An environmental scientist analyzes 8 organic soil samples to determine if there is a relationship between nitrogen content and the speed of decomposition.
The nitrogen content, nnn (measured in mg/kg), for each sample is recorded in the table below.
| Sample | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| Nitrogen (nnn) | 12.4 | 15.8 | 14.1 | 18.2 | 9.5 | 13.7 | 16.5 | 15.0 |
The samples were then ranked by decomposition speed from 1 (fastest) to 8 (slowest). The resulting order of the samples is given below:
D,B,H,G,C,A,F,E D, \quad B, \quad H, \quad G, \quad C, \quad A, \quad F, \quad E D,B,H,G,C,A,F,ECalculate Spearman's rank correlation coefficient between the nitrogen content and the decomposition speed.
Stating your hypotheses clearly, test at the 5% level of significance whether there is evidence of a positive correlation between nitrogen content and decomposition speed.
The scientist also measures the pH level of the 8 samples, resulting in the following data:
| Sample | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| pH level | 6.2 | 7.0 | 6.2 | 7.5 | 5.8 | 6.5 | 7.0 | 6.8 |
Without performing further calculations, explain how to calculate the Spearman's rank correlation coefficient between the Nitrogen results and the pH level results, noting any specific adjustments required by this data set.
