One-Way ANOVA

In previous lessons, you learned how to compare means between two groups using t-tests.

But what if you need to compare three or more groups at the same time?

The One-Way ANOVA (Analysis of Variance) is used to determine whether there are statistically significant differences between the means of three or more independent groups.

Why Not Multiple t-tests?

Running multiple t-tests increases the risk of false positives (Type I errors).

One-Way ANOVA solves this problem by testing all group means simultaneously using a single statistical test.

When to Use One-Way ANOVA

This test is appropriate when:

• You have one categorical independent variable (3+ groups)
• You have one numerical dependent variable
• Observations are independent

Common examples include:

• Comparing sales across multiple regions
• Comparing exam scores across teaching methods
• Comparing productivity across departments

Example Dataset

Consider exam scores from three different teaching methods:

The question is: Do exam scores differ based on teaching method?

Understanding the ANOVA Logic

One-Way ANOVA compares:

• Variation between groups
• Variation within groups

If variation between groups is much larger than variation within groups, the group means are likely different.

This comparison is summarized using the F-statistic.

Key Assumptions

Before using One-Way ANOVA:

• Dependent variable is approximately normal
• Groups have equal variances
• Observations are independent

SPSS automatically checks homogeneity of variances using Levene’s Test.

Running One-Way ANOVA (Menu)

To perform One-Way ANOVA using SPSS menus:

• Go to Analyze → Compare Means → One-Way ANOVA
• Move the numerical variable to Dependent List
• Move the grouping variable to Factor
• Click OK

SPSS outputs ANOVA tables and assumption checks.

Using SPSS Syntax

ONEWAY Score BY Method
  /STATISTICS DESCRIPTIVES
  /MISSING ANALYSIS.

This syntax compares mean scores across teaching methods.

Interpreting the Output

Key values to interpret:

• F-value – ratio of variances
• Sig. (p-value) – statistical significance

Interpretation rule:

• p < 0.05 → at least one group mean differs
• p ≥ 0.05 → no significant difference

ANOVA does not tell which groups differ — only that a difference exists.

Common Mistakes

Frequent mistakes include:

• Using ANOVA for two groups only
• Ignoring assumption violations
• Forgetting post-hoc analysis

Post-hoc tests are covered next.

Quiz 1

Why is ANOVA used instead of multiple t-tests?

Quiz 2

What does ANOVA compare?

Quiz 3

What does p < 0.05 indicate?

Quiz 4

Does ANOVA identify which groups differ?

Quiz 5

Which SPSS menu is used for One-Way ANOVA?

Mini Practice

A company compares employee performance across three departments.

Perform a One-Way ANOVA to determine whether average performance differs between departments.

What’s Next

In the next lesson, you will learn about Repeated Measures ANOVA, used when the same subjects are measured multiple times.