The Pearson statistic, a well-known goodness-of fit test in the analysis of contingency tables, gives little guidance as to why a null hypothesis is rejected. One approach to determine the source(s) of deviation from the null is the decomposition of a chi-squared statistic. This allows writing the statistic as the sum of independent chi-squared statistics.
First, three major types of contingency tables and the usual chi-squared tests are reviewed.
Three types of decompositions are presented and applied: one based on the partition of the
contingency table into independent subtables; one derived from smooth models and one from
the eigendecomposition of the central matrix defining the statistics. A comparison of some of the omnibus statistics decomposed above to a χ2(1)-distributed statistic shows that the omnibus statistics lack power compared to this statistic for testing hypothesis of equal success probabilities against monotonic trend in the success probabilities in a column-binomial contingency table.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OOU.#10393/30352 |
| Date | 20 December 2013 |
| Creators | Colas, Jo Ann |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thèse / Thesis |
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