# 05 reject the null hypothesis if the obtained is

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Unformatted text preview: ormative than the rank sum. This is obtained by dividing the rank sum Ri for a given group by the number of companies in that group and is shown in the table below for each group. If the null hypothesis is true, then these three average ranks should all be relatively close together. In this case the average ranks differ, this indicates the alternative hypothesis is true. 1<=DA<=5 6<=DA<=10 11<=DA<=14 10 5 4 9 12 2 13 6 7 11 3 1 14 t1= 5, R1=57, R/t = 11.4 8 t2=5, R2=34, R/t=6.8 t3=4, R3=14, R/t=3.5 3. The test statistic needs to reflect how different the average ranks are, that is it should be a measure of the dispersion of the ranks. Leach provides the proof of the formula (1979 pp149-150), here it will be take as given: 211 K= -3(n+1)+ 12 Σ Ri2 n(n+1) ti 4. In this case, K=8.1428 There are 2 degrees of freedom in this case. It is therefore possible to reject the null hypothesis at α=0.05 5. To find the locus of the difference, use the rank sum test and choose α=0.02 as the significance level. 6. Writing the groups in order of increasing R/T: 11<=DA<=14 6<=DA<=10 1<=DA<=5 4 5 10 2 12 9 7 6 13 1 3 11 t1= 5, R1=57, R/t = 11.4 8 t2=5, R2=34, R/t=6.8 14 t3=4, R3=14, R/t=3.5 7. Then comparing 11<=DA<=14 with 1<=DA<=5 gives: p’s q’s 5 0 5 0 5 0 5 P=20 0 Q=0 S=P-Q=20, which is significant at α=0.02 8. Then comparing 11<=DA<=14 with 6<=DA<=10 gives: 212 p’s q’s 4 1 5 0 3 2 5 P=17 0 Q=3 S=P-Q=14, which is not significant at α=0.02. 9. So the result of the Wilcoxon Rank Sum for PR is, 11<=DA<=14, 6<=DA<=10, 1<=DA<=5 213 APPENDIX 5:CRITICAL VALUES OF ρ FOR SPEARMAN TESTS Examples: For a two tailed test, with n=15 and α=0.05, reject the null hypothesis if the obtained ρ is larger than or equal to 0.521, or if it is smaller than or equal to -0.521. Examples: For a one tailed test, with n=15 and α=0.05, if an upper tail test is required, reject the null hypothesis if the obtained is larger than or equal to 0.446. If a lower tail test is required, reject if the obtained ρ is smaller than or equal to -0.446. One tailed significance level, α 0.1 0.05 0.025 0.01 0.005 0.001 Two tailed significance level, α n 0.2 0.1 0.05 0.02 0.01 0.002 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 0.8 0.657 0.571 0.524 0.483 0.455 0.427 0.406 0.385 0.367 0.354 0.341 0.328 0.317 0.309 0.299 1 0.9 0.829 0.714 0.643 0.6 0.564 0.536 0.503 0.484 0.464 0.446 0.429 0.414 0.401 0.391 0.38 1 0.866 0.786 0.738 0.7 0.648 0.618 0.587 0.560 0.538 0.521 0.503 0.488 0.474 0.46 0.447 1 0.943 0.893 0.833 0.783 0.745 0.709 0.678 0.648 0.626 0.604 0.585 0.566 0.550 0.535 0.522 1.00 0.929 0.881 0.833 0.794 0.755 0.727 0.703 0.679 0.657 0.635 0.618 0.6 0.584 0.57 1.00 0.952 0.917 0.879 0.845 0.818 0.791 0.771 0.750 0.729 0.711 0.692 0.674 0.66 From Leach (1979) 214 APPENDIX 6:CRITICAL VALUES OF K FOR KRUSKAL WALLIS TEST WITH 3 INDEPENDENT SAMPLES t1 is the number of observations in the largest sample t3 is t...
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