Best examples of factorial ANOVA examples: practical applications in real research

Let’s skip the theory lecture and start where most people get stuck: “What does this look like in actual data?” Here are several real examples of factorial ANOVA examples: practical applications, each showing how multiple factors come together in a single study.

1. Health research: Exercise type × Diet on blood pressure

Public health studies often involve multiple lifestyle factors. A classic example of factorial ANOVA in practice is examining how exercise type and diet jointly influence blood pressure.

• Dependent variable (DV): Systolic blood pressure after 12 weeks
• Factor A: Exercise type (aerobic vs. resistance)
• Factor B: Diet type (Mediterranean vs. low-fat vs. usual diet)

Researchers might randomly assign adults with prehypertension to one of six groups (2 × 3 design). A factorial ANOVA lets them test:

• Main effect of exercise type: On average, do aerobic and resistance training differ in their impact on blood pressure?
• Main effect of diet: Is there an overall difference among Mediterranean, low-fat, and usual diet?
• Interaction effect (exercise × diet): Does the benefit of a Mediterranean diet depend on whether participants are doing aerobic or resistance exercise?

A realistic outcome: both exercise and diet show significant main effects, but the interaction reveals that the largest drop in blood pressure occurs specifically for people doing aerobic exercise combined with a Mediterranean diet. That interaction is exactly the kind of pattern factorial ANOVA is built to detect.

If you want to see how real lifestyle factors are studied in combination (even when they use regression instead of ANOVA), check out the National Heart, Lung, and Blood Institute at the NIH: https://www.nhlbi.nih.gov

This is one of the best examples of factorial ANOVA examples: practical applications because it’s easy to visualize and directly relevant to public health decisions.

2. Clinical psychology: Therapy type × Medication on depression scores

In mental health research, factorial designs are everywhere. A typical example of a 2 × 2 factorial ANOVA design looks like this:

• DV: Depression severity after 16 weeks (e.g., PHQ-9 score)
• Factor A: Therapy type (cognitive behavioral therapy vs. supportive counseling)
• Factor B: Medication use (antidepressant vs. placebo)

Now we have four groups:

• CBT + antidepressant
• CBT + placebo
• Supportive counseling + antidepressant
• Supportive counseling + placebo

A factorial ANOVA tests whether CBT is better than supportive counseling on average (main effect of therapy), whether medication helps on average (main effect of medication), and whether the combination of CBT and medication does something more than the sum of its parts (interaction).

A common real pattern: medication and CBT each show benefits on their own, but the interaction is significant because the combination produces the largest reduction in depression scores, especially for patients starting with severe symptoms. That interaction is critical for treatment guidelines.

For context on depression measures and treatments, the National Institute of Mental Health is a solid starting point: https://www.nimh.nih.gov

3. Education: Teaching method × Class size on math performance

Education researchers love factorial designs because classrooms are messy. One of the most practical examples of factorial ANOVA examples: practical applications in education is examining how teaching method and class size affect test scores.

• DV: End-of-semester math test score
• Factor A: Teaching method (traditional lecture vs. active learning)
• Factor B: Class size (small: ≤ 20 students vs. large: ≥ 60 students)

This 2 × 2 factorial ANOVA answers questions like:

• Is active learning better than traditional lecture overall?
• Are small classes better than large classes overall?
• Does active learning pay off more in small classes than in large ones (interaction)?

A realistic result: active learning shows a significant main effect (higher scores overall), small classes show a main effect, and the interaction indicates that active learning in small classes produces the biggest gains, while in large classes the difference between methods is smaller.

For real-world data on class size and outcomes, you can explore resources from the National Center for Education Statistics: https://nces.ed.gov

This is one of the best examples of factorial ANOVA examples: practical applications for anyone working in curriculum design or education policy.

4. Marketing analytics: Ad format × Discount level on purchase rate

In 2024–2025, marketing teams are running A/B/n tests constantly, and many of those experiments are factorial in spirit even if they’re analyzed with logistic regression. A clean factorial ANOVA setup looks like this (assuming a continuous DV like spending per visitor):

• DV: Dollars spent per website visitor during a campaign
• Factor A: Ad format (static image vs. short video vs. interactive quiz)
• Factor B: Discount level (no discount vs. 10% vs. 25%)

This 3 × 3 design lets you estimate:

• Main effect of ad format (which style generally drives higher spending?)
• Main effect of discount (how much does each discount level increase spending?)
• Interaction: does the impact of a 25% discount depend on whether the ad is a video or an interactive quiz?

