One-Way ANOVA
One-Way ANOVA is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Education Sciences sample dataset — how the analysis is run, what the MerQur output looks like, and how the result is reported in APA 7 format.
🎯 What is it for?
One-Way ANOVA automatically applies all necessary assumption checks (normality, homogeneity of variance, etc.) for the relevant data type in the background and presents the results with a clear table + chart. Automated interpretation to the APA 7 standard, effect sizes such as Cohen’s d/η²/R², and 95% confidence intervals are reported.
📌 When is it used?
- Statistical analysis of measurements in the Education Sciences domain
- To produce APA 7-compatible result tables for academic publications
- Hypothesis testing and decision-making processes
- Undergraduate / master’s / PhD theses after the appropriate method has been selected
📐 Assumptions
- Appropriate scale — Variables must be at the measurement level required by the analysis (nominal/ordinal/interval/ratio)
- Independent observations — Observations must come from individuals independent of one another
- Sufficient sample size — The minimum n requirement for the analysis must be met
- Outlier check — Outliers must be detected and evaluated
If assumptions are violated, MerQur automatically suggests a non-parametric or robust alternative.
🛠 How to do it in MerQur
Load the data. Select the sample file from File → Open. MerQur auto-detects column types.
Select the analysis. From the left side select One-Way ANOVA.
Panel assignments (form fields in the program):
- Group Column:
ogretim_yontemi - Value Column:
sinif - Post-hoc:
tukey
Optional settings. Effect size ✓ · 95% confidence interval ✓ · Assumption checks (automatic).
▶ Run — click the button. Results are produced automatically as a table + chart.
📄 Export to Word. APA 7-formatted report with italic statistical symbols.
📊 Sample Dataset — Education Sciences
ℹ Note: The scenario, MerQur output and interpretation below were produced by actually running the real example dataset in MerQur. Numeric results on your own data will differ; the goal is to show how the analysis is set up and interpreted end-to-end.
🎬 Example File
This analysis is demonstrated on the following example dataset for Education Sciences:
Egitim_Bilimleri/06_anova_instruction_method.xlsx
🎬 Scenario
Suppose we want to know whether teaching method affects achievement. 140 students each received one of four instruction methods: traditional, cooperative, project, or mixed (blended), and we recorded their achievement score afterward. The question is whether mean achievement differs across these four methods. We use one-way ANOVA because the outcome is continuous and the predictor is a single categorical factor with several levels.
⚙️ Variable Selection
- Factor (group): instruction_method (traditional, cooperative, project, mixed (blended))
- Dependent variable: achievement_score
- >> ADVANCED PARAMETERS (optional in the form — what they do):
- ANOVA variant: Classic (Fisher) or Welch (robust to unequal variances).
- Effect sizes: omega-squared and epsilon-squared (less biased than eta-squared).
- Assumptions: Levene, Bartlett, per-group Shapiro.
- Descriptives per group; post-hoc (Tukey/Duncan/Bonferroni/Scheffe/Games-Howell).
Data Preview (First 5 Rows)
| student_id | instruction_method | achievement_score | class |
|---|---|---|---|
| 1 | traditional | 73.0 | 10 |
| 2 | traditional | 62.5 | 12 |
| 3 | traditional | 74.2 | 11 |
| 4 | traditional | 68.4 | 10 |
| 5 | traditional | 59.9 | 9 |
n = 140 · Columns: student_id, instruction_method, achievement_score, class
📈 MerQur Output
💬 Interpretation
We compared the effect of four instruction methods on achievement with one-way ANOVA. The result is significant (F(3,136) = 18.00, p < .001), effect size η² = 0.28 — about 28% of achievement is explained by instruction method, a strong effect in educational research. ANOVA says at least one method differs from the others; a post-hoc test is needed to see which. “Which instruction method is more effective” is one of the most basic research questions in education; ANOVA is the standard way to answer it across multiple groups. >> ADVANCED PARAMETERS (optional in the form — what they do): – ANOVA variant: Classic (Fisher) or Welch (robust to unequal variances). – Effect sizes: omega-squared and epsilon-squared (less biased than eta-squared). – Assumptions: Levene, Bartlett, per-group Shapiro. – Descriptives per group; post-hoc (Tukey/Duncan/Bonferroni/Scheffe/Games-Howell).
⚠ Common Mistakes
- Misidentifying the data type (e.g., loading a categorical variable as numeric)
- Skipping assumption checks and going straight to the p-value
- Failing to report effect size — APA 7 requires both p and effect size
- Failing to apply a Type I error correction (Bonferroni/Tukey) in multiple comparisons
- Not switching to a non-parametric alternative when n is insufficient
📹 Video Walkthrough
Watch the video below for an end-to-end walkthrough of this analysis on a Education Sciences file.
▶ One-Way ANOVA — video walkthrough
This section is part of the Veriye İlk Bakış ve Parametrik Testler video (14 analyses in one video). The link below jumps straight to 10:59, where this analysis begins. Narration is in Turkish.
🧪 Natural Sciences & Mathematics · 🏛 Architecture, Planning & Design · ⚙ Engineering · 🏥 Health Sciences · 📊 Social, Humanities & Admin Sciences · 🏃 Sport Sciences · 🌾 Agriculture, Forestry & Aquatic
📚 If You Used This Analysis, Cite MerQur
If you performed this analysis using MerQur in a scientific study, please use the citation below as part of your academic citation obligations (APA 7):
Örücü, Ö. K. (2026). MerQur: Integrated Academic Data Analysis & Reporting Platform [Computer software] (Version 1.0.0). https://doi.org/10.53463/merqur.2026001
For BibTeX, RIS, EndNote and the English citation form: all citation formats →
- American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.).
- Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). Sage.
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.