Essentials

NONPARAMETRIC STATISTICS 219where N is the number of pairs (i.e., the number of discrepancies that are beingranked).Dealing with TiesIf you are dealing with fewer than 15 pairs, many introductory statistics texts havetables for Wilcoxon’s T that you can use to perform an exact test. If you havemore than a few ties and therefore need a correction factor, see Spiegel andCastellan (1988). There is one kind of tie that is particularly problematic with thiskind of test. If for a specific pair it is impossible to say which painting is more creative,that pair must be given a zero. If there is just one zero, that pair should beeliminated from the analysis. If there are several zeroes they can all be eliminated—asis usually recommended for the sign test—but for the Wilcoxon T testa more conservative solution is recommended. If there is an odd number of zeroes,delete one of them. Half of an even number of zeroes should be arbitrarilyassigned to be positive and the other half negative, and all should be included inthe ranking (of course, all of the zeroes will be tied with each other).Comparisons to Other TestsRanking discrepancies that can’t be quantified precisely is difficult, which probablyaccounts for why Wilcoxon’s T is rarely used in that way. The more commonuse for this test is as an alternative to the matched t test. Suppose each participantsolves two similar puzzles under different conditions, and solution times differwildly (sometimes the participant gets it right away, sometimes not). If there areonly 10 participants, the matched t test may not be appropriate. However, thereis no need to throw away quantitative information and merely determine whichcondition had the shorter time. The differences between the conditions can berank-ordered easily (ties are unlikely) and the sum of ranks found for each direction(i.e., condition 1 has the longer time, or condition 2 has the longer time).Wilcoxon’s T test can then be applied (an exact table is suggested for thisexample because N 10). TheWilcoxon test will usually have asmuch as 90% of the power of thematched t test; the sign test will haveconsiderably less power.The Friedman TestWhat if each participant solves threeproblems, each under a different condition?If the data are not appropriateCAUTIONAn assumption of ordinal tests is thatthe variable being measured ordinallyis actually continuous, so that tiesshould be rare. Although there arecorrection factors for ordinal testswhen ties do occur, a large percentageof ties will diminish the accuracy of thep values associated with those tests.