Quantitative analysis, by purpose
Quantitative analysis breaks into four families, distinguished by what each is trying to learn.
Descriptive statistics summarize what the responses look like in aggregate — frequencies, means, medians, standard deviations, ranges. These are the numbers that fit on a one-slide overview, and the place where most reports stop. Descriptive answers what is, not whether what is matters.
Inferential statistics test whether observed differences between groups are likely to be real or to have occurred by chance. The most common tests are t-tests for two-group comparisons, ANOVA for three or more, and chi-square for categorical relationships. Inferential analysis pairs naturally with effect-size measures, which answer the question that always follows a significant result: is the difference practically meaningful, not just statistically detectable?
Cross-tabulation breaks aggregate findings by subgroup. It is descriptive analysis applied to slices: the same percentage that summarized the whole sample, recomputed for each demographic, cohort, or program track. Cross-tabulation is also the most direct method for surfacing equity gaps, because it asks whether the program produced the same result for every group it served.
Regression estimates how variables relate — which inputs predict an outcome, and by how much. Regression is what produces explanatory claims rather than comparative ones, but it is also the family with the strictest data requirements: enough observations, enough variation, enough confidence in the model’s assumptions to make the result defensible.
For the full catalogue of tests inside each family, see the methods page.