values –for n 1 =10, n 2 = 10 »critical = 83, 127 T 127, reject H 0 –there is a significant difference large sample

Matched Pairs –Wilcoxon signed ranks test –Example reading test scores Table 12.5 critical values –critical (  =0.05, 2-tail, n=10) = 8 –T - < = 8, reject H 0 »there is a significant difference Large sample

Kruskal-Wallis H Test –multiple rank-sums instead of ANOVA –H 0 : medians are equal H a : at least one is different Test stat »if ranks are equal, H close to 0 Chi-square test Example 12.6 –H = 6.70 –  2.05 = 5.99 –H >5.99, reject H 0 »there is a significant difference

Rank Correlation test –correlate ranks