Universidad Complutense de Madrid
E-Prints Complutense

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

Impacto

Descargas

Último año

García Pérez, Miguel Ángel y Núñez Antón, Vicente y 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

[img] PDF
Restringido a Sólo personal autorizado del repositorio

828kB

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




Resumen

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.


Tipo de documento:Artículo
Palabras clave:Contingency tables; Residual analysis; Chi-square tests; Multiple testing; Bootstrap
Materias:Ciencias > Matemáticas > Estadística aplicada
Código ID:35687
Depositado:19 Jul 2016 09:28
Última Modificación:21 Oct 2016 13:32

Descargas en el último año

Sólo personal del repositorio: página de control del artículo