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Assume you are trying to test the effect of condition X. You sample people randomly and put them in a manipulation group (condition X) and a control group (condition Y). Simultaneously you want to control for another variable, say gender, so you measure gender, and then when you compare the manipulation group to the control group you control for the gender variable (e.g. through including it in an ANCOVA or a regression).

Is it correct to control for gender in this way, or is it unnecessary, since the sample is random?

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With random allocation to treatment and control groups, and as your sample size increases, it should become increasingly unnecessary to control for any covariates. However, if chance results in an unusually disproportionate number of females in one of your groups, it's certainly not wrong to control for gender in your analysis. But you will likely need to make it clear why you did control for it and others, or it and not others, by describing the characteristics of each group clearly.

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It is unnecessary but a good idea since including gender or any other covariate can reduce error and increase power. I don't know what your variables are but gender interacts with many things so I would probably start by looking at the Gender x Condition interaction. Keep in mind that the purpose of randomization is not to equalize the uncontrolled variables but rather to allow their combined effects to be estimated so as to asses the plausiblity that they together with measurement error account for the effect.

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