Difference between dependent and independent group designs It seems to make common sense that a dependent (repeated measures) design would yield a lower critical value for t than an independent sample design since in the former variance should be lower. Yet when I run the two different t-tests in Excel using the same data I get a lower critical value for t using the independent t-test.
Am I missing something or do I just need more coffee?
 A: You are misinterpreting the meaning of critical value of t which is, excepting your sample size, unrelated to your data.
Different samples will surely produce different t statistics. And of course, if you have the same sample size in group 1 as in group 2 (or in measurement 1 as in measurement 2), then the paired and unpaired t test statistics be different numbers for the same sample. However, the critical value of t is not a statistic drawn from your sample data. Rather it is a value of t—given your sample size/degrees of freedom, and preferred rate of making a type I error—that marks the threshold between "reject" and "fail to reject" the null hypothesis. We can know what this critical value of t is (given the sample size), because we have a theory describing the behavior of Student's t distribution, specifically with values of t that are unlikely to occur if the null hypothesis is true.
A: The general principle at work here is that dependent samples give you less information than independent samples.
So, with the same number of samples an experiment with independent samples will have more power than an otherwise identical experiment with dependent samples that targets the same estimand. Similarly,  an analysis that assumes independence of observations will generally have a lower p-value / smaller standard errors - but to do such an analysis, if the samples were dependent is an exercise in (self-) deception (as pointed out by Cornfield in 1978 and perhaps others before that).
On the other hand, if you have independent samples and can add a few more dependent ones, this will give you more information - just not as much as adding independent samples (but it may also be cheaper/easier/more feasible). 
