 # Power: The B.E.A.N. Mnemonic

#### Four interrelated features of power can be summarized using BEAN

 B Beta Error (Power = 1 – Beta Error): Beta error (or Type II error) is the probability that a test of statistical significance will fail to reject the null hypothesis when it is false (e.g., when there really is an effect of training). As beta error increases, power decreases. E Effect Size: The effect size is the magnitude of the difference between the actual population mean and the null hypothesized mean (μ1 – μ0) relative to standard deviation of scores (σ). When the effect size d = (μ1 – μ0) / σ in the population is larger, the null and population sampling distributions overlap less and power is greater. As effect size increases, power increases (assuming no change in alpha or sample size). A Alpha error: Alpha error (or Type I error) is the probability that a statistical test will produce a statistically significant finding when the null hypothesis is true (e.g., there is no effect of training). For example, if alpha error = .05 and the null hypothesis is true, then out of 100 statistical tests, false significance would be found on average 5 times. The risk of false significance would be 5%. In practice, alpha is typically set by the researcher at .01 or .05 As alpha error increases, power increases (assuming no change in effect size or sample size). N Sample Size: As the sample size increases, the variability of sample means decreases. The population and null sampling distributions become narrower, overlapping to a lesser extent and making it easier to detect a difference between these distributions. This results in greater power. As sample size increases, power increases (assuming no change in alpha or effect size).

Select true or false for each scenario:

(Assuming no other changes) True False
1. As effect size increases, power decreases.
2. As sample size increases, power increases.
3. As alpha error increases, power decreases.
4. Beta error is unrelated to power.

False; as effect size increases, power increases.

True; as sample size increases, power increases.