Confidence interval and type 1 error cumulation I have a sample of 15 subjects that did a test multiple times. Now I would like to see if the subjects differ in their mean performance. The usual approach would be a test for differences in means (e.g. t-test), but if I compare the subject with each other, I get a large type 1 error rate. Because of that, I thought about calculating a confidence interval for each subject and to see if they overlap. 
What happens with the Type 1 Error here? Is there an alternative method to analyse the data?
Thanks for your patience and answers!
 A: I would approach this as a repeated measures design, which can be done in a multilevel model framework which is robust to imbalance in the number of observations per subject.
Think about it this way:
$score_{it}=\beta_{i}+\mu_i+\epsilon_{it}$
or rewritten in a two-level framework:
$score_{it}=\beta_{i}+\epsilon_{it}$
$\beta_i=\gamma_i+\mu_i$
Where $\beta_i$ is the mean score for each subject across all their tests, $\mu_i$ is the random effect for the subject (i.e. the variability in score due to the subject), and $\epsilon_it$ is the random error for each individual test-subject unit (i.e. the within subject variability). This is flexible to put in additional level 1 or level 2 variables, like if you think subjects improve over time, you can add that in as well and it becomes a growth-curve model.
This doesn't suffer from multiple testing, and you can see how much variability is due to the subjects themselves, by the intra-class correlation coefficient (ICC):
$\sigma_{\mu}/(\sigma_{\mu}+\sigma_{\epsilon})$
