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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 Chisquare 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(k1)
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 twotailed test carry out the Wilcoxon Rank Sum tests as follows. Using
the ordering given in 4 and the table in Appendix 8, compare the leftmost sample
first with the right most, next with the second from the right, and so on until a
nonsignificant 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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 Summer '14
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