Approximately how many research participants would be required for 80% power for a
study using the t test for dependent means (assume a one-tailed hypothesis with an
expected medium effect size of .50):
To determine the approximate number of research participants required for 80% power for a study using the t test for dependent means, you need to perform a power analysis. This analysis estimates the sample size needed to detect a specific effect size with a given level of power.
Here are the steps to calculate the sample size:
1. Determine the desired power: In this case, it is 80%. Power is the likelihood of detecting a statistically significant effect if it truly exists.
2. Specify the expected effect size: In this example, the expected medium effect size is .50. The effect size represents the magnitude of the difference or relationship between variables.
3. Select the significance level: The significance level, usually denoted as alpha (α), determines the probability of incorrectly rejecting a null hypothesis. In this case, if you assume a one-tailed hypothesis, you would typically select alpha as .05. However, please confirm the specific significance level required for your study.
4. Choose the statistical test: For a study using the t test for dependent means, you would select the paired t-test.
5. Conduct the power analysis: You can use various power analysis software or online calculators to perform the calculation. There are also statistical software packages (e.g., R, SPSS) that provide power analysis functions. These tools require you to input the expected effect size, power, significance level, and specific test being used.
Using a power analysis calculator or software, input the values:
- Effect Size (Cohen's d) = .50
- Power = 0.80 (80%)
- Alpha (Significance level) = 0.05 (or confirm the required level)
After performing the power analysis, you will obtain the estimated sample size needed for your study. The result may vary depending on the specific tools or software you use. It is important to note that power analysis provides an estimate, and rounding up to the nearest whole number is advisable to ensure an adequate sample size.
By following these steps and using appropriate power analysis tools, you can determine the approximate number of research participants required for 80% power in a study using the t test for dependent means.