Question

Explain how critical value variations influence statistical power.

Answer 1

Statistical power is the likelihood that a test (statistical test) will detect an effect when there is an effect there to be detected. Statistical power is inversely related to the probability of making a Type II error (Type II errors, or false negatives, occur when you don’t see things that are there) = beta.
statistical power = 1 – β. The critical value is the value corresponding to a given significance level.  The statistical power is influenced by the choice of significance level for the test (by the critical value). Larger critical value means increased power of the test:  the chance of obtaining a statistically significant result is increased (reduces the risk of a Type II error (false negative regarding whether an effect exists) is reduced) . 

Answer 2

If a researcher establishes the critical values of a study to be more conservative, the more power the researcher has in finding significant support for a hypothesis. In the same sense, the less conservative the established critical values are, the less power a researcher has in finding significant support for a hypothesis.