Standard Error

$SE=\sqrt{\frac{(s_1{)}^2}{n_1}+\frac{(s_2{)}^2}{n_2}}$

where s_1 and s_2 are the sample standard deviations and n_1 and n_2 are the sample sizes.

“Standard error of the mean” is the standard deviation of the Sampling distributions of means. ${\sigma }_{\bar{X}}=\frac{{\sigma }_x}{\sqrt{N}}$; It calculates how much the sample mean is likely to vary from the true population mean.

When doing t-tests, we need to know the estimated standard error of the mean ($s_{\bar{x}}$). To know that, we need to know the estimated population variance ($s_x^2$). $s_{\bar{x}}=\sqrt{\frac{s_x^2}{N}}$