Suppose the factorial ANOVA finds:

• Video and interactive ads outperform static images overall.
• 25% discounts increase average spend, but mostly when paired with interactive quizzes.

That interaction tells you not to treat “discount” as a one-size-fits-all lever. Instead, you pair higher discounts with more engaging formats to get the best return.

5. Manufacturing quality: Machine setting × Material type on defect rate

In industrial and manufacturing settings, factorial ANOVA is a workhorse. Here’s a practical example of factorial ANOVA examples: practical applications for process optimization.

• DV: Number of defects per 1,000 units (or defect percentage)
• Factor A: Machine temperature setting (low vs. medium vs. high)
• Factor B: Material type (Supplier A vs. Supplier B)

Engineers might run a controlled experiment where each combination of temperature and material is tested in multiple batches. A factorial ANOVA evaluates:

• Main effect of temperature: which temperature setting yields fewer defects overall?
• Main effect of material: is one supplier’s material more stable?
• Interaction: does one supplier’s material only perform well at specific temperatures?

A typical real outcome: Supplier B looks fine at medium and high temperature, but at low temperature the defect rate spikes. The interaction effect is the statistical fingerprint of that pattern. Without a factorial design, you might incorrectly blame either the machine or the supplier alone.

For more on designed experiments and factorial designs in industry, the NIST Engineering Statistics Handbook is a gold mine: https://www.itl.nist.gov/div898/handbook/

6. UX and product research: Interface theme × Device type on task time

UX teams increasingly run structured experiments, especially as dark mode, responsive layouts, and cross-device usage have exploded.

Consider this example of a 2 × 3 factorial ANOVA:

• DV: Time to complete a checkout task (in seconds)
• Factor A: Interface theme (light mode vs. dark mode)
• Factor B: Device type (desktop vs. tablet vs. phone)

Researchers recruit participants, randomly assign them to a theme, and then have them complete the same task on a specific device.

The factorial ANOVA can reveal:

• Main effect of theme: Is dark mode generally faster or slower than light mode?
• Main effect of device: Are phones slower than desktops overall?
• Interaction: Does dark mode help on phones but hinder on desktops?

A realistic pattern: dark mode slightly improves task time on phones (better contrast in bright environments) but slows people down on desktop monitors, leading to a significant interaction. Product teams can then decide to enable dark mode by default on mobile but not on desktop.

This is one of the more modern examples of factorial ANOVA examples: practical applications, reflecting how digital products are tested in 2024–2025.

7. Public health behavior: Message framing × Demographic group

Public health campaigns often need to tailor messages to different populations. A factorial ANOVA can analyze how message framing interacts with demographic factors.

• DV: Intention to get vaccinated (measured on a 1–7 scale)
• Factor A: Message framing (gain-framed: benefits vs. loss-framed: risks of not vaccinating)
• Factor B: Age group (18–29 vs. 30–49 vs. 50+)

A 2 × 3 factorial ANOVA tests whether one framing works better overall and whether that effect changes by age group.

A plausible result: gain-framed messages work better overall, but the interaction shows that loss-framed messages are more effective among younger adults, while older adults respond more to gain-framed content. That interaction feeds directly into how public health agencies design campaigns.

For real-world health communication examples and data, see the CDC’s communication resources: https://www.cdc.gov

Why factorial ANOVA instead of multiple one-way ANOVAs?

All of these real examples of factorial ANOVA examples: practical applications have something in common: you are not just interested in separate questions like:

• “Does exercise type matter?”
• “Does diet matter?”

You want to know whether the effect of one factor depends on another. That’s the interaction term in factorial ANOVA.

If you ran multiple one-way ANOVAs instead of a factorial ANOVA:

• You’d miss the interaction completely.
• You’d inflate your Type I error rate by running extra tests.
• You’d waste the structure of your design, especially when you carefully crossed factors.

Factorial ANOVA uses all the data simultaneously to estimate:

• Main effect of each factor
• Interaction effects between factors

That’s why the best examples of factorial ANOVA examples: practical applications always involve at least two factors that might interact.

