State whether each of the following will increase or...

State whether each of the following will increase or decrease the power of a one-way between. subjects ANOVA.
a. The effect size increases.
b. Mean square error decreases
c. Mean square between groups decreases.
d. The sample size decreases.

Key Concepts

Statistical Power

Statistical power is the probability that a statistical test will correctly reject a false null hypothesis. It reflects the sensitivity of an experiment in detecting a true effect when one exists, and is influenced by factors such as effect size, error variance, and sample size.

Effect Size

Effect size measures the magnitude of differences among groups. In the context of ANOVA, a larger effect size means that the true differences between group means are more pronounced relative to the variability in the data, thereby increasing the power of the test.

Mean Square Error (Error Variance)

Mean square error represents the variability within the groups that is not attributable to the experimental manipulation. A lower mean square error indicates less random variability, which enhances the contrast between group differences and increases the power of the ANOVA test.

Mean Square Between Groups (Between-Group Variance)

Mean square between groups quantifies the variance due to the differences among group means. If this value decreases, it implies that the differences among the groups are smaller, which lowers the signal relative to the noise, thereby reducing the power of the ANOVA test.

Sample Size

The sample size is the number of observations in each group included in the analysis. Larger sample sizes generally yield more precise estimates and reduce the standard error, leading to increased statistical power, while a decrease in sample size tends to reduce power.

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