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The Mann-Whitney U test is used to test for differences between two conditions with an unrelated measures IV. (See Section 10.2 of the book if you are unfamiliar with the term unrelated measures IV.) The statistic is U. It is the smaller of two calculated values, U and U prime. This statistic, U, must be less than or equal to the critical value to be statistically significant. The information you need to provide to enable someone to check U is the number of participants in group 1 and the number of participants in group 2.
In an experiment to test whether the 16 students who received a positive comment from their tutor once in every class gave different overall ratings of satisfaction with the tutor's teaching at the end of the course when compared with the control group. The control group of 14 students did not receive the positive comment. The obtained value of U = 56 with an associated probability = .02 (two-tailed test).
These findings are reported succinctly in Section 4.6.4 of the book.
If the result is statistically significant, is the difference in the direction you predicted? If any of the participants have the same score then there will be ties and you should report the version of U corrected for ties. Statistical software packages may not bother to print out U prime, so do not be concerned if you cannot find it in the print out. If the result is not statistically significant, did you run enough participants? (See section 13.1.1 of the book for more about this.)
The Wilcoxon test is used to test for differences between two conditions with a related measures IV. (See Section 10.2 of the book if you are unfamiliar with the term related measures IV.) The statistic is T (some people refer to it as W ). It is the smaller of two rank totals. This statistic, T (or W), must be less than or equal to the critical value to be statistically significant. The information you need to provide to enable someone to check T is the number of participants overall, not counting those with tied ranks (i.e., not counting those with the same scores in each condition).
Twenty four students took part in a study to test whether their overall ratings of their chances of experiencing a series of eight life-threatening diseases (such as cancer, HIV and meningitis) were different from their overall ratings of the chances of the average student at their university experiencing these same diseases. Six participants gave the same mean ratings to themselves and the average student (i.e., had tied ranks). The obtained T = 27 with associated probability = .01 (two-tailed test).
These findings are reported succinctly in Section 4.6.5 of the book.
If the result is statistically significant, is the difference in the direction you predicted? You should mention the number of participants excluded because of tied ranks.
This test is used to test for differences between three or more conditions with an unrelated measures IV. (See Section 10.2 of the book if you are unfamiliar with the term unrelated measures IV.) The statistic is H. This statistic, H, must be greater than or equal to the critical value to be statistically significant. The information you generally need to provide to enable someone to check H is the degrees of freedom, which is given by the number of conditions minus 1.
In an experiment to test whether students who received a positive comment from their tutor once in every class gave different overall ratings of satisfaction with the tutor's teaching at the end of the course from those who received a mildly critical comment from their tutor once in every class and the control students who received neither comment. The obtained H = 7.38 with associated probability = .025.
These findings are reported succinctly in Section 4.6.6 of the book.
If the result is statistically significant, are the differences as you predicted? How do you know, given that it only tests for overall differences? That is, in the above example we do not know for sure which of the three ratings - those given by the positive comment group, the mildly critical comment group, or the control group - differ from each other. To find this out we would need to do follow up tests. We could for example run some Mann-Whitney U tests on pairs of groups, but controlling for type 1 errors in the process. (You can find out more about this in Pallant, third edition, Chapter 16.) If the result of your Kruskal-Wallis test is not statistically significant, did you run enough participants? (See sections 5.2 and 13.1.1 of the book for more about this.) Your statistical package may report a value of chi-square ( χ² ) instead of H . If so, report the value of χ² instead of H , together with the degrees of freedom and the N (see section B2.1 of this Web site for more on chi-square). If any participants have the same score on the DV, report the version of H (or of χ² ) corrected for ties. If you are using tables to look up significance levels you may find that you need the number of participants in each condition instead of the degrees of freedom, especially where you have only two or three conditions and the sample sizes are small. (You can find out more about this in Greene & D'Oliveira, third edition, Chapter 12.)
Friedman's test is used to test for differences between three or more conditions with a related measures IV. (See Section 10.2 of the book if you are unfamiliar with the term related measures IV.) The statistic is based on chi-square and is χ²r (some people refer to it as χ²F ). This statistic, χ²r (or χ²F ), must be greater than or equal to the critical value to be statistically significant. The information you generally need to provide to enable someone to check χ²r is the degrees of freedom, given by the number of conditions minus 1.
In a study to test whether students' overall ratings of their chances of experiencing a series of eight life-threatening diseases (such as cancer, HIV and meningitis) were different from their overall ratings of the chances of their best friend experiencing these diseases and those of the average student at their university experiencing these diseases, the obtained χ²r = 9.21 with associated probability = .01.
These findings are reported succinctly in Section 4.6.7 of the book.
If the result is statistically significant, are the differences as you predicted? How do you know, given that it only tests for overall differences? That is, in the above example we do not know for sure which of the three overall ratings - those given for the chances for the self, the best friend or the average student - differ from each other. To find this out we would need to do follow up tests. We could for example run some Wilcoxon tests on pairs of groups, but controlling for type 1 errors in the process. (You can find out more about this in Pallant, third edition, Chapter 16.) When reporting you overall Friedman test, report the version corrected for ties if any participant has the same score in at least two conditions of the dependent variable (in this case, the same overall rating for any two of the self, best friend or average student). If your sample size is small (10 or below) you should report this fact along with the statistic, as there are tables of significance for χ²r for situations with few conditions and sample sizes below 10. (You can find out more about this in Greene & D'Oliveira, third edition, Chapter 11.) |
