Say you are testing hundreds of hypotheses, each with a t-test. What considerations would you take into account when doing this?

Running many hypothesis tests increases the chance of Type I errors (false positives).

For example, with $100$ tests at $\alpha = 0.05$, we expect around $100 \times 0.05 = 5$ false positives just by chance.

To control for this, we apply Bonferroni correction, where the significance threshold becomes $\alpha / m$ (e.g., $0.05 / 100 = 0.0005$). While this reduces Type I error, it increases Type II error (false negatives), especially when many hypotheses are tested.

Bonferroni is best used when only a few comparisons are expected to be significant. Other corrections like False Discovery Rate ($\mathrm{FDR}$) may be used to balance sensitivity and specificity better.