Hi,

Mixed models with a Generalized linear approach where all these factors and repeated measures can be tested. See that there are adequate sample sizes and that standard errors are low..

You can go through design of experiments books for such an analysis and statistical software for analysis.

Your experiment involves a factorial design with multiple independent variables (season, location, position, window size) and their combinations. Given the complexity of the design, you'll likely need to use a multivariate statistical approach to analyze the data effectively. Here's a step-by-step approach to help you determine the appropriate statistical test and estimate the required sample size:

1. **Design and Variables:**

- Identify your dependent variables (e.g., privacy perception, view quality).

- List all your independent variables and their levels (season, location, position, window size).

2. **Experimental Design Analysis:**

- Since you have a factorial design, a multivariate analysis of variance (MANOVA) or a repeated measures MANOVA (RM-MANOVA) could be suitable to analyze the effects of your independent variables on the dependent variables.

- MANOVA allows you to analyze multiple dependent variables simultaneously, which is beneficial in your scenario where you likely have multiple measures of privacy and view quality.

3. **Sample Size Estimation:**

- To estimate the required sample size for MANOVA, you'll need to consider factors such as effect size, alpha level, power, and the number of groups and dependent variables.

- It's important to determine the smallest meaningful effect size for your study, which could be based on previous research or your expectations.

4. **Power Analysis:**

- Conduct a power analysis using a statistical software or online tool specifically designed for MANOVA.

- Input the effect size, desired alpha level (e.g., 0.05), power (e.g., 0.80 or higher), and the number of groups and dependent variables.

5. **Interpretation:**

- After conducting the experiment and analyzing the data using MANOVA, interpret the results to understand the effects of the independent variables on the dependent variables.

- Post hoc tests (e.g., Tukey's HSD) may be needed to identify specific group differences if the MANOVA results are significant.

6. **Additional Analyses:**

- Depending on your research questions, you may need to conduct additional analyses, such as regression, to examine relationships between specific independent and dependent variables.

7. **Consider Consulting a Statistician:**

- Given the complexity of your design and analysis, consider consulting with a statistician to ensure the appropriate statistical approach and interpretation of results.

Remember to carefully plan your experimental design, ensure randomization and counterbalancing where needed, and adequately control for confounding variables to obtain valid and reliable results.

Davood Omidian Thank you for a detailed answer. I Appreciate it a lot.

I am using the GPower tool, and was wondering which of the MANOVA types are more sufficient?

MANOVA: Repeated measures, between factors

MANOVA: Repeated measures, within factors

MANOVA: Repeated measures, within-between interaction

And for the "Number of Groups" i should pick 6, and the "Number of measurements" i should pick 2 (If i am measuring privacy and view-out)?

The number of measurements does not have anything to do with the 12 different scenarios happening within one group?

Hope I described it clear enough,

Best Regards,

Louis H