Approximately how many participants per sample are required to reach a statistical power of 0.80 for an independent-samples t-test with a large population effect?

True or False: In an independent-samples t-test with a large population effect, a researcher who wants to increase their statistical power from 0.80 to 0.99 would need to more than double their sample size per group (increasing from 26 to 59 participants).

A research lab is planning several studies using independent-samples t-tests and expecting a large population effect size in each case. Match each researcher's specific recruitment goal with the correct number of participants required for each of their sample groups.

A researcher is planning an independent-samples $t$-test and expects a large population effect size. Arrange the following recruitment requirements in order from the lowest number of participants to the highest number of participants required per sample.

You are formulating a recruitment strategy for a study using an independent-samples $t$-test where a large population effect is expected. Your goal is to design two protocol options: Protocol A for $0.80$ power and Protocol B for $0.99$ power. Which of the following recruitment summaries correctly assembles the total number of participants you must recruit across both group samples for each protocol?

A psychological researcher is planning an independent-samples $t$-test and expects a large effect size in the population. Match each of the researcher's goals or general observations with the appropriate sample size requirement according to statistical power standards.

In an independent-samples $t$-test with a large population effect, a researcher requires a smaller sample size (approximately 26 participants per sample) to achieve a statistical power of 0.99 than they do to achieve a power of 0.80 (approximately 59 participants per sample).

A researcher is planning an independent-samples $t$-test and expects a large population effect. Arrange the following group sample sizes in order of the statistical power they would provide, from the lowest power (top) to the highest power (bottom).

A researcher conducting an independent-samples $t$-test with a large population effect size evaluates their study design and determines that a power level of $0.80$ (requiring $26$ participants per group) provides too high a risk of a Type II error. To achieve a more rigorous 'near-certainty' power level of $0.99$, the researcher must increase their recruitment to _____ participants per sample group.

Imagine you are evaluating the methodological rigor of a study using an independent-samples $t$-test with a large population effect. If the study currently uses $26$ participants per group to achieve a power of $0.80$, but your evaluation criteria require a much higher power level of $0.99$, you should recommend increasing the sample size to _____ participants per group.

Explain the relationship between sample size requirements and target statistical power for an independent-samples $t$-test when assuming a large population effect. In your explanation, detail how the required sample size per group changes as the researcher seeks to increase power from $0.80$ to $0.99$, and explain why sample sizes in psychological research must generally be larger than researchers might intuitively expect to achieve high power.

Apply the sample size benchmarks for an independent-samples $t$-test with a large population effect to Dr. Aris's study. Determine how many participants she must recruit per group to achieve a power of $0.80$, how many she would need to achieve a power of $0.99$, and justify whether she should adjust her initial plan of $20$ participants per group.

Analyze how the required sample size per group changes when a researcher decides to increase the statistical power of an independent-samples $t$-test (assuming a large population effect) from $0.80$ to $0.99$. What does this comparison reveal about the relationship between sample size increases and statistical power gains?