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I am assessing the acceptability of a sentence in a within-subjects design with two crossed factors (type of sentence, missing word). After reading each sentence, the participants answer a simple yes/no question which is my dependent variable.

Because a dichotomous variable is not normally distributed I am guessing I can't use an ANOVA, what is my alternative? I want to test which group of sentences is less/more acceptable than the others.

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You'll want to use a mixed effects model treating subject as a random effect, type_of_sentence and missing_word as fixed effects, and specifying the binomial error family. Search this site for mixed effect models for more detail.

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