 Statistics for the Behavioral Sciences, 4/e Michael Thorne,
Mississippi State University  Mississippi State Martin Giesen,
Mississippi State University  Mississippi State
Alternatives to t and F
Symbols and FormulasSYMBOLS Symbol  Stands For 
 U or M–W U or U´  statistic computed for the Mann–Whitney (MW) test of significance  N_{1}, N_{2}  number of subjects in the first and second groups, respectively  R_{1}, R_{2}  sum of the ranks of the scores in the first and second groups, respectively  d  differences between pairs of scores in the Wilcoxon test  T  sum of the ranks of the scores with the less frequent sign (Wilcoxon test)  H or K–W H  statistic computed for the Kruskal–Wallis (K–W) test  N_{i}  number of observations in a particular sample  R_{i}  sum of the ranks for a particular sample  K  number of samples 
FORMULAS Formula 151. Computational formula for the MannWhitney U test (1.0K) N_{1} is the number of observations in the first sample, N_{2} is the number of observations in the second sample,
and R_{1} is the sum of the ranks of the scores in the first sample.Formula 152. Equation for U´U´ = N_{1}N_{2}  U
The smaller of U and U´ is used in the test of significance.
Formula 154. Equation for converting largesample U to a z score (2.0K) U or U´ is converted to a z score when sample sizes are larger than N = 20.
Formula 155. Equation for converting a largesample T to a z score (2.0K) T is the sum of the ranks with the less frequently occurring sign. With samples of 25 or more, T is
converted to a z score.
Formula 156. Computational formula for the KruskalWallis test (2.0K) N_{i} is the number of observations for a particular sample, N is the total number of observations, and R_{i} is the
sum of the ranks for a particular sample. With sample sizes of at least 5 and at least three samples, H is
distributed approximately as c2 with df = K  1, where K is the number of samples. 