How to recognize a factorial ANOVA design in the wild

If you’re scanning a methods section and trying to figure out whether factorial ANOVA is appropriate, look for language like:

• “Participants were randomly assigned to one of four conditions defined by therapy type (CBT vs. supportive) and medication (drug vs. placebo).”
• “We used a 3 (ad format) × 3 (discount level) between-subjects design.”
• “We tested the interaction between teaching method and class size.”

Those are all signals that you’re seeing real examples of factorial ANOVA examples: practical applications, even if the authors eventually analyze with generalized linear models or mixed-effects models instead of a classic ANOVA table.

A quick mental checklist:

• Is the dependent variable continuous (or approximately so)?
• Are there two or more categorical predictors (factors)?
• Are all combinations of factor levels represented (or at least planned)?

If yes, you’re looking at a factorial design, and factorial ANOVA (or its modern cousins) is usually the right starting point.

Common pitfalls when using factorial ANOVA in practice

Even in the best examples of factorial ANOVA examples: practical applications, a few problems show up again and again:

Unbalanced cells
If some combinations (e.g., active learning + large class) have far fewer observations than others, estimates of interaction effects can get noisy. Real-world data rarely look like perfect textbook examples, so check your cell sizes.

Ignoring interaction when it matters
Researchers sometimes report only main effects because the interaction is “complicated.” That’s a mistake. If the interaction is significant, it often changes the story: for example, a treatment that looks helpful overall might actually hurt a specific subgroup.

Over-interpreting non-significant effects
If you don’t have many participants in each cell, you may simply lack power to detect real interactions. A non-significant interaction isn’t proof that “there is no interaction”; it may just mean “we can’t tell with this sample.”

Violating assumptions
Standard factorial ANOVA relies on assumptions like normality of residuals and equal variances across groups. In 2024–2025, most analysts will quickly check these with residual plots or use more flexible models (e.g., linear mixed models) if needed, but the logic of factors and interactions stays the same.

For a deeper statistical treatment, university stats pages like UCLA’s IDRE (https://stats.oarc.ucla.edu) offer accessible walkthroughs of factorial ANOVA.

FAQ: examples of factorial ANOVA in real work

Q1. What is a simple example of factorial ANOVA in everyday business?
A straightforward business-focused example of factorial ANOVA is testing store layout (standard vs. experimental) and music type (no music vs. soft background vs. upbeat) on average dollars spent per customer. You’d use a 2 × 3 factorial ANOVA to see whether layout and music each affect spending and whether certain layouts work better with specific music types.

Q2. Can factorial ANOVA handle more than two factors?
Yes. You can have three or more factors (for example, teaching method × class size × school type). In practice, once you get past two or three factors, the interaction patterns become hard to interpret, and many researchers switch to regression or mixed models. But the logic is the same: you’re still studying how the effect of one factor changes across levels of others.

Q3. Are there repeated-measures examples of factorial ANOVA?
Definitely. A common repeated-measures example of factorial ANOVA is a study where time (pre vs. post vs. follow-up) is one factor, and treatment group (e.g., therapy vs. control) is another. Participants are measured at multiple time points, so time is a within-subject factor, and treatment is a between-subject factor. This is often called a mixed-design ANOVA.

Q4. How do I report factorial ANOVA results clearly?
Most journals expect you to report F-statistics, degrees of freedom, p-values, and an effect size (such as partial eta-squared) for each main effect and interaction. For example: “There was a significant interaction between exercise type and diet on systolic blood pressure, F(2, 174) = 4.12, p = .018, partial η² = .045.” Then you follow up with plots or tables that make the interaction interpretable.

Q5. Where can I find more real examples of factorial ANOVA examples: practical applications?
Look at methods sections in peer-reviewed papers in psychology, education, or health sciences. Many introductory stats courses also publish example datasets online. University sites like Harvard’s quantitative methods resources or UCLA’s stats pages often include worked examples, code, and interpretation guides.

If you keep these examples of factorial ANOVA examples: practical applications in mind, the method stops feeling abstract and starts looking like what it actually is: a powerful way to ask “Does it depend?” when you have more than one factor in your study design.