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5. What size samples do you need for a 2-group design if you expect to have an effect size of .40 and you want your power to be .60?

5. What size samples do you need for a 2-group design if you expect to have an effect size of .40 and you want your power to be .60?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Sample Size Determination for 2-Group Design** **Question:** What size samples do you need for a 2-group design if you expect to have an effect size of .40 and you want your power to be .60? **Explanation:** In statistical hypothesis testing, determining the appropriate sample size is crucial to ensure the study has enough power to detect a meaningful effect. Power is the probability that the test will correctly reject the null hypothesis when a specific alternative hypothesis is true. Here, we aim for a power of 0.60 (or 60%), meaning we want a 60% chance of detecting an effect if one exists. Here's how to approach this problem: 1. **Effect Size (Cohen's d)**: A measure of the strength of the relationship between two groups. An effect size of 0.40 is considered a medium effect. 2. **Power**: The probability that the test will reject a false null hypothesis. A power of 0.60 is relatively low but can be used in exploratory studies. 3. **Sample Size Calculation**: There are statistical formulas and software tools (e.g., G*Power) available to calculate the required sample size based on the desired effect size and power. **Graph or Diagram Explanation:** If there were a graph or diagram associated with this question, it would likely illustrate the relationship between sample size, power, and effect size. Typically, such a plot would show: - **X-Axis**: Sample size (number of participants) - **Y-Axis**: Power (probability of correctly rejecting the null hypothesis) - **Curves**: Multiple curves representing different effect sizes (e.g., small, medium, large). Using these curves, one would locate the desired power level (0.60) on the Y-axis and find the corresponding sample size for an effect size of 0.40. **Conclusion:** To determine the exact sample size, you would typically use statistical software or consult sample size tables that incorporate these parameters. Pre-studying these calculations ensures an adequately powered study, enhancing the reliability and validity of the study's findings.
Transcribed Image Text:**Sample Size Determination for 2-Group Design** **Question:** What size samples do you need for a 2-group design if you expect to have an effect size of .40 and you want your power to be .60? **Explanation:** In statistical hypothesis testing, determining the appropriate sample size is crucial to ensure the study has enough power to detect a meaningful effect. Power is the probability that the test will correctly reject the null hypothesis when a specific alternative hypothesis is true. Here, we aim for a power of 0.60 (or 60%), meaning we want a 60% chance of detecting an effect if one exists. Here's how to approach this problem: 1. **Effect Size (Cohen's d)**: A measure of the strength of the relationship between two groups. An effect size of 0.40 is considered a medium effect. 2. **Power**: The probability that the test will reject a false null hypothesis. A power of 0.60 is relatively low but can be used in exploratory studies. 3. **Sample Size Calculation**: There are statistical formulas and software tools (e.g., G*Power) available to calculate the required sample size based on the desired effect size and power. **Graph or Diagram Explanation:** If there were a graph or diagram associated with this question, it would likely illustrate the relationship between sample size, power, and effect size. Typically, such a plot would show: - **X-Axis**: Sample size (number of participants) - **Y-Axis**: Power (probability of correctly rejecting the null hypothesis) - **Curves**: Multiple curves representing different effect sizes (e.g., small, medium, large). Using these curves, one would locate the desired power level (0.60) on the Y-axis and find the corresponding sample size for an effect size of 0.40. **Conclusion:** To determine the exact sample size, you would typically use statistical software or consult sample size tables that incorporate these parameters. Pre-studying these calculations ensures an adequately powered study, enhancing the reliability and validity of the study's findings.
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