the tradeoff for working with a manageable sample requires that we account for sample error.

Power analysis helps you manage an essential tradeoff. As you increase the sample size, the hypothesis test gains a greater ability to detect small effects. This situation sounds fantastic. However, larger sample sizes cost more money. And, there is a point where an effect becomes so miniscule that it is meaningless in a practical sense.

Descriptive statistics describe a sample. That’s pretty straightforward. You simply take a group that you’re interested in, record data about the group members, and then use summary statistics and graphs to present the group properties.

Keep in mind that variability and effect size are estimates and guesses. Consequently, power and the Type II error rate are just estimates rather than something you set directly.

Because population parameters are unknown, we also never know exactly the sampling error for a study. However, using hypothesis testing, we can estimate the error and factor it into the test results.

there are multiple reasons for Type II errors—small effect sizes, small sample sizes, and high data variability.

Inferential statistics takes data from a sample and makes inferences about the larger population from which the sample was drawn. Consequently, we need to have confidence that our sample accurately reflects the population.

As the power level increases, more moderate effect sizes become significant. That’s precisely how hypothesis tests are supposed to work!

statistical significance of any effect depends collectively on the size of the effect, the sample size, and the variability present in the sample data.