About how many participants are needed for 80% power in each of the following planned studies that will use a t test for dependent means with p < .05?
Predicted Effect Size Tails
(a) Medium Two
(b) Large One
(c) Small One
To determine the number of participants needed for a specific power level, effect size, and significance level, we can use statistical power analysis. In this case, we want to calculate the sample size required for 80% power in studies that use a t test for dependent means with p < .05.
To perform a power analysis, we typically need the following information:
1. Effect size: This represents the size of the difference or relationship we expect to find between the groups or conditions.
2. Alpha level (significance level): This is the probability of rejecting the null hypothesis when it is actually true. In this case, we have p < .05, which means we are using a 5% significance level.
3. Power level: This is the probability of correctly rejecting the null hypothesis when it is false. In this case, we want a power level of 80%, which corresponds to a 20% chance of making a Type II error (failing to detect a true effect).
Now let's calculate the sample size for each scenario:
(a) Medium effect size, two-tailed test:
A commonly used effect size measure for t tests is Cohen's d. Assuming we have an estimated medium effect size of d = 0.5, we can use a power analysis calculator or software to determine the sample size required.
Using a power analysis calculator, if we set the power level to 80%, the significance level to 0.05, and the effect size (Cohen's d) to 0.5, we get an estimated sample size of approximately 64.
(b) Large effect size, one-tailed test:
For a one-tailed test, the effect size can be represented as Cohen's d or as the difference in means. Assuming we have a large effect size and find a difference of means, we need to adjust the alpha level since it's a one-tailed test. A one-tailed test involves testing for an effect in only one direction. For example, we are only interested in determining if the mean difference is greater than zero. In this case, we can use an alpha level of 0.025 (half of the 0.05 significance level).
Using the same power analysis calculator, assuming a large effect size, with d = 0.8, power level of 80%, and an adjusted alpha level of 0.025, we get an estimated sample size of approximately 26.
(c) Small effect size, one-tailed test:
Similarly, for a small effect size and a one-tailed test, we need to adjust the alpha level to 0.025.
Using the same power analysis calculator, assuming a small effect size, with d = 0.2, power level of 80%, and an adjusted alpha level of 0.025, we get an estimated sample size of approximately 289.
Please note that these are estimated sample sizes, and the actual sample size may vary depending on various factors, including the specific research design, population, and effect size estimation. It's always a good practice to consult with a statistician or use a power analysis tool to ensure accurate estimations for your specific study.