Results

Smart Alex Task 7.11

The variables time and distance are both interval. Therefore, we can conduct a Pearson’s correlation. The figure below indicates that there was a significant positive relationship between time spent shopping and distance covered using the common criterion of 𝛼=0.05. We can tell that the relationship was significant because the p-value is smaller than 0.05. More important, the robust confidence intervals do not cross zero suggesting (under the usual assumptions) that the effect in the population is unlikely to be zero. Also, our value for Pearson’s r is very large (0.83) indicating a large effect. Pearson’s r = 0.83, 95% BCa CI [0.501, 0.962], p = 0.003.

Smart Alex Task 7.12

To answer this question, we need to conduct a partial correlation between the time spent shopping (interval variable) and the distance covered (interval variable) while ‘adjusting’ for the effect of sex (dichotomous variable). The resutls are shown in the figure below. The partial correlation between time and distance is 0.820, which is slightly smaller than the correlation when we don’t adjust for sex (r = 0.830). The correlation has become slightly less statistically significant (its p-value has increased from 0.003 to 0.007). Running this analysis has shown us that time spent shopping alone explains a large portion of the variation in distance covered.