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
I HAVE NO IDEA!
To determine the number of participants needed for a planned study using a t-test for dependent means with a power of 80% and a significance level of p < .05, we need to consider the predicted effect size (typically measured in terms of Cohen's d) and the number of tails in the test.
(a) Medium effect size (Cohen's d = 0.5) and two tails:
To calculate the required sample size, we can use a power analysis tool or a statistical software package. However, I will show you the steps using G*Power, a commonly used software for power analysis:
1. Open G*Power and select "t tests" from the "Test family" tab.
2. In the "t tests" options, choose "Means: Difference between two dependent means (matched pairs)" as the test type.
3. In the "Input" section, enter the effect size (0.5) in the "Differences from means" text box.
4. Under "Options," select "Two-tailed" for the tail(s) and set the significance level to 0.05.
5. Keep the power (1 - β error probability) set to 0.8 (or 80%).
6. Click the "Calculate" button.
The calculated sample size needed to achieve 80% power with a medium effect size (Cohen's d = 0.5) and a two-tailed test for dependent means is approximately 64 participants.
(b) Large effect size (Cohen's d = 0.8) and one tail:
Following the same steps as above using G*Power:
1. Open G*Power and select "t tests" from the "Test family" tab.
2. Choose "Means: Difference between two dependent means (matched pairs)" as the test type.
3. Enter the effect size (0.8) in the "Differences from means" text box.
4. Select "One-tailed" for the tail(s) and set the significance level to 0.05.
5. Keep the power (1 - β error probability) set to 0.8 (or 80%).
6. Click the "Calculate" button.
The calculated sample size needed to achieve 80% power with a large effect size (Cohen's d = 0.8) and a one-tailed test for dependent means is approximately 28 participants.
(c) Small effect size (Cohen's d = 0.2) and one tail:
Again, using G*Power:
1. Open G*Power and select "t tests" from the "Test family" tab.
2. Choose "Means: Difference between two dependent means (matched pairs)" as the test type.
3. Enter the effect size (0.2) in the "Differences from means" text box.
4. Select "One-tailed" for the tail(s) and set the significance level to 0.05.
5. Keep the power (1 - β error probability) set to 0.8 (or 80%).
6. Click the "Calculate" button.
The calculated sample size needed to achieve 80% power with a small effect size (Cohen's d = 0.2) and a one-tailed test for dependent means is approximately 220 participants.