The Kolmogorov–Smirnov test is a more general, often-used nonparametric method that can be used to test whether the data come from a hypothesized distribution, such as the normal. The Shapiro–Wilk test, which is a well-known nonparametric test for evaluating whether the observations deviate from the normal curve, yields a value equal to 0.894 ( P < 0.000) thus, the hypothesis of normality is rejected. A glance at the graph shows that the normal seems to overestimate the lower-score frequencies and underestimate the higher-score frequencies. The smooth dashed curve in Figure 1 shows the normal approximation to the histogram. Example of an estimated distribution of sum scores (e.g., the number-correct score on an educational test) by means of a histogram, kernel smoothing (solid curve), and a normal approximation (dashed curve). Then clickĪnalyze > Nonparametric tests > 2 Independent samples … > move Brand to Grouping Variable: and Price to Test Variable list: > click Define Groups… > enter 1 in Group 1:, and 2 in Group 2: > click continue > choose Mann–Whitney U > OKįigure 1. Enter tire brands as 1 to identify brand 1 and 2 to identify brand 2, in C1. For the same data set, any p values generated from one test will be identical to those generated from the other. The Mann–Whitney U-test is equivalent to the Wilcoxon rank sum test, although we calculate it in a slightly different way. Solutionīecause the SPSS pull-down menu does not have the Wilcoxon rank sum test, we will use the Mann–Whitney U-test. (Wilcoxon rank sum test): For the data of Example 12.4.2, use the Wilcoxon rank sum test at the significance level of 0.05 to test the null hypothesis that the two population medians are the same against the alternative hypothesis that the population medians are different. To use a 2-tailed table of critical U values for a 1-tailed test, we should double the significance level of the 1-tailed test, for example, we can use Table A.4 for a 1-tailed test at 0.025 significance level. For other significance levels, a different table would be required.
Note that Table A.4 is for a 2-tailed test at 0.05 significance level only. As 14.5 is not less than 6, we cannot reject the null hypothesis, meaning that the team cannot conclude with 95% confidence that the heights of the two cohorts are different. The critical values for a 2-tailed Mann–Whitney U test at 0.05 significance can be found in Table A.4 in the Appendix. We then take the lower of these two values, U t = 14.5, as our test statistic. We have U c + U t = 27.5 + 14.5 = 42 and n c × n t = 6 × 7 = 42, so that is fine. Īs a check that nothing has gone awry during the calculation, U c + U d should equal n c × n t.
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