# Binomial test for nested data

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.

• Are you comparing groups or controlling for covariates? Jan 29 '16 at 17:05
• Nope I am not. It's a pilot study so we just want to find out if frequency of hits and misses differ. Jan 29 '16 at 17:14
• You refer to "hits" & "misses". Was this a signal detection study? Jan 29 '16 at 17:31

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