A t-test is a statistical test used when you want to compare the means of two groups on a given (continuous) variable. A t-test allows you to differentiate between group differences that occur because of chance variation and meaningful between-group differences by taking the number of people you included in your sample and the variability of responses within each group into consideration when comparing the means of the two groups. Common differences that we hear reported on a regular basis, such as differences in income between male and female employees or differences in number of car accidents per year between drivers who use hand-held devices while driving versus those who do not, rely on t-tests for their validity.
Because it is rare that comparisons are being made between two identical groups, the equation that is used in the StudentVoice Benchmarking calculations is for a t-test statistic that assumes unequal sample sizes. This equation, in essence, creates a weighted average of the variance components typically included in the t-test. A weighted average takes sample size into consideration when averaging the two components, allowing the component that comes from a larger sample to have more sway (weight) on the final average. This equation assumes that the two variance statistics are estimating the same population variance, however. That is, it is assumed that the two groups do not have different true variances in the population situation and can therefore reasonably be averaged together to create a better estimate of the population variance.