What does the 1-sided vs 2-sided distinction mean for general $M \times N$ independence tests like Fisher exact, $\chi^2$ or $G$-test?
Which makes more sense?
What is the "negative" side in these tests?
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Potential test-bias aside, deviation from the null will tend to take the chi-squared statistic higher, so all the alternatives will be in the "same direction". [There's a similar effect with the Fisher exact test.]
This is similar to the case with the F-test in one-way ANOVA -- any possible differences in means will tend to make the test statistic larger.
Small values of the F in ANOVA would be a case where the sample means were surprisingly close together, which is completely consistent with the null hypothesis of equal population means (you might consider questioning your assumptions but there's nothing to indicate you should doubt your null). (For more discussion of that related case, see under point (1) in my answer here)
It's the same here -- the test statistic tends to become discrepant in the same direction when the null is false, no matter which way it's false.
[In particular situations the chi-squared test can exhibit bias (generally in cases with highly unbalanced expected values), but that's a somewhat separate issue.]
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$\begingroup$ That is what I kind of suspected, but software packages for these tests offer the option and tend to make 2-sided the default, which if I understand you correctly (and personally also think) is not really what is wanted here. Correct? $\endgroup$ Commented Jul 28, 2017 at 3:53
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$\begingroup$ I can't say because it's impossible to confidently guess what they might actually be doing in the absence of any information beyond the assertion that some packages offer the option. Which packages? What does their help say about this option? What happens when you use this option on tables larger than 2x2? $\endgroup$– Glen_bCommented Jul 28, 2017 at 4:06