Does job satisfaction differ between teachers holding a diploma, a bachelor’s degree and a master’s degree? When the independent variable has three or more categories, running a t-test for every pair is the wrong approach: three comparisons raise the probability of at least one false positive from 5% to about 14%. The correct route is a one-way analysis of variance (ANOVA), followed by a post hoc test that identifies which groups differ. This guide explains the assumptions, the SPSS steps, how to read the ANOVA table and compute eta squared, how Tukey, Scheffé, LSD, Bonferroni and Games-Howell differ and when each is appropriate, and how to report the result in APA style, ending with the errors examiners mark most often.
This article is part of our guide How to Write a Master’s Thesis by the Mastermind PhD team and relates to our Statistical Analysis service. Sources last checked: November 2026.
What is one-way ANOVA? One-way analysis of variance is a parametric test that compares the means of three or more independent groups on a continuous dependent variable. It partitions the total variability in the scores into variability between groups and variability within groups; their ratio is the F statistic. A significant F means that at least one group mean differs from another, but not which one. Identifying the specific pairs requires a post hoc test, which adjusts for the number of comparisons made.
When should you use one-way ANOVA?
Use one-way ANOVA when you have one nominal independent variable with three or more independent categories (qualification, experience bands, faculty, three teaching methods) and one continuous dependent variable (a scale score, an achievement score). If two independent variables act together (gender and qualification), you need a two-way ANOVA, which also tests their interaction. If the same participants are measured three or more times (pre-test, post-test, follow-up), you need repeated measures ANOVA. If the dependent variable is ordinal or the groups are small and skewed, the Kruskal-Wallis test is the non-parametric alternative.
What are the assumptions and how do you check them?
| Assumption | How to check it | If it fails |
|---|---|---|
| Continuous dependent variable; three or more independent groups | Study design; averaged scale scores count as continuous | Kruskal-Wallis for ordinal data |
| Independence of observations | Each participant in exactly one group | A different design |
| Approximate normality within each group | Shapiro-Wilk, skewness and kurtosis per group (Explore with a factor) | Robustness if every group exceeds about 30; otherwise Kruskal-Wallis |
| Homogeneity of variance | Levene’s test in the output (use the row Based on Mean) | Welch’s ANOVA with Games-Howell post hoc tests |
| No influential outliers | Boxplot for each group | Correct entry errors; document any exclusion |
Group size matters in one-way ANOVA as well. A category of 7 participants beside one of 200 makes the comparison unstable. Merge small adjacent categories that make sense together (for example “under 5 years” with “5 to 10 years”) before the analysis, and say so in the methodology.
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How do you run one-way ANOVA in SPSS?
- Analyze, then Compare Means, then One-Way ANOVA.
- Move the dependent variable to Dependent List and the grouping variable to Factor.
- Options: tick Descriptive, Homogeneity of variance test, Welch and Means plot. In version 27 and later, also tick Estimate effect size for overall tests.
- Post Hoc: tick Tukey under Equal Variances Assumed and Games-Howell under Equal Variances Not Assumed, so that both are available once you have read Levene’s test.
- Click OK. The output contains Descriptives, Test of Homogeneity of Variances, ANOVA, ANOVA Effect Sizes (version 27 and later), Robust Tests of Equality of Means (Welch), Post Hoc Tests (Multiple Comparisons) and Homogeneous Subsets.
How do you read the ANOVA table and what follows it?
Test of Homogeneity of Variances. If Levene’s significance (Based on Mean) is greater than .05, variances are treated as equal and the standard one-way ANOVA table is read. If it is .05 or less, read the Welch row in Robust Tests of Equality of Means instead of the standard F, and use Games-Howell for the post hoc comparisons.
ANOVA. Three rows: Between Groups, Within Groups and Total, each with a sum of squares, degrees of freedom and mean square. F is the between-groups mean square divided by the within-groups mean square, and the Sig. column gives p. The degrees of freedom are written (k − 1, N − k), where k is the number of groups and N the total sample.
Effect size. Eta squared (η²) is the between-groups sum of squares divided by the total sum of squares; SPSS prints it in the ANOVA Effect Sizes table in recent versions. Cohen’s benchmarks, as summarized by Richardson (2011), are .01 small, .06 medium and .14 large. Always report it with F: a significant difference among five groups in a sample of 500 may explain 1% of the variance.
Which post hoc test should you choose?
| Test | When to use it | Character |
|---|---|---|
| Tukey HSD | Default choice with equal variances and similar group sizes; all pairwise comparisons | Balances protection against Type I error with power |
| Scheffé | Complex contrasts (one group versus two combined) or very unequal group sizes | The most conservative; detects fewer differences |
| LSD (Fisher’s protected) | Only three groups and only after a significant F | No adjustment; liberal, criticized with four or more groups |
| Bonferroni | A small number of comparisons specified in advance | Divides alpha by the number of comparisons; conservative |
| Games-Howell | Unequal variances or clearly unequal group sizes | Does not assume equal variances; most accurate in that situation |
| Dunnett | Each experimental group against one control group | Designed for that purpose only |
The practice examiners accept after a one-way ANOVA: Tukey when variances are equal, Games-Howell when they are not, Scheffé if your supervisor wants the most conservative option or you need complex contrasts. Choose one test, justify it, and report it. Running three post hoc tests and reporting the one that produced differences is selective reporting.
The Multiple Comparisons table lists, for every pair of groups, the mean difference, its standard error, the adjusted p value and a confidence interval; pairs flagged with an asterisk or with p below .05 differ significantly. The Homogeneous Subsets table places groups that do not differ in the same column, which is useful for a visual summary.
Worked example: qualification and job satisfaction
A sample of 300 teachers divided by qualification: diploma (n = 48), bachelor’s degree (n = 171), master’s degree or higher (n = 81). Descriptives: diploma M = 3.45, SD = 0.80; bachelor’s M = 3.68, SD = 0.74; master’s M = 3.88, SD = 0.62. Levene’s test p = .23, so variances are equal and the standard table is read.
ANOVA table: between groups SS = 5.69, df = 2, MS = 2.85; within groups SS = 153.9, df = 297, MS = 0.52; F = 5.49, p = .005. Eta squared = 5.69 ÷ (5.69 + 153.9) = .036, so qualification explains 3.6% of the variance in satisfaction, a small-to-medium effect.
Tukey HSD: master’s versus diploma, difference = 0.43, p = .003 (significant); bachelor’s versus diploma, difference = 0.23, p = .11; master’s versus bachelor’s, difference = 0.20, p = .09. The Homogeneous Subsets table places the diploma group in the first subset, the master’s group in the second, and the bachelor’s group in both.
APA sentence: “A one-way ANOVA showed a significant effect of qualification on job satisfaction, F(2, 297) = 5.49, p = .005, η² = .036. Tukey HSD comparisons indicated that teachers with a master’s degree or higher (M = 3.88, SD = 0.62) reported higher satisfaction than diploma holders (M = 3.45, SD = 0.80), p = .003; the remaining pairwise differences were not significant.” Comment on the comparison that approached significance without calling it significant. Had Levene’s test been significant, the sentence would read: “Welch’s F(2, 141.3) = 4.87, p = .009, with Games-Howell post hoc comparisons.”
How do you present the results in APA style?
In the thesis you normally present two tables. The first gives the descriptives for each group (n, M, SD). The second is the ANOVA table with source of variation, SS, df, MS, F, p and η², with the significant post hoc pairs listed below it or in a third table; the full Multiple Comparisons table can go in an appendix. Follow APA 7 number rules: two decimals for means, standard deviations, F and η² (three for η² if the second decimal is zero), exact p values to two or three decimals, and p < .001 instead of .000. Italicize F, df, p, M, SD and n, but not η².
Which mistakes do examiners mark most often?
- Running post hoc tests after a non-significant F. Post hoc comparisons follow a significant overall result, except for contrasts planned in advance.
- Reading the standard ANOVA table when Levene’s test was significant, instead of the Welch row.
- Using LSD with five or more groups without any adjustment.
- Omitting η², or interpreting it as a percentage of participants rather than of variance.
- Analyzing a qualification variable that contains a category of five people without merging or comment.
- Writing the degrees of freedom incorrectly; the pair is (between groups, within groups), not the total sample size.
- Reporting three post hoc tests and discussing only the one that showed differences.
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Frequently asked questions
What is the difference between one-way and two-way ANOVA?
One-way ANOVA has a single independent variable with several categories. Two-way ANOVA has two independent variables (gender and qualification) and tests, in addition to each main effect, their interaction. If your question is “does the effect of qualification differ between men and women”, you need the two-way design.
Should I use ANOVA or Kruskal-Wallis for Likert-scale scores?
Averaged scale scores are treated as continuous and analyzed with one-way ANOVA when the distribution is acceptable and each group has roughly 30 or more cases. Use Kruskal-Wallis when groups are small, when the distribution is clearly skewed, or when the variable is a single Likert item.
F is significant but Tukey shows no significant pair. What now?
This happens when small differences are spread across several groups. Report the result as it is, inspect the Homogeneous Subsets table, consider Games-Howell if variances differ, or a Scheffé contrast if you have a theoretical reason to combine groups. Do not switch to LSD simply to obtain a significant pair.
How do I choose between Tukey and Scheffé if my supervisor asks for one of them?
Both are acceptable with equal variances. Tukey is more powerful for pairwise comparisons; Scheffé is more conservative and suits complex contrasts and very unequal group sizes. Following your supervisor’s request and documenting the reason matters more than the choice itself.
Can I run ANOVA with only two groups?
Yes, and the result is identical to the independent samples t-test (*F* = *t*²). The convention in theses is to use the t-test for two groups and ANOVA for three or more, because the t-test shows the direction of the difference directly.
Sources
- 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.
- Richardson, J. T. E. (2011). Eta squared and partial eta squared as measures of effect size in educational research. Educational Research Review, 6(2), 135–147. https://doi.org/10.1016/j.edurev.2010.12.001
- Pallant, J. (2020). SPSS Survival Manual (7th ed.). Open University Press.
- Laerd Statistics. One-way ANOVA using SPSS Statistics. https://statistics.laerd.com/spss-tutorials/one-way-anova-using-spss-statistics.php
- IBM. IBM SPSS Statistics documentation: One-Way ANOVA and Post Hoc Multiple Comparisons. https://www.ibm.com/docs/en/spss-statistics
- American Psychological Association. (2020). Publication Manual of the American Psychological Association (7th ed.).
Sources last checked: November 2026. This article is general educational guidance and does not replace your university regulations or your supervisor’s instructions. How we prepare our content.