Power Cumulative Test: What affects Statistical Power?

Select True or False for each of the following questions.

If nothing else is changed, power is greater when…

True False
C1. The difference between the null and alternative population means is greater.
C2. The standard deviation of the populations is greater.
C3. The alpha error rate is changed from .01 to .05.
C4. The sample size is changed from 30 to 40.

C1. Answer

True. All else being equal, power is greater as the mean difference between the null and alternative distributions increases. In this case, the amount of overlap between the sampling distributions for the null and alternative distributions is less and the probability of correctly rejecting the null hypothesis increases.

C2. Answer

False. All else being equal, as the standard deviation for the null and alternative distributions increases, the sampling distributions overlap to a larger extent and the probability of correctly rejecting the null hypothesis decreases.

C3. Answer

True. All else being equal, as the alpha error increases, power is greater. As alpha error increases, power is greater. As alpha error is increased, the cutoff score (represented in the applet by a dashed red line) moves to the left, the proportion of the alternate distribution to the right of the criterion increases, and so the probability of correctly rejecting the null hypothesis increases.

C4. Answer

True. All else being equal, as the sample size increases, power is greater. As the sample size increases, the null and alternative sampling distributions become narrower and overlap to a lesser extent. Consequently, it is less likely that a randomly sampled mean from the alternative distribution will be mistaken to have come from the null distribution.

More challenging questions:

True False
C5. Power is always greater when the effect size is greater.
C6. Power is always greater when the Type II error (i.e., beta error) is smaller.
C7. To compute power, all I need to know is effect size, sample size, and alpha.

C5. Answer

False. While larger effect size can indicate greater power, the sample size and alpha error also affect power. Even if the effect size is larger, there may be less power if the sample size is smaller or the alpha error is smaller.

C6. Answer

True. Power is inversely related to beta error (Power = 1 – β). Thus, as beta error decreases, power increases.

C7. Answer

True. Power can be directly calculated if the effect size, sample size, and alpha error are known. The BEAN acronym can help identify what information is needed to compute any of the factors related to statistical power. We assume that we have random, independent sampling from the populations and the sampling distributions of the means are very close to normal.

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