Confidence interval for a set of means with no standard errors Is it possible to construct a confidence interval for a set of means, from samples with equal numbers of observations, if the standard errors of those samples are unknown?
 A: If you assume that the standard deviations of the underlying populations the samples are drawn from are the same* then you could compute a CI for an underlying common mean.
* (as they would be if they were in reality a single population that it would make sense to compute a CI for the mean of).
That is, if you have $g$ samples each of size $n$, from which you observe $y_i = \bar{x}_i, i=1,2,...,g$, then the standard deviation of the $y$'s is a sensible estimate of $\sigma_\bar{X} = \sigma_x/\sqrt{n}$.
In particular if $X_{ij}\sim N(\mu,\sigma^2)$ then you can directly construct a CI for $\mu$ from the $\bar{x}_i$ values; if you don't assume normality for the common distribution of the $X$'s but the $n$'s are "large enough" then you can still construct an approximate CI for $\mu$ based off the $t$-distribution - even if $g$ is small - because the distribution of the $\bar{X}$'s should be close to normal.
On the other hand, if $n$ is small but $g$ is large then you can use a different argument to construct an asymptotically normal CI for $\mu$.
