Global and Local Statistical Methods of Analysis for Contingency Tables by Size Effects and Confidence Intervals: This paper presents global and local analyses of a contingency table along the lines of Wilkinson et al. (1999) defining good statistical practices as using effect sizes, confidence intervals and plots instead of tests of significance. On one hand, the global relationship between the two qualitative variables is measured by Cramér's V. A confidence interval may be calculated using the decentred chi-squared distribution by inverting the corresponding significance test. A bootstrap confidence interval is also proposed. On the other hand, Cibois's PEM (percentage of maximum deviation from independence) is a local effect size that can be computed for every cell of the contingency table giving its specific distance from the independence hypothesis. A corresponding confidence interval is calculated by the resampling bootstrap technique. An original plot summarizing these différent aspects for the entire contingency table is proposed.
Agresti, A. ( 1990). Categorical data analysis, John Wiley & Sons, New-York.
2.
Agresti, A., & Finlay B. ( 2007). Statistical methods for the social sciences, Pearson/Prentice Hall, Upper Saddle River .
3.
Cibois, P. ( 1990). L'analyse de données en sociologie, PUF, Paris.
4.
Cibois, P. ( 1993). Le PEM, pourcentage de l'écart maximum: Un indice de liaison entre modalités d'un tableau de contingence, Bulletin de Méthodologie Sociologique, 40, 43-63.
5.
Cibois, P. ( 2004). Les écarts à l'indépendance. Techniques simples pour analyser des données d'enquête, Collection en ligne « Méthodes quantitatives pour les sciences sociales »de Sciences Humaines.
6.
Cibois, P. ( 2007). Les méthodes d'analyse d'enquêtes, PUF, Paris.
7.
Cohen, J. ( 1988). Statistical power analysis for the behavioral sciences , Lawrence Erlbaum Associates, Hillsdale.
8.
Cumming, G., & Finch, S. ( 2001). A primer on the understanding, use and calculation of confidence intervals that are based on central and noncentral distributions , Educational and Psychological Measurement, 61, 532-575.
9.
Efron, B., & Tibshirani, R.J. (1993). An introduction to the bootstrap, Chapman & Hall, London.
10.
Ely, M. ( 1999). The importance of estimates and confidence intervals rather than P values, Sociology, 33, 185-190.
11.
Fidler, F., Thomason, N., Cumming, G.Finch, S., & Leeman, J. ( 2004). Editors can lead researchers to confidence intervals, but can't make them think: Statistical reform lessons from medicine, Psychological Science, 15 (2), 119-126.
12.
Johnson, R.W. ( 2001). An introduction to the bootstrap, Teaching Statistics, 23 (1), 49-54.
13.
Kline, R.B. ( 2004). Beyond significance testing, American Psychological Association, Washington D.C.
14.
Martin, O. ( 2005). L'analyse des données quantitatives, Armand Colin, Paris.
15.
R Development Core Team (2007). R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org.
Thompson, B. ( 2002). What future quantitative social science research could look like: Confidence intervals for effect sizes, Educational Researcher, 31(3), 25-32.
18.
Wilkinson, L., & the Task Force on Statistical Inference ( 1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54, 594-604.
