Quick questions on Non-parametric tests explained: H2 Further Mathematics

The sign test tests a hypothesis about the median (or that paired differences have median zero). For paired data, record the sign of each difference (positive or negative), discarding any zero differences. Under $H_0$ a positive and a negative sign are equally likely, so the number of one sign follows

The Wilcoxon signed-rank test also uses the differences but keeps more information: it ranks the absolute differences, then sums the ranks of the positive (or negative) differences to form the test statistic $T$. Because it uses the magnitudes as well as the signs, it is more powerful than the sign test when the symmetry assumption it requires holds. The statistic is compared with critical values from Wilcoxon tables (or a normal approximation for large $n$).

For the Wilcoxon signed-rank test a small $T$ indicates significance; comparing the wrong direction reverses the conclusion.

When is a non-parametric test preferred over a $t$-test? [2 marks]

Under $H_0$, what distribution does the sign-test count follow? [1 mark]

What is the main disadvantage of the sign test compared with the Wilcoxon signed-rank test? [1 mark]