Four statistics used for the analysis of categorical data were observed in the presence of many zero cell frequencies in two way classification contingency tables. The purpose of this study was to determine the effect of many zero cell frequencies upon the distribution properties of each of the four statistics studied. It was found that Light and Margolin's C and Pearson's Chi-square statistic closely approximated the Chi-square distribution as long as less than one-third of the table cells were empty. It was found that the mean and variance of Kullbach's 21 were larger than the expected values in the presence of few empty cells. The mean for 21 was found to become small in the presence of large numbers of empty cells. Ku's corrected 21 statistic was found, in the presence of many zero cell frequencies, to have a much larger mean value than would be expected in a Chi-square distribution. Kullback's 21 demonstrated a peculiar distribution change in the presence of large numbers of zero cell frequencies. 21 first enlarged, then decreased in average value.
| Identifer | oai:union.ndltd.org:UTAHS/oai:digitalcommons.usu.edu:etd-8047 |
| Date | 01 May 1975 |
| Creators | Post, Jane R. |
| Publisher | DigitalCommons@USU |
| Source Sets | Utah State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | All Graduate Theses and Dissertations |
| Rights | Copyright for this work is held by the author. Transmission or reproduction of materials protected by copyright beyond that allowed by fair use requires the written permission of the copyright owners. Works not in the public domain cannot be commercially exploited without permission of the copyright owner. Responsibility for any use rests exclusively with the user. For more information contact digitalcommons@usu.edu. |
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