Because the numbers of cups of tea and cognitive function are both interval variables, we can conduct a Pearson’s correlation coefficient. If we request bootstrapped confidence intervals then we don’t need to worry about checking whether the data are normal because they are robust. The figure below indicates that the relationship between number of cups of tea drunk per day and cognitive function was not significant. We can tell this because our p-value is greater than 0.05 (the typical criterion), and the bootstrapped confidence intervals cross zero, indicating that under the usual assumption that this sample is one of the 95% that generated a confidence interval containing the true value, the effect in the population could be zero (i.e. no effect). Pearson’s r = 0.078, 95% BCa CI [–0.391, 0.529], p = 0.783.
| Variable | tea | cog_fun | |||||
|---|---|---|---|---|---|---|---|
| 1. tea | n | — | |||||
| Pearson's r | — | ||||||
| p-value | — | ||||||
| Lower 95% CI | — | ||||||
| Upper 95% CI | — | ||||||
| 2. cog_fun | n | 15 | — | ||||
| Pearson's r | 0.078 | — | |||||
| p-value | 0.783 | — | |||||
| Lower 95% CI | -0.391 | — | |||||
| Upper 95% CI | 0.529 | — | |||||
| Note. Confidence intervals based on 1000 bootstrap replicates. | |||||||