Introduction to SPSS One-Way ANOVA

One-Way ANOVA (Analysis of Variance) is a powerful statistical test that allows you to compare means across three or more groups. In this tutorial, we will learn how to perform One-Way ANOVA using SPSS software and explain it with a practical example.

Data Details

• Dependent Variable: Test Score (Continuous variable, in the form of marks)
• Independent Variable: Teaching Method (Categorical variable, with three groups: Method A, Method B, Method C)

Our data looks something like this:

Now we will perform One-Way ANOVA in SPSS and check whether there is a significant difference in test scores between these teaching methods.

1 Data Entry in SPSS

1. Open SPSS: Launch SPSS software and create a new data set.
2. Define Variables:
   • Variable 1: Test_Score (Type: Numeric, Label: Test Score)
   • Variable 2: Teaching_Method (Type: Numeric, Label: Teaching Method, Values: 1 = Method A, 2 = Method B, 3 = Method C)
3. Enter Data:
   • Enter the scores given above in the Test_Score column.
   • In the Teaching_Method column, enter the code (1, 2, or 3) corresponding to each score.

The above shows how the Data View will look in SPSS.

2 Performing One-Way ANOVA

1. Go to Menu:
   • In the SPSS menu bar, click on Analyze > Compare Means > One-Way ANOVA.
2. Select Variables:
   • The One-Way ANOVA dialog box will open.
   • Add Test_Score to the Dependent List (click and use the right arrow).
   • Add Teaching_Method to the Factor box.
3. Set Options:
   • Click on the Options button.
   • Check these options:
     • Descriptive: For group means, standard deviation, and sample size.
     • Homogeneity of variance test: For Levene’s test (this checks the assumption that variances are equal).
     • Means plot: For visual representation.
   • Click Continue.
4. Post Hoc Tests (Optional):
   • If ANOVA gives a significant result, you need to perform post hoc tests to find out which groups differ.
   • Click on the Post Hoc button.
   • Select the Tukey option (this is a common post hoc test when variances are equal).
   • Click Continue.
5. Click OK:
   • After confirming all settings, click OK.
   • The results will appear in the SPSS Output window.

3 Analyzing the Output

The SPSS output will show several tables. We will understand the main tables:

Descriptive Statistics Table

This table shows the mean, standard deviation, and sample size for each group.

Interpretation: Method C has the highest mean score (92.60), and Method B has the lowest (80.00).

Levene’s Test for Homogeneity of Variances

This test checks whether the variances of the groups are equal.

If the Sig. value > 0.05, the variances are equal (assumption met).

Example: If Sig. = 0.153, the assumption is met.

ANOVA Table

This table indicates whether there is a statistically significant difference between the group means.

Interpretation:

• Sig. value (p-value) = 0.000, which is less than 0.05.
• This means the null hypothesis (that all group means are equal) is rejected.
• Conclusion: There is a significant difference in test scores between teaching methods.

Post Hoc Tests (Multiple Comparisons)

This table shows which specific group means differ.

Interpretation:

• There is a significant difference between Method A and Method B (p = 0.015 < 0.05).
• The difference between Method A and Method C is not significant (p = 0.236 > 0.05).
• There is a significant difference between Method B and Method C (p = 0.001 < 0.05).

Means Plot

This is a graph that visually shows the mean scores for each group.

It allows you to see that Method C’s scores are higher than Method A and Method B.

4 Reporting Results (APA Style)

To report results in APA format, you can write:

Checking ANOVA Assumptions

It is essential to check some assumptions for One-Way ANOVA:

1. The dependent variable must be continuous: Test scores are continuous, so this assumption is met.
2. The independent variable must be categorical: Teaching method is categorical (3 groups), so this is also met.
3. No significant outliers: Check using a boxplot (Graphs > Chart Builder > Boxplot). If there are no extreme values, the assumption is met.
4. Normality: Check using the Shapiro-Wilk test (Analyze > Descriptive Statistics > Explore > Plots > Normality plots with tests). If p > 0.05, the data is approximately normal.
5. Homogeneity of variances: Already checked using Levene’s test (Sig. > 0.05).