I am running a series of Fisher's test to analyse some 2x2 contingency tables with small values. I have found significance. Is there anything equivalent to Cramer's V or the odds ratio or some sort of post-hoc test that I can use to tell me more about my results?
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If you have used Fisher's exact test on a 2x2 table, then your p-value reflects the probability of obtaining cell counts as deviant (or more deviant) as what you observed if the proportions of the margins were fixed at the observed values. This is similar to the sort of question that is answered by a chi-square test of independence (you may want to look there for more guidance on interpreting your result). As far as I am aware, because you have a 2x2 table, there is no generally sensible post-hoc to perform here. You know where the differences are (the effect of row is not the same across columns aka the effect of column is not the same across rows)... and because you have only two columns and two rows there is no "which columns and which rows" question to ask.
answered Apr 4, 2014 at 18:02
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$\begingroup$ Fantastic thank you! Do I have to correct for multiple testing if it's just 2x2 tables? Bonferroni? One more question! Do you know what effect size measure I would use for a Chi-squared goodness of fit? Finding mixed answers! $\endgroup$– KayCommented Apr 5, 2014 at 18:56
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$\begingroup$ Not sure what you mean by 'effect size measure' for chi-squared test. If you have a 2x2 table its pretty straight forward to calculate the chi-squared test $\endgroup$ Commented Apr 5, 2014 at 21:00
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$\begingroup$ Thank you Bejamin. I meant once my goodness of fit test has shown to be significant, what do I use to measure effect size? I know a chi-square of association has certain measures, but not sure about goodness of fit. $\endgroup$– KayCommented Apr 6, 2014 at 21:24
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1$\begingroup$ @Benjamin: A test statistic is not a direct measure of effect size as it is influenced by sample size. Regardless, given that Kay was asking about Fisher's exact, I think the follow up question should probably be asked separately (although the answer for goodness of fit is similar to that for chi-square of association/independence). The short answer to it is ... there are various answers. Almost every measure of effect size you might be interested in has some sort of restricted range that is related to the marginal probabilities. $\endgroup$ Commented Apr 7, 2014 at 11:47
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2$\begingroup$ Whether you correct for testing multiple 2x2 tables is up to you/a matter of convention. There is no familywise error rate correction applicable to a single test. However, if you are running multiple tests that you consider part of a single analysis you may wish to do some sort of correction to control for error rate within your series of tests. I'm rather taken with FDR (False Discovery Rate) corrections. Bonferroni has name recognition and simplicity in its favor, however it is conservative. Holm-Bonferroni is always reasonable and Šidák is sometimes reasonable. $\endgroup$ Commented Apr 7, 2014 at 11:55
p.adjustor you can do something simple like Bonferroni correction (Call something significant if its p-value is less than $\alpha/m$ where $m$ is number of tables). $\endgroup$