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The effects of ties on the distribution of the range of rank sums in the one-way classification

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Title: The effects of ties on the distribution of the range of rank sums in the one-way classification
Authors: Soe, Kyaw
Issue Date: 1993
Abstract: Under a null hypothesis of no treatment differences, and assuming ties can occur, tables are computed for exact probabilities of the ranges in the Wilcoxon method of multiple comparisons in the one-way classification. A total of 1399 exact cumulative probability tables of larger ranges for i = 2 and k = 2(1)6, i = 3 and k = 2(1)4, and i = 4(1)6 and k = 2 where i = number of groups and k = number of replications in each group were computed for all tie cases where up to 50% of observations were involved in ties. Analyses of the distribution of the range of rank sums and their deviations from no-tie cases revealed the following points. 1. The results of an experiment can be different when ties occur-irrespective of the fact that ties are in the same treatment group. 2. The pair of probability distribution tables are identical for tie cases symmetrical about the mid-point of the serially ordered ranks, suggesting that ranks can be assigned to raw data in ascending or descending order. 3. Except for the symmetrical tie case pairs, probability distributions of the range of rank sums are different for different tie cases. 4. For tie patterns with one group of ties, the greater the number of tied observations, the greater the deviations in cumulative probability of the ranges from that of no-tie case. But this is not apparent when there are more than one group of ties. 5. When the total number of observations involved in ties is the same, deviations in cumulative probability of a fixed range tend to become less for the larger number of tie groups involved. 6. Although deviations at the α = .01 level are less than those at the α = .05 level which in turn are less than those at the α = .1 level for most of the parameters of i and k this fact is not necessarily true in general. 7. Depending on the particular tie case, we can use the critical range for the no-tie case even if 50% of the observations are involved in ties, while in some tie cases, we cannot accurately use the no-tie critical range even if only one-sixth of the observations are involved in ties. 8. The normal range approximation for larger range values provides conservative estimates of the exact distribution for the no-tie case which in turn provides conservative estimates of the exact distribution for tie cases. In this study, a tie correction formula for the one-way classification was developed, tested, and proposed.
Description: Thesis (Ph. D.)--University of Hawaii at Manoa, 1993.
Microfiche.
xvi, 187 leaves, bound 29 cm
URI/DOI: http://hdl.handle.net/10125/9732
Rights: All UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner.
Appears in Collections:Ph.D. - Educational Psychology



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