To compute the $t$ statistic for an independent-samples $t$-test, researchers use the formula: $t = \frac{M_1 - M_2}{\sqrt{\frac{SD_1^2}{n_1} + \frac{SD_2^2}{n_2}}}$. In this equation, $M_1$ and $M_2$ represent the means of the two separate groups. The denominator requires squaring the standard deviations ($SD_1$ and $SD_2$) of each group to determine their variances, and then dividing each variance by its respective group sample size ($n_1$ and $n_2$). It is important to note that lowercase $n$ denotes the number of participants in a specific condition, whereas uppercase $N$ typically refers to the total combined sample size.