is it true that sample size required to detect an effect size of 0.25 is larger than the sample size required to detect an effect size of 0.05 with 80% power ansd a 5% level of signisicance?
False. For smaller effect sizes a larger sample size would be required.
To determine whether the sample size required to detect an effect size of 0.25 is larger than the sample size required to detect an effect size of 0.05, we need to consider the power and significance level.
Power refers to the likelihood of correctly rejecting a false null hypothesis, while the significance level (often denoted as alpha) is the probability of rejecting the null hypothesis when it is true.
Assuming an 80% power (or 0.80) and a 5% level of significance (or alpha = 0.05), we can compare the sample size required for each scenario.
The sample size required can be calculated using statistical power analysis. However, without specific additional information such as the anticipated effect size, population standard deviation, or desired statistical test, it is not possible to determine the exact sample sizes required.
In general, the smaller the effect size, the larger the required sample size needed for sufficient power. Given this, it is likely that the sample size needed to detect an effect size of 0.25 is larger than the sample size needed for an effect size of 0.05, assuming other parameters are held constant.
To obtain precise sample size estimations for your specific study, it is recommended to use a statistical power analysis software or consult with a statistician.
To determine if the statement is true, we need to calculate the sample sizes required to detect an effect size of 0.25 and 0.05, with 80% power and a 5% level of significance.
The sample size required to detect an effect size depends on several factors, including the desired power, level of significance, and the effect size itself. To calculate the required sample size, we can use statistical power analysis.
Here's how you can perform the calculations using the following information:
Effect size 1: 0.25
Effect size 2: 0.05
Power: 80%
Level of significance (α): 5%
Step 1: Determine the required sample size for effect size 1 (0.25):
To calculate the sample size, we can use a statistical power calculator or conduct a power analysis using a statistical software package or formula. For simplicity, let's assume we're using a two-sample t-test.
Step 1a: Calculate the effect size (Cohen's d):
Effect size (Cohen's d) = (Mean difference) / Standard deviation
Since we don't have specific details about the means and standard deviations, let's assume we have a common standard deviation of 1 for both groups:
Effect size 1 (Cohen's d) = 0.25 / 1 = 0.25
Step 1b: Use a power analysis calculator or formula to determine the required sample size for effect size 1, power of 80%, and level of significance of 5%.
For example, assuming a two-sample t-test, a power analysis might indicate that a sample size of around 63 participants in each group is needed to detect an effect size of 0.25 with 80% power and a 5% level of significance.
Step 2: Determine the required sample size for effect size 2 (0.05):
Again, assuming a common standard deviation of 1 for both groups:
Effect size 2 (Cohen's d) = 0.05 / 1 = 0.05
Using a power analysis calculator or formula with effect size 2, power of 80%, and a level of significance of 5%, we might find that a sample size of around 16 participants in each group is needed to detect an effect size of 0.05 with 80% power and a 5% level of significance.
Conclusion:
Based on the calculations, the sample size required to detect an effect size of 0.25 (around 63 participants per group) is larger compared to the sample size required to detect an effect size of 0.05 (around 16 participants per group) with 80% power and a 5% level of significance.