A conservation group monitored 10 protected forest sites to investigate the relationship between conservation priority and biodiversity. The table below displays the assigned Site Priority Rank (where 1 is the highest priority), the Soil Nitrate Level (mg/kgmg/kgmg/kg), and the Rare Species Density (average count per hectare).
| Site Priority Rank (PPP) | Soil Nitrate Level (NNN) | Rare Species Density (DDD) |
|---|---|---|
| 1 | 18.4 | 115 |
| 2 | 15.1 | 95 |
| 3 | 15.1 | 120 |
| 4 | 14.2 | 72 |
| 5 | 16.0 | 108 |
| 6 | 11.8 | 65 |
| 7 | 12.5 | 102 |
| 8 | 11.8 | 50 |
| 9 | 12.5 | 88 |
| 10 | 10.2 | 84 |
Explain how a researcher should handle the tied values in the 'Soil Nitrate Level' column if they were to calculate Spearman's rank correlation coefficient between priority and nitrate level.
Using the 'Rare Species Density' data (where the highest density is ranked 1), calculate Spearman's rank correlation coefficient, rsr_srs, between Site Priority Rank and Rare Species Density Rank.
Test, at the 5% level of significance, whether there is evidence of a positive correlation between Site Priority Rank and Rare Species Density Rank. State your hypotheses and critical value clearly.
Determine the largest level of significance (from standard statistical tables for n=10n=10n=10) that would lead to a conclusion that there is no evidence of a positive correlation. State the corresponding critical value.
