New methods for testing hypotheses in paired-comparison experiments are presented in this dissertation. The methods are developed on the basis of a very general mathematical model and they are, in general, quite easy to employ.
Two tests of the null hypothesis that all treatments have equal stimuli, against its general alternative, are proposed. One test is for the case in which it is assumed prior to the experiment that no interaction will take place between repetitions and preference probabilities (the probabilities of the possible comparison preferences). The other test is for the case in which the above assumption cannot be made. The number of times a treatment is preferred is called its score. For the “no interaction" case, the test procedure is based on a test statistic that is a function D of the corrected sum of squares of the treatment scores. In the other case, the value of D is calculated for each group of homogeneous repetitions and then the values are summed to give the new test statistic. It is established that a X²-approximation may be used to determine the critical value of the test statistic for experiments outside the range of the tabled distributions. This test procedure is shown to be simpler than other approximate tests and, in general, at least as accurate with respect to errors of the first kind.
It is shown that the two test methods discussed above may be extended to ranking experiments in balanced incomplete block designs with more than two treatments per block.
To test the null hypothesis of no interaction between preference probabilities and repetitions, against its general alternative, a test method based on the theory of X² homogeneity tests is introduced.
Means are presented for testing whether (1) a particular treatment is better than the average of the treatment stimuli; (2) two particular treatment stimuli are not equal; and (3) the treatment receiving the highest score is better than the average. The three test procedures are based essentially on the binomial distribution of the treatment scores under the null hypothesis. In each case, the test procedure is conservative.
A procedure analogous to Tukey's test based on allowances is developed to test the null hypothesis of equal treatment stimuli and to separate the significantly different treatment scores when it rejects the null hypothesis.
A method for judging contrasts of treatment scores similar to Scheffe's (1953) method for judging contrasts in the analysis of variance is proposed. The test method based on D, mentioned earlier, is used in place of the F-test employed in the Scheffe method.
The use of paired-comparison experiments to test factorial effects is discussed and a test method based on orthogonal contrasts of the treatment scores is suggested. Because of correlations that arise, it is necessary to restrict this method to cases in which the only factors that are allowed to appear at more than two levels are those that will not interact with the other factors in the experiment.
The test methods are illustrated through application on the data from two paired-comparison experiments. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/87298 |
| Date | January 1958 |
| Creators | Starks, Thomas Harold |
| Contributors | Statistics, Statistics |
| Publisher | Virginia Polytechnic Institute |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | 120, [3] leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 20425322 |
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