Discuss the Pearson r statistic. What type of relationships does it measure?

Question

What will be an ideal response?

Answer 1

Ans: Answers vary
The Pearson r statistic tests linear relationships. The values of the statistic range from ?1.0 to +1.0. A Pearson r of +1.0 represents a perfect positive relationship. A Pearson r of ?1.0 represents a perfect negative relationship. A value of 0 indicates no relationship. The Pearson r statistic can be used as a descriptive statistic to simply describe the type and degree of relationship for the sample distributions. Values closer to +1.0 and ?1.0 are stronger relationships. Values closer to 0 represent weaker relationships. Pearson r can also be used as an inferential statistic to determine if a significant relationship exists between two variables. The test relies on the same principles as the comparison tests described above. The Pearson r value calculated from the sample distributions (based on overlap in scores between the distributions with sampling error removed) is compared with the distribution of possible Pearson r values for samples of that size when there is no relationship in the population. If the sample Pearson r is an extreme score, in the most extreme 5% of the distribution, for example, there is evidence to reject the null hypothesis that there is no relationship (i.e., the test is significant) and accept the alternative hypothesis that there is a relationship (or a specific relationship if a one-tailed test is used).