Question

Define power. How are sample size and power related? How are effect size and power related?

Answer 1

Power :-

• Power is the probability of rejecting the null hypothesis when in fact it is false.
• Power is the probability of making a correct decision (to reject the null hypothesis) when the null hypothesis is false.
• Power is the probability that a test of significance will pick up on an effect that is present.
• Power is the probability that a test of significance will detect a deviation from the null hypothesis, should such a deviation exist.
• Power is the probability of avoiding a Type II error.

Realtion with sample size:-

Sample size (n). Other things being equal, the greater the sample size, the greater the power of the test.

Relation with Effect Size:-

To compute the power of the test, one offers an alternative view about the "true" value of the population parameter, assuming that the null hypothesis is false. The effect size is the difference between the true value and the value specified in the null hypothesis.

Effect size = True value - Hypothesized value

For example, suppose the null hypothesis states that a population mean is equal to 100. A researcher might ask: What is the probability of rejecting the null hypothesis if the true population mean is equal to 90? In this example, the effect size would be 90 - 100, which equals -10.