Question

Discuss how the concept of statistical independence underlies statistical hypothesis testing in general. Based on statistical analysis, are we justified in asserting that two variables are statistically dependent? Why or why not? Explain why researchers typically focus on statistical independence rather than statistical dependence.

Answer 1

In general, we compare two or more different variables hence the concept of statistical independence underlies in statistical hypothesis testing. Two variables are statistically dependent if the values of these two variables are taken on the same unit. For example, the weight of males measured in summer and the weight of same males measured in winter and a hypothesis test is run to check whether there exists a difference between the weights in summer and winter, here the males are same for both seasons hence the sample weights would be dependent. Researchers typically focus on statistical independence rather than statistical dependence because most of the times the data for independent samples are collected and compared, statistical dependence is only used when we repeat the measurements.