Why ranks: ordered levels such as weak, pass and good, and giving tied values the mean of their places
Pearson’s coefficient needs numbers we can add and multiply. Many data are only ordered: a teacher marks handwriting as weak, pass, good, very good or excellent. We know the order but not how far “good” is from “pass”. For such ordinal data we use ranks: put the values in order from the smallest and give each its place, 1, 2, 3 and so on. The same method works for numbers when only the order matters. If two or more values are equal they are tied, and they share the places they would have taken. Each gets the mean of those places. Two “weak” pupils would take places 1 and 2, so each gets (1 + 2) ÷ 2 = 1.5; three equal values for places 3, 4 and 5 each get 4. Never skip a place and never give the same rank to different values. A quick check: for n values the ranks must add up to n(n + 1) ÷ 2. The table ranks the handwriting of seven pupils; they add up to 28 = 7 × 8 ÷ 2.
| Pupil | Level | Place | Rank |
|---|---|---|---|
| B | weak | 1 | 1.5 |
| F | weak | 2 | 1.5 |
| C | pass | 3 | 3.5 |
| G | pass | 4 | 3.5 |
| A | good | 5 | 5.5 |
| D | good | 6 | 5.5 |
| E | excellent | 7 | 7 |
Ask six family members or friends to rate a dish from 1 to 5 stars. Rank the ratings from the smallest, share the places of equal ratings, and check that the ranks add up to 21.