Question

Several factors influence statistical power for a one-sample t test. How does statistical power change (increase or decrease) for each of the following changes? When d (effect size) increases. When N (sample size) increases. When the alpha level is made smaller. Explain your answer. For example, if we know ahead of time that the effect size d is very small, what does this tell us about the N we will need in order to have adequate statistical power? (We assume that all other terms included in the r ratio remain the same.)

Answer 1

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The power of any test of statistical significance is defined as the probability that it will reject a false null hypothesis. Statistical power is inversely related to beta or the probability of making a Type II error. In short, power = 1 – β.

1. When d (effect size) increases - probability of getting a statistically significant result will be high i.e. when the effect size is large,

2. When N (sample size) increases -  probability of getting a statistically significant result will be high i.e. when the sample size is large,

3. When the alpha level is made smaller - when the chosen level of alpha is relatively high (or relaxed)

We say that each of factor leads to a strong statistical power, when the factor is the abovementioned