An environmental psychologist wanted to investigate whether cognitive scores on a Recycling Knowledge Test are related to the level of contamination in household recycling bins. Eight participants completed a Recycling Knowledge Test (scored from 1 to 100, where higher scores indicate greater cognitive awareness of sorting guidelines). Over the subsequent three weeks, the number of non-recyclable items mistakenly placed in each participant's recycling bin was recorded.
| Participant | Recycling Knowledge Test Score (1 to 100) | Number of contaminated recycling items |
|---|---|---|
| A | 95 | 24 |
| B | 82 | 13 |
| C | 74 | 19 |
| D | 61 | 35 |
| E | 53 | 8 |
| F | 40 | 48 |
| G | 29 | 42 |
| H | 18 | 29 |
Given that the sum of squared differences in ranks is ∑d2=126\sum d^2 = 126∑d2=126, use the formula for Spearman's rho provided below to calculate the value of rsr_srs. Show your workings.
rs=1−6(∑d2)n(n2−1) r_s = 1 - \frac{6 (\sum d^2)}{n (n^2 - 1)} rs=1−n(n2−1)6(∑d2)
