Repeated Measures Anova Using Spss

Repeated Measures ANOVA Using SPSS: A Comprehensive Guide

Repeated measures ANOVA (Analysis of Variance) is a powerful statistical technique used to analyze data where the same subjects are measured multiple times. This contrasts with between-subjects ANOVA, where different groups of subjects are compared. Understanding when to use repeated measures ANOVA and how to interpret its results is crucial for researchers across various fields. This comprehensive guide will walk you through the process of conducting a repeated measures ANOVA using SPSS, covering everything from the underlying assumptions to interpreting the output.

Introduction: Understanding Repeated Measures ANOVA

Repeated measures ANOVA is particularly useful when examining changes within individuals over time or across different conditions. Imagine a study investigating the effectiveness of a new drug. Researchers might measure blood pressure in the same participants before treatment, immediately after treatment, and at several follow-up points. This type of data, where the same subjects are measured repeatedly, necessitates the use of repeated measures ANOVA. The key advantage of this method lies in its ability to control for individual differences, leading to a more powerful analysis than a between-subjects design. This is because the variability within individuals is removed from the analysis, leaving only the variability between conditions or time points. This increased statistical power allows for the detection of smaller effects.

When to Use Repeated Measures ANOVA

Repeated measures ANOVA is appropriate when the following conditions are met:

• The dependent variable is continuous: The outcome you are measuring should be on an interval or ratio scale (e.g., blood pressure, test scores, reaction time).
• The independent variable is within-subjects: The same subjects are measured under different conditions or at different time points.
• The data are normally distributed (or approximately normally distributed): The distribution of the dependent variable within each condition should be roughly normal. We'll explore how to check this assumption later.
• The data meet the assumption of sphericity: This assumption implies that the variances of the differences between all pairs of levels of the within-subjects factor are equal. We'll discuss how to address violations of this assumption as well.

Steps for Conducting Repeated Measures ANOVA in SPSS

Let's assume we have data from a study investigating the effect of three different teaching methods (Method A, Method B, Method C) on student performance. The same group of students (n=20) participated in all three teaching methods. Their scores on a final exam are recorded for each method.

Here's how to perform the repeated measures ANOVA in SPSS:

1. Inputting your data: Enter your data into SPSS. Each row should represent a participant, and you'll need separate columns for each condition or time point (Method A, Method B, Method C in our example).

2. Analyze > General Linear Model > Repeated Measures: Navigate to this menu in SPSS.

3. Define within-subject factors: In the "Within-Subject Factor Name" box, enter a name for your within-subject factor (e.g., "Teaching Method"). Specify the number of levels (3 in our case). Click "Add."

4. Define measures: In the "Measure Name" box, enter the names of your variables (Method A, Method B, Method C). Match each measure to the corresponding column in your data set. Click "Add" after each variable name. Click "Define."

5. Specify the model: This is where you define any between-subject factors (e.g., gender, age group). If you have none, leave this section blank. Click "Options."

6. Select options: You can request descriptive statistics (means, standard deviations), effect sizes (partial eta-squared), and homogeneity tests (Mauchly's Test of Sphericity). Check the boxes accordingly. Click "Continue," then "OK."

Interpreting the SPSS Output

The SPSS output will contain several tables. The most important are:

• Descriptive Statistics: This table shows the mean and standard deviation for each teaching method. This provides a quick overview of the data.

• Mauchly's Test of Sphericity: This test assesses the assumption of sphericity. If the p-value is greater than your chosen alpha level (typically .05), the assumption of sphericity is met. If the p-value is less than .05, sphericity is violated.

• Tests of Within-Subjects Effects: This table contains the key results of the repeated measures ANOVA. It shows the F-statistic, degrees of freedom, and p-value for the main effect of your within-subject factor (Teaching Method in our example). If the p-value is less than .05, you can reject the null hypothesis and conclude that there is a statistically significant difference between at least two of the teaching methods.

• Greenhouse-Geisser and Huynh-Feldt Corrections: If sphericity is violated (Mauchly's test is significant), SPSS will provide corrected p-values based on Greenhouse-Geisser and Huynh-Feldt corrections. These adjustments compensate for the violation of sphericity. Generally, the Greenhouse-Geisser correction is more conservative. Report the corrected p-value if sphericity is violated.

• Pairwise Comparisons: If the overall F-test is significant, you'll need to conduct post-hoc tests (pairwise comparisons) to determine which specific teaching methods differ significantly from each other. SPSS provides various options for post-hoc tests, such as Bonferroni, Tukey, and Sidak. Choose a method appropriate for your data and interpret the resulting p-values. Bonferroni is a commonly used conservative approach, adjusting for multiple comparisons.

Addressing Violations of Sphericity

If the assumption of sphericity is violated, you have several options:

• Use a corrected p-value: As mentioned earlier, the Greenhouse-Geisser and Huynh-Feldt corrections adjust the degrees of freedom to account for the violation of sphericity. Report the corrected p-value instead of the uncorrected one.

• Use a different statistical test: If the violation of sphericity is severe, consider using a non-parametric alternative to repeated measures ANOVA, such as the Friedman test. However, this test is less powerful than repeated measures ANOVA.

Assumptions of Repeated Measures ANOVA and How to Check Them

Several assumptions underlie the validity of repeated measures ANOVA. Violations of these assumptions can lead to inaccurate results. Here's how to check them:

• Normality: Examine the distribution of the dependent variable within each condition. You can use histograms, Q-Q plots, and tests of normality (e.g., Shapiro-Wilk test) in SPSS to assess normality. Slight departures from normality are generally acceptable, especially with larger sample sizes.

• Sphericity: This assumption is tested using Mauchly's Test of Sphericity, as described earlier.

• Independence of Observations: This assumption is critical. The observations within each subject should be independent. For instance, if you're measuring blood pressure repeatedly over a short period, the measurements may be correlated, violating this assumption. Careful experimental design is essential to ensure independence.

Frequently Asked Questions (FAQ)

• What if I have more than one within-subject factor? Repeated measures ANOVA can handle multiple within-subject factors. The process in SPSS is similar, but you'll define multiple within-subject factors in step 3.

• What if I have between-subject factors? You can include between-subject factors in your analysis. SPSS will then test for main effects of both within-subject and between-subject factors, as well as their interaction.

• How do I report the results of a repeated measures ANOVA? Your report should include the descriptive statistics, the results of Mauchly's Test of Sphericity (including corrected p-values if sphericity is violated), the results of the repeated measures ANOVA (including effect sizes), and the results of any post-hoc tests.

Conclusion

Repeated measures ANOVA is a valuable tool for analyzing data with repeated measurements on the same subjects. Understanding its assumptions, conducting the analysis in SPSS, and correctly interpreting the results are crucial for drawing valid conclusions from your research. Remember to always check the assumptions of your analysis and consider appropriate corrections or alternative tests when necessary. By carefully following the steps outlined in this guide and thoroughly understanding the output, researchers can confidently utilize repeated measures ANOVA to draw meaningful insights from their data. This powerful statistical method allows for the efficient and precise analysis of changes within individuals, enabling researchers to contribute significantly to their respective fields. Mastering this technique is a valuable asset for any researcher dealing with longitudinal or repeated-measures data.