# How to control for type-1-error inflation with multiple chi-squared tests?

I have two between-subject factors, each with two levels (so 4 conditions). Furthermore, I have one dependent variable (qualitative), also consisting of two levels.

Now I want to make pairwise comparisons (so I have 6 chi-squared tests in total). Is there any way I can control type-1-errors? In the literature I saw they often calculated interaction with a chi-squared test. Is this the way to do it, and if so, how do I do it?

I can work with both SPSS and MATLAB.

An example of what I want to accomplish:

Independent chi-squared tests analyzing the interaction between the experimental conditions and the participant’s compliance with the request were performed. With the participants who first accepted to participate in the study, significant interaction was found [x2(1, N = 199) = 21.06, p<0.001, r = 0.30]. Pairwise comparisons revealed that the control condition was significantly different from the FITD condition [40.0% vs. 60.0%, x2 (1, N = 100) = 4.00, p<0.05, ϕ = 0.20] and the FITD-‘‘but you are free . . .’’ condition [40.0% vs. 56.0%, x2 (1, N = 100) = 14.92, p<.001, ϕ = 0.36] but not with the ‘‘but you are free . . .’’ condition [40.0% vs. 60.0, x2 (1, N = 100) = 2.56, nonsignificant (ns), ϕ = 0.16]. No statistical differences were found between the FITD condition and the ‘‘but you are free . . .’’ condition [60.0% vs. 56.0, x2 (1, N = 100) = 0.16, ns, ϕ = 0.04] and between the FITD condition and the FITD-‘‘but you are free . . .’’ condition [60.0% vs. 78.0%, x2 (1, N = 100) = 3.78, p = .06, ϕ = 0.19]. However, a significant difference was found between the ‘‘but you are free . . .’’ condition and the FITD -‘but you are free . . .’’ condition [56.0% vs. 78.0%, x2 (1, N = 100) = 5.47, p<0.02, ϕ = 0.23].

Reference:
Guéguen, N. Meineri, S. Martin, A. & Grandjean, I. (2010). The combined effect of the foot in-the-door technique and the “but you are free” technique: an evaluation on the selective sorting of household wastes. Ecopsychology. 2(4), 231 – 237. doi: 10.1089/eco.2009.0051

• I do not quite follow your comment about using chi-squared tests for interactions. I gather your data are appropriate for a logistic regression & you can use tests w/ chi-squared distributions in LR, can you clarify your comment? Commented May 2, 2014 at 16:19
• First of all, thanks for your edits. I will provide a citation of an article which accactly does what I want to accomplish. Commented May 2, 2014 at 16:25