One sample t-test equivalent for repeated measures design I might be looking for something fairly obvious but here is my setup:
I have one group of participants who will perform multiple (different) tasks in an experiment. For each one of the tasks, I want to compare the performance of the participants against a given, fixed value. I might be comparing the tasks against each other as well (then using a linear mixed model) but this does not help me for the comparison to the constant.
When looking at the design, I am tempted to perform multiple one-sample t-tests and correcting for alpha error inflation.
However, I have a feeling that I might be missing a better fitting approach.
Therefore I would like to find an answer to the following question:
Is there a validated approach to compare data from repeated measure designs against a (non-changing) constant value?

A couple of options:
You can still do this using a mixed effects model, it sounds like you would be fitting only the intercept as fixed (then include your random effects to account for the grouping).  The intercept is then the estimate of the overall mean.
To use this information to test the mean against a fixed value you can compute the confidence interval for the intercept/grand mean then see if the fixed null value is in the confidence interval.
Another approach is to subtract the fixed null value from all of the $y$ values (response values) then fit the mixed effects model on the adjusted response.  The test that the intercept in this model is different from 0 is the test that the intercept on the original scale is different from your null value.
If using R, you can include the fixed null value in an offset so that the tests and CI now give what you want.  There is probably similar functionality in other tools, I am just not familiar enough with them to point you the correct direction.
You could  fit a hierarchical Bayesian model (similar to the mixed effects model)  then not worry about formal testing but compare your fixed values of interest to the posterior distribution.
