What is ANOVA?
ANOVA (Analysis of Variance) is used to compare means across three or more groups. It tests whether at least one group mean significantly differs from the others.
When to Use One-Way ANOVA
- Comparing satisfaction levels across 3+ departments
- Comparing performance scores across education levels (Bachelor, Master, PhD)
- Comparing attitudes across age groups
Example Hypothesis
"There are statistically significant differences in job satisfaction based on education level (Bachelor, Master, PhD)."
SPSS Steps: One-Way ANOVA
- Analyze → Compare Means → One-Way ANOVA
- Move dependent variable (e.g., Satisfaction_Avg) to "Dependent List"
- Move factor variable (e.g., Education) to "Factor"
- Click Post Hoc → check Scheffe (or LSD, Tukey)
- Click Options → check Descriptive and Homogeneity of variance test
- Click OK
Reading the Output
Step 1: Check Levene's Test (Homogeneity of Variances)
| Levene Statistic | Sig. |
|---|---|
| 1.234 | .298 |
Sig. = .298 > .05 → variances are equal → we can proceed with ANOVA ✓
Step 2: Read the ANOVA Table
| Source | Sum of Squares | df | Mean Square | F | Sig. |
|---|---|---|---|---|---|
| Between Groups | 4.521 | 2 | 2.261 | 5.894 | .004 |
| Within Groups | 38.765 | 97 | .383 | ||
| Total | 43.286 | 99 |
Sig. = .004 < .05 → Reject H₀ → Significant differences exist between groups ✓
Step 3: Read Post Hoc Tests (Scheffe)
Post Hoc tests tell you which specific groups differ:
| (I) Education | (J) Education | Mean Difference | Sig. |
|---|---|---|---|
| Bachelor | Master | -.312 | .421 |
| Bachelor | PhD | -.687* | .003 |
| Master | PhD | -.375 | .198 |
* = significant at 0.05 level. The significant difference is between Bachelor and PhD holders.
Reporting ANOVA Results
In your research report:
"One-Way ANOVA revealed statistically significant differences in job satisfaction based on education level, F(2, 97) = 5.894, p = .004. Post hoc comparisons using the Scheffe test indicated that PhD holders (M = 4.21, SD = 0.65) reported significantly higher satisfaction than Bachelor holders (M = 3.52, SD = 0.71)."
Remember: ANOVA only tells you that differences exist. You must use Post Hoc tests to identify which specific groups differ.