When this happens join the two sample names with a

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Unformatted text preview: ation to the 209 null distribution of a test statistic. This is the case with K. The table in Appendix 7 gives critical values of the Chi-square distribution that may be used with sample sizes beyond the scope of the exact table in Appendix 6. To obtain the relevant critical value: • Find the number of degrees of freedom, the number of samples minus 1. • Find the relevant critical value in the table in Appendix 7. Reject the null hypothesis if the obtained K (corrected for ties as in 9 if necessary) is larger than or equal to the critical value. If the null hypothesis is rejected, use multiple comparisons to locate the effects. Otherwise, stop. Adapted from Leach (1979) 2. MULTIPLE COMPARISONS USING THE WILCOXON RANK SUM TEST When a significant result has been obtained in the Kruskal Wallis test, all that is known is that there is some difference in location between the samples. The locus of this difference is unknown. The Wilcoxon Rank Sum test is frequently used for this purpose and the procedure generally followed is: 1. Select the per experiment significance level, α 2. Decide on c, the number of comparisons you wish to make. Normally you will wish to compare all possible pairs of samples. If there are k samples, the number of pairs will be c=k(k-1) 3. Order the k samples with respect to their average ranks (given by R i/ti) and write the sample names in order. 4. Using a two-tailed test carry out the Wilcoxon Rank Sum tests as follows. Using the ordering given in 4 and the table in Appendix 8, compare the left-most sample first with the right most, next with the second from the right, and so on until a non-significant result is obtained. When this happens, join the two sample names with a line. Then take the second sample from the left and compare it first with the right most, next with the second from the right, and so on until either a nonsignificant result is obtained or two samples are being compared that are already joined by a line. Continue in this way until all comparisons have been exhausted. Adapted from Leach (1979) 210 3. THE KRUSKAL WALLIS AND WILCOXON RANK SUM TESTS FOR PR 1. Arrange the companies into groups depending on their ranking position in the sophistication of decision analysis rank. (For example, column 1<=DA<=5 contains companies that were ranked in the top 5 in the decision analysis ranking). Then note companies proved reserves under the appropriate heading. The following simple notation will be used, n will be the total number of companies, t 1 will be the number in 1<=DA<=5, t 2 will be the number in 6<=DA<=10, t 3 will be the number in 11<=DA<=14. 2. Rank the data from low to high (with rank of 1 being assigned to the company with the least proved reserves). Compute the rank sums for the three samples. This is done in the table below, where Ri refers to the rank sum of the ith group, so R1=57, R2=34 and R3=14. The test statistic will need to take account of what is going on in all 3 groups to give an adequate picture of the data. Since there are different numbers of companies in some of the groups, the mean rank in each group is more inf...
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This document was uploaded on 03/30/2014.

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