Reporting ANOVA and ANCOVA

Reporting Analyses of Variance (ANOVA) and Covariance (ANCOVA) in Academic Research

Analysis of Variance (ANOVA) and Analysis of Covariance (ANCOVA) are important statistical methods in research, as they allow researchers to compare means from groups as well as control for all covariates.

Reporting ANOVA and ANCOVA

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Introduction

Analysis of Variance (ANOVA) and Analysis of Covariance (ANCOVA) are important statistical methods in research, as they allow researchers to compare means from groups as well as control for all covariates. Proper reporting of these analyses is critical for credibility, transparency, validity, and replicability in research. This article will outline the important aspects of reporting ANOVA and ANCOVA, referring to a few more recent research studies as examples of good practices when reporting statistical results.

1. Purpose of the Analysis

  • The first step of reporting ANOVA or ANCOVA is to clearly articulate the purpose for which these analyses were conducted. ANOVA is conventionally reported to compare the means of three or more groups (independent groups). For ANCOVA, as its name indicates, an ANCOVA is used to control for one or more covariates (e.g., age, baseline readings such as BP, blood glucose, etc.).
  • For example, Mistry et al. (2022) used ANCOVA to compare the National Institutes of Health Stroke Scale across groups, with the baseline stroke severity covariate controlled. This drew attention to the essential consideration of the nature of baseline differences in medical studies. In the same context, Stanley (2022) acknowledges that by accounting for covariates, ANCOVA estimates can be more precise, as there can be less variation in treatments potentially favouring substance groups and thus improve statistical power.
  • A brief rationale should state why the researcher is using ANOVA or ANCOVA, which will assist in determining how ANOVA or ANCOVA will assist in answering the research problem. For example, “To determine the effect of three treatments on cholesterol levels with age and BMI controlled” sequentially states what the analysis will accomplish.

    • 2. Identifying and Summarizing Variables

  • When reporting ANOVA or ANCOVA, you must indicate your dependent and independent (explanatory) variables. It is also important for the reader to know descriptive statistics (e.g., mean, standard deviation, and range) for each variable so that the reader can better appreciate the data set.
  • For example, Martini et al. (2025) reported pharmacokinetics and used ANCOVA comparing the effectiveness of different drugs along with drug efficacy while controlling for different covariates. It would be critical to summarise descriptive statistics for each drug, demonstrating both the mean pharmacokinetic measure along with that total drug group context, so the reader could gauge the breadth of the study. Also consider Brorsen et al. (2025) and where they underscore the importance of summarising covariates and outcomes in a clear manner so that the mean is available for the reader to draw proper inferences on the results of ANCOVA.
  • ANOVA and ANCOVA have assumptions that need to be tested. Some of these assumptions are linearity of covariates (ANCOVA), normality of residuals, and homogeneity of variances among groups. Shieh (2023) argues that researchers must test and report whether these assumptions were tested before conducting an ANCOVA. If assumptions are violated, the researchers may apply data transformations or conduct non-parametric tests.
  • It is also important to report whether residual analysis was performed to ensure that the data meet the assumptions. Hedges et al. (2023) argue that it is important to perform a residual analysis to verify the robustness of the ANCOVA obtained.
  • Outliers may drastically change the findings, resulting in biased or non-objective estimates of ANOVA or ANCOVA. When the possibility of outlier data exists, Buderer and Brannan (2024) stated it is important to address the outlier data correctly using methods such as transformation, elimination, or exclusion. Missing data is another concern to deal with, and missing data should be properly dealt with in an honest way. Ideally, there are two common methods: listwise deletion, where missing data is deleted, or imputation methods where the missing values are estimates based on the non-missing data.
  • Cheverko et al. (2023) provided an example from archaeology, which is a field that has used ANCOVA and is currently being explored regarding skeletal remains. The researchers were faced with missing data due to incomplete records, and it was critical for the research to treat the missing data correctly to keep the analysis intact and credible.
  • Whether reporting ANOVA or ANCOVA results, it is necessary to note if you tested potential interaction effects between explanatory variables. Interaction effects happen when the effect of a given explanatory variable on the dependent variable is different depending on the level of another explanatory variable. Brorsen et al. (2025) present the importance of testing for interaction effects before conducting ANCOVA since omitting to do so can result in misleading conclusions.
  • Extending the example mentioned above (at the end of section 4), Mistry et al. (2022) tested interactions between treatment types and observed baseline characteristics, where they pointed out significant interaction effects that spoke to their conclusions about treatment effectiveness. These examples call attention to the importance of evaluating how different variables can potentially interact and potentially impact the outcome.

