Yes, you can still report the ANCOVA results, but given the assumption violations, you should proceed with caution and consider adjustments to improve the robustness of your findings. Here’s how you can handle the issues:

1. Addressing the Levene’s Test Violation

A significant Levene’s test (p = 0.007) at post-test suggests heterogeneity of variances, which can inflate Type I errors.

Since follow-ups don’t show violations (p > 0.5), the main concern is with the post-test comparison.

Given your small sample, Levene’s test can be sensitive. Check whether the violation is due to one group having extreme variance. If one group (e.g., control) has a much larger or smaller variance, consider robust alternatives.

2. Box’s M Test Significance (p = 0.001)

Box’s M is very sensitive in small samples. A significant result suggests non-homogeneity of covariance matrices, but ANCOVA can still be used if group sizes are reasonably similar.

Your groups are fairly balanced (27, 32, 31), so this violation is concerning but not necessarily a deal-breaker.

Use Pillai’s trace instead of Wilks’ Lambda, as Pillai’s is more robust to violations of homogeneity.

3. Mauchly’s Test Violation (p = 0.020)

A violation of sphericity means that repeated measures assumptions are not met.

Use Greenhouse-Geisser or Huynh-Feldt corrections when interpreting within-subject effects.

4. Alternative Approaches

Since transformations didn’t resolve the issues, consider these alternatives:

Robust ANCOVA: Use heteroscedasticity-robust standard errors.

Generalized Estimating Equations (GEE): Works well for small samples and accounts for correlation in repeated measures.

Mixed Effects Model (Linear Mixed Model - LMM): More flexible than ANCOVA, allows for individual variance modeling, and can handle assumption violations better.

5. Reporting & Justification

Clearly acknowledge assumption violations and their implications.

Justify why you still proceed with ANCOVA (e.g., group sizes are balanced, follow-up tests are fine).

Consider running sensitivity analyses (e.g., compare ANCOVA results with robust methods like GEE or LMM).

Final Recommendation

If ANCOVA results remain consistent with a mixed-effects model or robust ANCOVA, you can cautiously interpret the findings. Otherwise, shifting to LMM may be a stronger choice given your design.

Can you please show your complete model? Which covariables did you use and what was the rational to use them? Did you use directed acyclic graphs (DAGs) to determine for which variables you should adjust and for which you must not(!) adjust to prevent bias?

Generally it is not recommended to only use statistical tests to evaluate and check assumptions. This is because 1) these tests also rely on assumptions themselves, 2) they rely on power to detect violations, 3) they so not tell you anything where, why, and how the violations occur, therefore you are not able to assess the severity of the violation, and 4) a non-significant test is not evidence that there is not violation, since in NHST this is not evidence that the H0 is true.

Therefore, it is much more important to visualize the assumptions and interpret the values itself (e.g. how much larger is the variance in one group as compared to the other).

As mentioned above, there may be alternative models, which do not rely on the typical assumptions (e.g. bootstrapping), can handle them (heteroscedasticity robust estimators) or use a much more flexible model itself (e.g. linear mixed models).

Blind application of transformations is also not recommended. How do the conditional distributions look like? What is the data generating process? For example, if the effect of the intervention on trauma is how often do intrusive thoughts occur, this would be a count variable. These variables have a natural lower bound (i.e. zero). Therefore, it is not expected that a typical OLS regression / AN(C)OVA is a good choice in the first place. For such data, a Poisson or negative binomial regression would be much more suitable. Hence, we need to know much more about your model and data to give an educated answer. There is no solution which can fix all problems.

I can help you structure a model, discuss covariate selection, and guide you on using Directed Acyclic Graphs (DAGs) for confounder adjustment.

1. Covariate Selection & Rationale

The choice of covariates depends on the research question and data-generating process. Common categories include:

• Confounders: Variables that affect both the exposure and outcome (must adjust for them).
• Mediators: Variables that lie on the causal path between exposure and outcome (do NOT adjust for them).
• Colliders: Variables influenced by both exposure and outcome (adjusting creates bias).
• Effect Modifiers: Variables that change the strength of the association (can stratify by them).

Using DAGs is a best practice to visually map relationships and determine proper adjustment strategies.

2. DAG-Based Adjustment

DAGs help avoid "adjustment bias" by:

• Identifying true confounders to control.
• Preventing over adjustment (e.g., adjusting for mediators).
• Avoiding collider stratification bias.

A mixed-design ANCOVA is a good choice to control for baseline differences while examining within- and between-group effects.

1. Covariate Selection & Rationale

Which covariates did you adjust for? Common choices in intervention studies include:

• Pre-intervention symptom severity (to control for baseline differences)
• Demographic factors (e.g., age, gender, education) if they influence outcomes
• Engagement with the intervention (e.g., app usage time) if relevant
• Pre-existing mental health conditions (if known and relevant)

2. DAGs for Confounder Selection

Did you use a Directed Acyclic Graph (DAG) to map relationships between variables? This can help prevent:

• Overadjustment bias (e.g., controlling for mediators like post-intervention distress)
• Collider bias (e.g., adjusting for variables caused by both intervention and outcome)

Would you like to discuss a possible DAG structure for your study? I can also help interpret the ANCOVA results in light of your model.

Mahendra Kumar Verma no thanks for your AI generated answer, even without mentioning it. Have at least some dignity.