Compare two (or more?) groups of regression coefficients Short version: I need to compare two small (~10) groups of numbers, usual setup for a non-paired t-test, or Mann-Whitney. But -- the numbers come each with its own SE, and since the groups are small, this is presumably relevant. Question -- how do I take the individual SEs into account?
Longer version: There are two groups of patients, treatment and placebo. The test to assess the influence of the treatment involves making many (~100) measurements for a period of time, for each patient. Then an exponential decay curve is fitted into these measurements; the relevant outcome is the time constant of the decay. Since it's estimated from noisy measurements, it has a SE. How do I take the individual SEs into account when comparing the two groups?
Artificial example: is the mean of the (approximately estimated with given SEs) numbers in group A different from the mean of group B? $A=\{13\pm2,15\pm4,10\pm2\}$, $B=\{12\pm4,10\pm3,16\pm3,14\pm5\}$.
Follow-up: What if there are more than two groups?
 A: The t-test can compare groups with different standard deviations. This is apparently also called Welch's t-test according to Wikipedia.
First, the calculate the combined means and variances of each group. Assuming two sets of observations of size $n_1$ and $n_2$ with means and variances $\mu_1,\mu_2,s_1^2,s_2^2$, the combined mean is simply
$$ \mu = \frac{n_1\mu_1+n_2\mu_2}{n_1+n_2} $$
The combined variance becomes
$$ s^2 = \frac{n_1(s_1^2+(\mu_1-\mu)^2)+n_2(s_2^2+(\mu_2-\mu)^2)}{n_1+n_2}  $$
After which you can compare the means of the two groups with the t-test. The test statistic is 
$$T=\frac{\bar{X_1}-\bar{X_2}}{\sqrt{s_1^2/n_1+s_2^2/n_2}}$$ 
Which follows t distribution under the null hypothesis with degrees of freedom : 
$$ \frac{ (s_1^2/n_1+s_2^2/n_2)^2}{\frac{s_1^4}{N_1^2(N_1-1)}+\frac{s_2^4}{N_2^2(N_2-1)})} $$
Where $N_1,N_2$ represent the degrees of freedom      for each group, and $s_1,s_2$ their standard deviations.                 
For comparing multiple groups, you'll need to be more specific. What hypothesis do you want to test? That the estimations of the parameters (1/means for an exponential distribution) are all equivalent? Perhaps an F-test.
