Homework Help is Here – Start Your Trial Now!
Math
Statistics
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
See similar textbooks
icon
Related questions
Question
**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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS