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One-way ANOVA
Do exam scores differ between three self-study formats? 60 students were randomly allocated to Lecture recordings, Worked examples or Practice quizzes (20 per format), studied on their own for two weeks, then sat the same exam.
Only the parts of the output needed to read this result are shown. Where SPSS prints more, a note under the table says what has been left out and why.
| N | Mean | Std. Deviation | Std. Error | 95% Confidence Interval for Mean | Minimum | Maximum | ||
|---|---|---|---|---|---|---|---|---|
| Lower Bound | Upper Bound | |||||||
| Lecture recordings | 20 | 1.613 | 56.22 | 62.98 | 40 | 74 | ||
| Worked examples | 20 | 1.810 | 64.76 | 72.34 | 54 | 84 | ||
| Practice quizzes | 20 | 2.003 | 63.66 | 72.04 | 51 | 85 | ||
| Total | 60 | 65.33 | 8.972 | 1.158 | 63.02 | 67.65 | 40 | 85 |
| Levene Statistic | df1 | df2 | Sig. | ||
|---|---|---|---|---|---|
| Exam score | Based on Mean | 2 | 57 | ||
Selected output. Not shown: the Based on Median, Based on Median and with adjusted df, and Based on trimmed mean rows. SPSS prints these too, but only the mean-based version has been independently calculated for this example.
| Sum of Squares | df | Mean Square | F | Sig. | |
|---|---|---|---|---|---|
| Between Groups | |||||
| Within Groups | |||||
| Total | 4749.333 | 59 |
| Point Estimate | ||
|---|---|---|
| Exam score | Eta-squared | |
Selected output. Not shown: the 95% confidence interval columns, and the Epsilon-squared and Omega-squared rows. SPSS prints these, but its calculation methods for them have not yet been independently confirmed, so they are left out rather than risk showing an incorrect value.
| (I) Format | (J) Format | Mean Difference (I-J) | Std. Error | Sig. | 95% Confidence Interval | |
|---|---|---|---|---|---|---|
| Lower Bound | Upper Bound | |||||
| Lecture recordings | Worked examples | 2.568 | -15.129 | -2.771 | ||
| Practice quizzes | 2.568 | -14.429 | -2.071 | |||
| Worked examples | Lecture recordings | 2.568 | 2.771 | 15.129 | ||
| Practice quizzes | 2.568 | -5.479 | 6.879 | |||
| Practice quizzes | Lecture recordings | 2.568 | 2.071 | 14.429 | ||
| Worked examples | 2.568 | -6.879 | 5.479 | |||
*. The mean difference is significant at the 0.05 level.
Selected output. Not shown: the Homogeneous Subsets table, which SPSS also prints for Tukey HSD. The Multiple Comparisons table above contains the same comparisons.
End of the Multiple Comparisons table
About this example
Randomised between-subjects design: 60 students were randomly allocated to one of three self-study formats, 20 per format. Each student used one format only and studied on their own, so the scores are independent. Exam scores could range from 0 to 100. One student in the Lecture recordings group scored well below the rest of that group (40). The score is plausible, so it was kept; the conclusions do not change when it is removed.
Limitations
- The data are simulated for teaching.
- How closely students followed their format was not measured.
- The study used one course and one exam only, so the results may not apply to other subjects or assessments.
- A statistically significant F does not mean that every pair of formats differs; only the Tukey comparisons show which pairs differ.
What can be concluded
Because students were randomly allocated, the statistically significant differences support a causal interpretation within the limitations above: the format may have contributed to the differences, with students using Worked examples or Practice quizzes scoring higher on average than students using Lecture recordings. The difference between Worked examples and Practice quizzes is not statistically significant, and this does not show that those two formats are equally effective. Report the result cautiously: give the ANOVA result and effect size, then the Tukey comparisons that show where the differences lie.
Working on your own one-way ANOVA?
This Explorer is a free teaching resource. Its examples use simulated data, and it does not run analyses or look at your own output.
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