Statistics · medium

When would you use a t-test vs a chi-square test?

Asked in Data Analyst interviews, in the Statistics round.

Short answer

t-test compares means (continuous); chi-square tests association between categorical variables.

How to answer it

It comes down to the type of the outcome.

• t-test: the outcome is a number per unit, and you are comparing means. Average order value, session length, revenue per user.
• Chi-square test: the outcome is a category per unit, and you are asking whether the category depends on the group. Converted or not, plan chosen, churned or not.

So "did the new page raise average order value?" is a t-test (Welch's, which does not assume equal variances). "Did the new page change the conversion rate?" is a chi-square test on a 2x2 table of converted/not by variant, which is equivalent to a two-proportion z-test.

from scipy import stats
# means: Welch's t-test
t, p = stats.ttest_ind(aov_a, aov_b, equal_var=False)
# rates: chi-square on the contingency table
table = [[1600, 48_400], [1500, 48_500]]   # [converted, not] per variant
chi2, p, dof, _ = stats.chi2_contingency(table)

Conditions to mention: the t-test wants independent observations and, for small n, roughly normal means (the CLT covers large n); chi-square wants expected counts of at least about 5 per cell, otherwise use Fisher's exact test. If the numeric metric is heavily skewed and n is small, a Mann-Whitney test or a bootstrap is safer than either.

• What they are checking: whether you classify by outcome type first, and whether you know Welch's is the default.
• Common mistake: running a t-test on a 0/1 conversion column. It roughly works at large n, but it signals you did not think about the data type.

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