Question

A researcher is investigating the effects of income on fresh fruit and vegetable consumption. Her data show that income and fresh orange juice consumption are positively associated at a p level of 0.001. What conclusion(s) can be drawn from the p value?

1) The association between income and fresh orange juice consumption is statistically significant.
2) There is no relationship between income and fresh orange juice consumption.
3) The income level affects the consumption of fresh orange juice.
4) The p value indicates the strength of the association between income and fresh orange juice consumption.

Answer 1

A p-value of 0.001 indicates that there is a statistically significant association between income and fresh orange juice consumption, which allows us to reject the null hypothesis. However, the p-value does not measure the strength of the association or establish causality.

The student asked about the conclusions that can be drawn from a p-value of 0.001 in the context of a study on income and fresh orange juice consumption. The p-value measures the probability of obtaining the observed results, or more extreme, if the null hypothesis of no effect is true. A p-value of 0.001 is very small, indicating a very low probability that the observed association is due to chance. Therefore, conclusion (1) is correct: The association between income and fresh orange juice consumption is statistically significant. This means we reject the null hypothesis of no association, leading to acknowledgement of a potential relationship between the variables. However, while the p-value can suggest a statistically significant relationship, it does not indicate the strength of such an association, so conclusion (4) is not correct. Moreover, the p-value cannot establish causality, so while conclusion (3) might be true, it cannot be conclusively determined from the p-value alone.