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Analysis of residuals in contingency tables: another nail in the coffin of conditional approaches to significance testing.

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García Pérez, Miguel Ángel and Núñez Antón, Vicente and Alcalá Quintana, Rocío (2015) Analysis of residuals in contingency tables: another nail in the coffin of conditional approaches to significance testing. Behavior research methods, 47 (1). pp. 147-161. ISSN 1554-3528

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Official URL: http://dx.doi.org/10.3758/s13428-014-0472-0




Abstract

Omnibus tests of significance in contingency tables use statistics of the chi-square type. When the null is rejected, residual analyses are conducted to identify cells in which observed frequencies differ significantly from expected frequencies. Residual analyses are thus conditioned on a significant omnibus test. Conditional approaches have been shown to substantially alter type I error rates in cases involving t tests conditional on the results of a test of equality of variances, or tests of regression coefficients conditional on the results of tests of heteroscedasticity. We show that residual analyses conditional on a significant omnibus test are also affected by this problem, yielding type I error rates that can be up to 6 times larger than nominal rates, depending on the size of the table and the form of the marginal distributions. We explored several unconditional approaches in search for a method that maintains the nominal type I error rate and found out that a bootstrap correction for multiple testing achieved this goal. The validity of this approach is documented for two-way contingency tables in the contexts of tests of independence, tests of homogeneity, and fitting psychometric functions. Computer code in MATLAB and R to conduct these analyses is provided as Supplementary Material.


Item Type:Article
Uncontrolled Keywords:Contingency tables; Residual analysis; Chi-square tests; Multiple testing; Bootstrap
Subjects:Sciences > Mathematics > Applied statistics
ID Code:35687
Deposited On:19 Jul 2016 09:28
Last Modified:21 Oct 2016 13:32

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