Hi, I asked the following questions and received the answer below, in part. I'm wondering if the following information can help to give me a precise minimum and maximum sample size: 1. The independent variables are gender (male or female - 2 levels) and training (with or without gamification - 2 levels). 2. The overall population is 1086. Thanks for reconsidering this question with the additional information above! Please note that this is not part of a graded assignment. This is for research that I am conducting. ___________________________________________________________________________________________ Using the G*Power Calculator, what are the minimum and maximum sample sizes for a two-way MANOVA (with 2 independent variables and 3 dependent variables) when assuming a medium effect size with statistical power of .7 at the .05 alpha level? Conclusion To summarize, for a two-way MANOVA with two independent variables and three dependent variables, assuming a medium effect size, statistical power of 0.7, and an alpha level of 0.05, the required minimum sample size will generally fall around 90-100 participants, and the maximum sample size can be as high as 150-200 participants depending on the number of levels in your independent variables. More levels increase the complexity of the analysis, necessitating a larger sample size to maintain statistical power and avoid Type II errors. By carefully considering the number of groups, effect size, power, and alpha, you can ensure that your study is adequately powered for reliable results. To determine the minimum and maximum sample sizes for a two-way MANOVA with G*Power, you'll need to consider the specific details related to your design and the assumptions you mentioned: Effect size: Medium (as specified) Statistical power: 0.7 (which means a 70% probability of correctly rejecting the null hypothesis when it is false) Alpha level (α): 0.05 (the significance level or Type I error rate) Number of independent variables: 2 Number of dependent variables: 3 Key Considerations: Effect Size (f²): For a MANOVA, G*Power typically uses Cohen's f² to define the effect size. A "medium" effect size in this context is often represented as f² = 0.0625 (which corresponds to Cohen's medium value in MANOVA settings). Number of Groups: The two independent variables will form a certain number of groups, depending on their levels. For example, if each independent variable has 3 levels, you will have 3 × 3 = 9 groups. Number of Dependent Variables: Since you have 3 dependent variables, the test will assess the collective variance among these dependent variables. G*Power Calculation for MANOVA (Repeated Measures, Between Factors): Steps for calculation in G*Power: Test family: Select "F tests". Statistical test: Choose "MANOVA: Global effects". Type of power analysis: Choose "A priori: Compute required sample size". Effect size: Input f²(V) = 0.0625 for a medium effect size. α error probability: Set to 0.05. Power (1-β error probability): Set to 0.7. Number of groups: Input the number of groups based on the levels of your independent variables (e.g., if both IVs have 3 levels, input 9). Number of response variables (dependent variables): Input 3. After running this setup, you will be given a required sample size to achieve a medium effect size with 70% power at the 0.05 significance level. Approximate Values: Minimum Sample Size: The G*Power calculator will suggest a minimum sample size of around 90-100 participants for a medium effect size with these settings. Maximum Sample Size: The upper limit depends on how many levels you have for each independent variable, but if you're assuming 3 levels for both, the maximum sample size required might be around 150-200 participants. Summary: The minimum sample size for your setup is likely to be around 90-100 participants. The maximum sample size (if your design has more levels or complexity) could be 150-200 participants, depending on the complexity of your independent variables' levels. If you have specific details about the levels of the independent variables, you can input them directly to get a more precise sample size estimate.
Hi, I asked the following questions and received the answer below, in part. I'm wondering if the following information can help to give me a precise minimum and maximum sample size:
1. The independent variables are gender (male or female - 2 levels) and training (with or without gamification - 2 levels).
2. The overall population is 1086.
Thanks for reconsidering this question with the additional information above! Please note that this is not part of a graded assignment. This is for research that I am conducting.
___________________________________________________________________________________________
Using the G*Power Calculator, what are the minimum and maximum sample sizes for a two-way MANOVA (with 2 independent variables and 3 dependent variables) when assuming a medium effect size with statistical power of .7 at the .05 alpha level?
Conclusion
To summarize, for a two-way MANOVA with two independent variables and three dependent variables, assuming a medium effect size, statistical power of 0.7, and an alpha level of 0.05, the required minimum sample size will generally fall around 90-100 participants, and the maximum sample size can be as high as 150-200 participants depending on the number of levels in your independent variables. More levels increase the complexity of the analysis, necessitating a larger sample size to maintain statistical power and avoid Type II errors. By carefully considering the number of groups, effect size, power, and alpha, you can ensure that your study is adequately powered for reliable results.
- Effect size: Medium (as specified)
- Statistical power: 0.7 (which means a 70% probability of correctly rejecting the null hypothesis when it is false)
- Alpha level (α): 0.05 (the significance level or Type I error rate)
- Number of independent variables: 2
- Number of dependent variables: 3
Key Considerations:
Effect Size (f²): For a MANOVA, G*Power typically uses Cohen's f² to define the effect size. A "medium" effect size in this context is often represented as f² = 0.0625 (which corresponds to Cohen's medium value in MANOVA settings).
Number of Groups: The two independent variables will form a certain number of groups, depending on their levels. For example, if each independent variable has 3 levels, you will have 3 × 3 = 9 groups.
Number of Dependent Variables: Since you have 3 dependent variables, the test will assess the collective variance among these dependent variables.
G*Power Calculation for MANOVA (Repeated Measures, Between Factors):
Steps for calculation in G*Power:
- Test family: Select "F tests".
- Statistical test: Choose "MANOVA: Global effects".
- Type of power analysis: Choose "A priori: Compute required sample size".
- Effect size: Input f²(V) = 0.0625 for a medium effect size.
- α error probability: Set to 0.05.
- Power (1-β error probability): Set to 0.7.
- Number of groups: Input the number of groups based on the levels of your independent variables (e.g., if both IVs have 3 levels, input 9).
- Number of response variables (dependent variables): Input 3.
After running this setup, you will be given a required sample size to achieve a medium effect size with 70% power at the 0.05 significance level.
Approximate Values:
Minimum Sample Size: The G*Power calculator will suggest a minimum sample size of around 90-100 participants for a medium effect size with these settings.
Maximum Sample Size: The upper limit depends on how many levels you have for each independent variable, but if you're assuming 3 levels for both, the maximum sample size required might be around 150-200 participants.
Summary:
- The minimum sample size for your setup is likely to be around 90-100 participants.
- The maximum sample size (if your design has more levels or complexity) could be 150-200 participants, depending on the complexity of your independent variables' levels.
If you have specific details about the levels of the independent variables, you can input them directly to get a more precise sample size estimate.
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