Parametric Tests in MerQur: The Full Family from One-Sample t-Test to MANOVA
DOI:
https://doi.org/10.53463/merqur.20260445Keywords:
parametric tests, t-test, ANOVA, MANOVA, bootstrapAbstract
Parametric tests are a family of methods that test hypotheses about population parameters under the assumption that observations follow a parametric distribution (typically normal). Still the most frequently used analysis type in academic research, parametric tests — when applied correctly — provide the methods with the highest statistical power. This study introduces in detail the 11 analyses offered under the Parametric Tests category of MerQur: one-sample t-test, independent two-sample t-test, paired t-test, one-way ANOVA, two-way ANOVA, repeated-measures ANOVA, MANOVA, ANCOVA, bootstrap confidence interval, permutation test, and multiple-comparison correction. For each analysis, the following are presented: (i) the hypothesis tested and application context, (ii) required assumptions (normality, homogeneity of variance, independence, sphericity), (iii) form fields and parameter options in MerQur, (iv) reported statistics and effect sizes, and (v) an interpretation guide for a typical research question. Bootstrap CI and permutation tests are included in the same category as they offer resampling-based alternatives when assumptions of classical parametric tests are violated. The multiple-comparison correction section discusses Bonferroni, Holm, Hochberg, Benjamini-Hochberg (FDR), and Sidak methods together with appropriate-use criteria. Overall, MerQur’s Parametric Tests category presents a wide research spectrum — from simple group comparison to multivariate designs with covariates — together with assumption checks and effect sizes within a single graphical interface.
References
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.
Delacre, M., Lakens, D., & Leys, C. (2017). Why psychologists should by default use Welch’s t-test instead of Student’s t-test. International Review of Social Psychology, 30(1), 92–101. https://doi.org/10.5334/irsp.82
Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7(1), 1–26. https://doi.org/10.1214/aos/1176344552
Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. Chapman & Hall.
Fisher, R. A. (1925). Statistical methods for research workers. Oliver & Boyd.
Greenhouse, S. W., & Geisser, S. (1959). On methods in the analysis of profile data. Psychometrika, 24(2), 95–112. https://doi.org/10.1007/BF02289823
Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis. Academic Press.
Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6(2), 65–70.
Huynh, H., & Feldt, L. S. (1976). Estimation of the Box correction for degrees of freedom from sample data in randomized block and split-plot designs. Journal of Educational Statistics, 1(1), 69–82. https://doi.org/10.3102/10769986001001069
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863
Mauchly, J. W. (1940). Significance test for sphericity of a normal n-variate distribution. Annals of Mathematical Statistics, 11(2), 204–209. https://doi.org/10.1214/aoms/1177731915
Nuijten, M. B., Hartgerink, C. H. J., van Assen, M. A. L. M., Epskamp, S., & Wicherts, J. M. (2016). The prevalence of statistical reporting errors in psychology (1985–2013). Behavior Research Methods, 48(4), 1205–1226. https://doi.org/10.3758/s13428-015-0664-2
Olejnik, S., & Algina, J. (2003). Generalized eta and omega squared statistics: Measures of effect size for some common research designs. Psychological Methods, 8(4), 434–447. https://doi.org/10.1037/1082-989X.8.4.434
Pernet, C. R., Wilcox, R., & Rousselet, G. A. (2013). Robust correlation analyses: False positive and power validation using a new open source matlab toolbox. Frontiers in Psychology, 3, 606. https://doi.org/10.3389/fpsyg.2012.00606
Phipson, B., & Smyth, G. K. (2010). Permutation P-values should never be zero: Calculating exact P-values when permutations are randomly drawn. Statistical Applications in Genetics and Molecular Biology, 9(1), 39. https://doi.org/10.2202/1544-6115.1585
Pituch, K. A., & Stevens, J. P. (2016). Applied multivariate statistics for the social sciences (6th ed.). Routledge.
Rice, W. R. (1989). Analyzing tables of statistical tests. Evolution, 43(1), 223–225. https://doi.org/10.1111/j.1558-5646.1989.tb04220.x
Šidák, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions. Journal of the American Statistical Association, 62(318), 626–633. https://doi.org/10.2307/2283989
Tabachnick, B. G., & Fidell, L. S. (2019). Using multivariate statistics (7th ed.). Pearson.
Tukey, J. W. (1949). Comparing individual means in the analysis of variance. Biometrics, 5(2), 99–114. https://doi.org/10.2307/3001913
Welch, B. L. (1947). The generalization of “Student’s” problem when several different population variances are involved. Biometrika, 34(1–2), 28–35. https://doi.org/10.1093/biomet/34.1-2.28
Downloads
Published
Issue
Section
License
Copyright (c) 2026 MerQur
This work is licensed under a Creative Commons Attribution 4.0 International License.
This article is published under a Creative Commons Attribution 4.0 International License (CC-BY 4.0). Under this license you may:
- Share: Copy and redistribute the material in any medium or format.
- Adapt: Remix, transform and build upon the material for any purpose, including commercial use.
- Attribution: You must give appropriate credit, provide a link to the license, and indicate if changes were made.
