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I have 100 subjects who were scored on their performance in a series of trials (binary outcome for each trial: "hit" or "miss"). I want to find out whether overall there are more "hit" than "miss" trials. Since the trials are repeated for each individual (each subject has 4 trials), then the data may not be independent. If so, do I still use a binomial test? Or is there are other analysis I can use?

Thank you very much. Any help is deeply appreciated.

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  • $\begingroup$ Are you comparing groups or controlling for covariates? $\endgroup$ – gung Jan 29 '16 at 17:05
  • $\begingroup$ Nope I am not. It's a pilot study so we just want to find out if frequency of hits and misses differ. $\endgroup$ – Gooper Jan 29 '16 at 17:14
  • $\begingroup$ You refer to "hits" & "misses". Was this a signal detection study? $\endgroup$ – gung Jan 29 '16 at 17:31
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It sounds like you could add a random effect for subject in a GLM framework. For subject s, trial t let

$Y_{s,t} \sim Bernoulli(p_s), \quad p_s = logit(\theta + \beta_s), \quad \beta_s \sim N(0,\sigma_s^2)$.

Fitting this model would be pretty simple (using the R package lme4, for example).

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