An environmental psychologist conducted a study to explore the relationship between cognitive environmental concern and active conservation behaviour. Ten households (A A\,A to JJJ) were assessed. Each household's primary shopper completed a "Perceived Consumer Effectiveness" (PCE) questionnaire, scored from 10 to 50, where higher scores reflect a stronger cognitive belief that individual actions can mitigate environmental issues. The researcher also recorded the weight of dry recyclables (in kg) diverted from landfill by each household over a two-week period.
| Household | Perceived Consumer Effectiveness (PCE) Score | Weight of Dry Recyclables Diverted (kg) |
|---|---|---|
| A | 42 | 2.1 |
| B | 15 | 8.2 |
| C | 33 | 4.0 |
| D | 28 | 5.4 |
| E | 47 | 1.8 |
| F | 12 | 9.5 |
| G | 35 | 3.5 |
| H | 20 | 6.0 |
| I | 45 | 1.5 |
| J | 22 | 7.8 |
Using the ranked data from this study, the researcher calculated that ∑d2=280.5\sum d^2 = 280.5∑d2=280.5.
Use the formula for Spearman's rho provided below to calculate the value of rs r_s\,rs for this dataset. 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)
