Two-Way ANOVA vs Repeated Measures ANOVA vs Mixed-Effects Models: Which One Fits Your Experiment?
2 days ago
5 min read
If every measurement comes from a different animal, use ordinary two-way ANOVA. If the same animals are measured at every time point and nothing is missing, use repeated measures ANOVA. If they are measured repeatedly and even one value is missing, use a mixed-effects model. The two-way ANOVA vs repeated measures ANOVA decision turns on one question: was anything measured more than once?
Choosing wrong costs you in both directions: treat repeated measurements as independent and false positives multiply; run repeated measures ANOVA on incomplete data and it quietly discards whole animals. Below is how to match the model to your design, and how to set each up in GraphPad Prism.
Two-way ANOVA vs repeated measures ANOVA: one question decides it
Ordinary two-way ANOVA assumes every value is independent: one animal, one measurement. Weigh the same mouse at weeks 5, 9 and 13 and that assumption breaks, because a heavy mouse at week 5 is still a heavy mouse at week 13. Its three values carry less information than three different mice would.
Repeated measures ANOVA puts that dependence to work. Each animal becomes its own baseline, so stable differences between animals drop out of the error term.
Your design | Model | Prism Model tab |
Each animal measured once, in one group | Ordinary two-way ANOVA | "No matching. Use regular two-way ANOVA (not repeated measures)." |
Same animals measured at every time point, no missing values | Repeated measures two-way ANOVA | "Each row represents a different time point, so matched values are stacked into a subcolumn." |
Same animals measured repeatedly, any value missing | Mixed-effects model | Same choice; Prism fits a mixed-effects model automatically |
Many cells or neurons recorded per animal | Multilevel model with animal as a random effect | Not a two-way design |
What the wrong model costs you
Too lenient. Treat repeated measurements as independent and every extra reading masquerades as an extra animal. Of 314 papers in five leading neuroscience journals, 53% contained data like this, and ignoring the dependence can push the false-positive rate as high as 80% against a nominal 5%.
Real data show how far apart the answers land. Calcium event frequencies from 1,724 neurons, pooled across four mice, gave p = 4.8 × 10⁻⁶ for a change between 24 and 48 hours. A mixed-effects model on the same data gave p = 0.42. One mouse had contributed 43% of the cells. CLYTE's pseudoreplication guide covers prevention at the design stage.
Too strict. Repeated measures ANOVA needs complete data, and a single missing value removes the whole animal. Take 30 mice in three groups, weighed at weeks 5, 9 and 13, with ten weigh-ins missing across nine mice. Repeated measures ANOVA analyzes the 21 complete mice. A mixed-effects model uses all 80 measurements from all 30. In this simulated data set, it is the only approach that detects the week-5 difference between groups 2 and 3.
The right model can also be more powerful. Readings taken from the same cells before and after a treatment are positively correlated, so their difference is less noisy than two independent values. Treating the pairs as independent gave p = 0.0036. The mixed-effects model, which knows each pair belongs together, gave p = 0.0001. Correct modeling is sometimes stricter and sometimes more sensitive, and always more accurate.
When repeated measures ANOVA is not enough: mixed-effects models
A mixed-effects model treats each animal as a random draw from the population rather than a fixed category, and estimates the treatment effect from every measurement that exists. With complete data it matches repeated measures ANOVA. With missing values it keeps the animals ANOVA would discard, and it tolerates animals measured at slightly different times.
It does not rescue a thin design. With only two to four animals, a random effect for animal adds little. Power in a repeated design comes from more independent animals, not more readings per animal.
"Mixed ANOVA" and "mixed-effects model" are different things
The shared word causes constant confusion. A mixed ANOVA (also called a mixed-design or split-plot ANOVA) is still an ANOVA: it has one between-animal factor, such as genotype, and one within-animal factor, such as time. A mixed-effects model (also called a multilevel or hierarchical model) is a different estimation method with fixed and random effects.
A genotype-by-time experiment is a mixed design and can be analyzed either way. When a reviewer asks whether you used a mixed model, check which one they mean.
Setting up each model in Prism
Enter a Grouped table with time points as rows, groups as columns, and one subcolumn per animal, keeping each animal in the same subcolumn on every row. On the Model tab, pick the option from the table above. GraphPad warns that the wrong repeated-measures layout produces very misleading results, so confirm the option matches where your matched values sit.
For measurements over time, do not assume sphericity, the assumption that differences between every pair of time points have equal variance. Neighboring time points usually correlate more strongly than distant ones, so time courses tend to violate it. Declining the assumption applies the Geisser–Greenhouse correction, which only reduces the degrees of freedom and so raises the p-value.
If any value is missing, Prism fits a mixed-effects model in place of repeated measures ANOVA and reports it as such. Prism's version is deliberately narrow, with no covariates or custom covariance structures, so designs that need those, including many cells per animal, need a dedicated multilevel model. For a quick check, describe your design to Soφ in plain English: "three groups, ten mice each, weighed at weeks 5, 9 and 13, two weigh-ins missed."
Two-way ANOVA vs repeated measures ANOVA is a design decision you make at the bench
Whether your values are independent is settled the moment you decide which animals get measured when. Choose the model then. Power the study on animals rather than readings, and plan for missing values, because in a time course they almost always appear.
Designing the time course now?
Frequently asked questions
What is the difference between two-way ANOVA and repeated measures ANOVA? Two-way ANOVA assumes every measurement comes from a different subject. Repeated measures ANOVA is for the same subjects measured at several time points or conditions, using each as its own baseline.
What happens if I run repeated measures ANOVA with missing data? Every subject with any missing value is dropped entirely. A mixed-effects model keeps them.
Is a mixed ANOVA the same as a mixed-effects model? No. A mixed ANOVA has one between-subject and one within-subject factor. A mixed-effects model is an estimation method that can analyze that design.
Can I average each animal's measurements and run ordinary ANOVA? For a single endpoint, yes: averaging restores independence. But it discards the time course and can miss differences at individual time points.
Should I assume sphericity? Not for measurements over time. Let the software apply the Geisser–Greenhouse correction.
References
Aarts E, Verhage M, Veenvliet JV, Dolan CV, van der Sluis S. A solution to dependency: using multilevel analysis to accommodate nested data. Nature Neuroscience, 2014;17(4):491–496.
Yu Z, Guindani M, Grieco SF, Chen L, Holmes TC, Xu X. Beyond t test and ANOVA: applications of mixed-effects models for more rigorous statistical analysis in neuroscience research. Neuron, 2022;110(1):21–35. DOI
Muhammad LN. Guidelines for repeated measures statistical analysis approaches with basic science research considerations. Journal of Clinical Investigation, 2023;133(11):e171058. DOI
Gueorguieva R, Krystal JH. Move over ANOVA: progress in analyzing repeated-measures data and its reflection in papers published in the Archives of General Psychiatry. Archives of General Psychiatry, 2004;61(3):310–317. PubMed
GraphPad Prism 11 Statistics Guide. The mixed model approach to analyzing repeated measures data; Model tab: Two-way ANOVA; Sphericity and compound symmetry.
