When you have multiple research questions and plan to use several statistical tests (ANCOVA, MANCOVA, logistic regressions), the general recommendation is to focus first on your primary outcome or hypothesis. This is important because sample size calculations should primarily ensure adequate power for the most critical test of your study, while secondary analyses can be reported as exploratory or adjusted for multiplicity if needed Lakens, 2022.

Practical steps you can follow:

Using Mplus you can determine the different necessry sample sizes for different estimates in tha same model.

Se www.statmodel.com

Step 1: Identify the Primary Outcome(s)

Determine the primary outcome(s)Identify the most important outcome(s) that will answer your research question(s).

- Specify the effect size: Estimate the effect size for each primary outcome.

Step 2: Determine the Statistical Power

- Specify the desired statistical power Typically, 80% or 90% power is used.

- Determine the significance level: Typically, α = 0.05 is used.

Step 3: Calculate Sample Size for Each Research Question

- Use sample size formulas or software: Use formulas or software like GPower, SAS, or R to calculate the sample size for each research question.

- Consider the study design: Account for the study design, such as cluster randomized trials or surveys.

Step 4: Determine the Overall Sample Size

- Use the largest sample size: Use the largest sample size calculated for each research question.

- *Consider practical constraints*: Consider budget, time, and feasibility constraints.

Additional Considerations

-Multiple testing Consider adjusting for multiple testing using methods like Bonferroni correction.

- Pilot study: Conduct a pilot study to estimate effect sizes and variability.

Software and Resources

- GPower: A popular software for sample size calculation.

- *SAS*: A statistical software package that includes sample size calculation

By following these steps and considering the complexities of your study, you can determine an appropriate a-priori sample size for your research.

Thanks for your detailed question- it's a great one, and you're right that the literature often skimps on reporting power analyses, especially for studies with multiple tests. I'll walk you through a step-by-step approach based on standard statistical best practices. This should help you determine your required sample size a priori (before data collection) and decide how to report it. I'll draw from reliable sources like the G*Power manual and guidelines from statistical reviews.

Step 1: Understand the Goal of A Priori Power Analysis

A priori power analysis helps you estimate the minimum sample size needed to detect a statistically significant effect (if it exists) with a desired level of power (usually 80% or 0.80, meaning an 80% chance of correctly rejecting a false null hypothesis). Key inputs include:

• Effect size: Based on prior studies, pilot data, or conventions (e.g., small/medium/large per Cohen's guidelines: for ANCOVA, f = 0.25 is medium; for logistic regression, odds ratios or Cohen's f^2).
• Alpha level: Typically 0.05 (Type I error rate).
• Power: Typically 0.80.
• Test-specific details: Number of groups, covariates, predictors, etc.

Since you have multiple tests (ANCOVA, MANCOVA, and two binary logistic regressions), the key is to ensure your sample size powers all of them adequately without over- or under-sampling.

Step 2: Calculate Power for Each Test Separately

Don't pick just one method—calculate for all, as each test has different assumptions and sensitivities to sample size. Use G*Power (free and user-friendly) for this. Here's how to set it up for each:

• ANCOVA (Analysis of Covariance):In G*Power: Select "F tests" > "ANCOVA: Fixed effects, main effects, and interactions." Inputs: Effect size f (e.g., 0.25 for medium), alpha=0.05, power=0.80, number of groups, number of covariates (at least 1), and degrees of freedom for numerator (e.g., groups-1). Output: Total sample size needed. Tip: ANCOVA is efficient with covariates, so it might require a smaller sample than ANOVA.
• MANCOVA (Multivariate Analysis of Covariance):In G*Power: Select "F tests" > "MANOVA: Global effects" (MANCOVA is an extension of MANOVA with covariates; approximate by adding covariates here). Inputs: Effect size f (Pillai's trace or similar; e.g., 0.15 for medium in multivariate), alpha=0.05, power=0.80, number of groups, number of response variables (DVs), number of covariates. Output: Total sample size. MANCOVA often needs larger samples due to multiple DVs—aim for at least 20-30 cases per DV/group as a rule of thumb, but let G*Power guide you. Note: If your MANCOVA has many DVs, you might need to adjust degrees of freedom or use simulation tools like R's pwr package for precision, but G*Power is a solid start.
• Binary Logistic Regressions (two separate ones):In G*Power: Select "Z tests" > "Logistic regression." Inputs: Effect size as odds ratio (e.g., 1.5-2.0 for small-medium), alpha=0.05, power=0.80, base probability (e.g., 0.5 if unknown), number of predictors (for each model separately). Output: Sample size per regression. Logistic models are sensitive to event rates (e.g., proportion of "successes" in your binary outcome)—if rare events, you'll need more cases. Rule of thumb: At least 10-15 events per predictor to avoid overfitting, but power analysis will refine this.

Run these calculations assuming conservative effect sizes (smaller effects require larger samples). If you don't have effect sizes from literature, use Cohen's conventions or run a pilot study.

Step 3: Choose the Overall Sample Size

Once you have estimates for each test:

• Compare them and select the largest required sample size as your target. This ensures all analyses are powered at least to 80%, avoiding underpowered secondary tests. For example, if ANCOVA needs N=100, MANCOVA needs N=150, and logistics need N=120 and N=80, go with N=150 (or add 10-20% for attrition).
• Why the largest? Studies with multiple hypotheses risk Type I errors if underpowered for any test, and this conservative approach maximizes reliability without unnecessary data collection.
• If your tests share the same sample (common in one study), this works well. If they're on subsets, adjust accordingly.

Step 4: Reporting in Your Paper

Transparency is key, especially since many papers omit this (as you noted). Best practices:

• Report all power analyses in the Methods section (under "Sample Size Determination" or "Statistical Power"). Describe each calculation briefly: e.g., "A priori power analysis using G*Power indicated N=150 for the MANCOVA (effect size f=0.15, α=0.05, power=0.80, 2 groups, 3 DVs, 2 covariates), which was the largest required across tests."
• Explain why you chose the largest N: "To ensure adequate power for all planned analyses, the sample size was based on the most demanding test (MANCOVA)."
• If space is tight, prioritize reporting for your primary hypothesis/test, but note the others were considered.
• Include sensitivity analyses if actual effect sizes differ post-data (post-hoc power), but a priori is the focus for planning.
• Journals like those in psychology/education often expect this for rigor (e.g., APA guidelines encourage it).