    • 6. Reporting Statistical Outputs

    When reporting your ANOVA and ANCOVA, it is important to report all of the output in the correct manner. You should always report summary information for reporting ANOVA and ANCOVA as follows:

    • P-values related to all explanatory variables
    • Test statistics (e.g., F-ratios)
    • Degrees of freedom (df) associated with all terms

    In addition, Shieh (2023) discusses reporting a standardised contrast effect from an ANCOVA that allows readers to extract the significance and meaning of the analyses while also providing comparable measures of precision. Martini et al. (2025) suggested that statistically contextualising analyses in this manner helps to establish transparency and permits comparability in your studies.

    7. Assessing Model Fit

  • Another central component to report when interpreting ANOVA and ANCOVA is a measure of fit of the model to the data. Often, this simple measure is presented as R², which is the proportion of variance explained by the model. In the case of multiple predictors, adjusted R² is often reported to account for the quantity of terms in the model. Stanley (2022) indicates that R² is a critical statistic when judging the goodness-of-fit of the model, as it evaluates the portion of variability explained by the model.
  • As Shieh (2023) indicates, it is an important statistic when considering ANCOVA to report adjusted R² because ANCOVA accounts for the multiple covariates reflected by the complexity of the model. The use of adjusted R² will help determine whether the use of covariates improved the prediction of the model.

    • 8. Reporting Model Validation

  • Model validation is an important consideration in order to evaluate the robustness and generalisability of results. Researchers should also state whether the model has been validated through cross-validation, a residual analysis, or other methods. The suggestion of conducting a residual analysis to test the assumptions of the model is referenced by Buderer and Brannan (2024) and the issue of validating ANCOVA models to determine if they are overfitted by Shieh (2023).
  • Mistry et al. (2022) stated that model validation is particularly important and valuable if it occurs in the context of clinical trials, where the risk associated with a misspecified model can be substantial. The degree to which any model was validated provides, when reported, the evidence to support the credibility and reproducibility of findings.

    • 9. Statistical Software Used

    Finally, the statistical software or instrumentation which was used for ANOVA or ANCOVA should be referenced. Examples of statistical software packages include SPSS, R, SAS, and STATA. Hedges et al. (2023) and Brorsen et al. (2025) discussed the importance of reporting the software used, which provides potential for other researchers to replicate the study using an analogous method.

    Conclusion

    Reporting ANOVA and ANCOVA can be an important endeavour that requires attention to detail in the name of full transparency, accuracy, and reproducibility. Following the guidance provided in this article as well as the description of the required narrative of reporting ANOVA and ANCOVA (arguably) all contribute to information that, when reported in alcohol and substance use research, will be presented properly. In conclusion, researchers can reduce the burden on the science of academic research by enabling more reliable and transparent statistical reporting with any form of meta-analysis.

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    References

    1. Hedges, L. V., Tipton, E., Zejnullahi, R., & Diaz, K. G. (2023). Effect sizes in ANCOVA and difference‐in‐differences designs. British Journal of Mathematical and Statistical Psychology, 76(2), 259-282.

    2. Shieh, G. (2023). Assessing standardized contrast effects in ANCOVA: Confidence intervals, precision evaluations, and sample size requirements. PLoS One, 18(2), e0282161.

    3. Mistry, E. A., Yeatts, S. D., Khatri, P., Mistry, A. M., Detry, M., Viele, K., … & Lewis, R. J. (2022). National institutes of health stroke scale as an outcome in stroke research: value of ANCOVA over analyzing change from baseline. Stroke, 53(4), e150-e155.

    4. Martini, B. A., Ji, P., Liu, J., Taur, J. S., Chen, J., Doddapaneni, S., … & Schrieber, S. J. (2025). Comparison of Analysis of Covariance and Analysis of Variance in Pharmacokinetic Similarity Studies. The Journal of Clinical Pharmacology.

    5. Stanley, P. (2022). Analysis of covariance: A useful tool for the pharmacologist to reduce variation and improve precision using fewer animals. British Journal of Pharmacology, 179(14), 3645-3650.

    6. Buderer, N. M., & Brannan, G. D. (2024). Comparing the means of independent groups: ANOVA, ANCOVA, MANOVA, and MANCOVA. In StatPearls [Internet]. StatPearls Publishing.

    7. Brorsen, B. W., Lin, H., & Larzelere, R. E. (2025). Critique of enhanced power claimed for Quasi-ANCOVA and Dual-Centered ANCOVA. PloS One, 20(1), e0317860.

    8. Cheverko, C. M., Schrader, S. A., Torres, C. M., Pestle, W. J., & Hubbe, M. (2023). Emerging inequality in the San Pedro de Atacama