Introduction to Analysis of Variance (ANOVA)

Analysis of Variance, commonly known as ANOVA, is one of the most important statistical techniques and is used to study the effect of one or more factors on a dependent variable. Its goal is to examine whether statistically significant differences exist between means, checking whether these differences are due to the effect of factors or are simply the result of random variation. When examining the effect of only one factor, we refer to one-way ANOVA, while when two independent variables are considered, we speak of two-way ANOVA. In all cases, the procedure relies on the f-test, which compares the variance within groups to the variance between groups.

One-Way and Two-Way ANOVA

One-way ANOVA is applied when the independent variable is categorical and consists of specific levels, while the dependent variable is quantitative. The mathematical model is expressed as Yij = μ + αi + εij, where μ is the overall effect, αi is the effect of the factor level, and εij is the error term. In the case of two-way ANOVA, an additional independent variable is included in order to investigate the main effects of each factor as well as their possible interaction. The model is expressed as Yij = μ + αi + βj + εij.

Repeated Measures ANOVA

Repeated measures ANOVA is used when the same participants are measured more than once, either at different time points or under different conditions. This method allows control of individual differences, since each participant serves as their own control, reducing random variation. For example, it may be used to examine cigarette consumption before, one month after, and six months after a hypnotherapy program, with cigarette consumption as the dependent variable and time as the independent variable. Another example is measuring car breaking speed under different windshield tints, where speed is the dependent variable and tint condition is the independent variable. When there are two independent variables, such as time and condition, a two-way repeated measures ANOVA is required.

Assumptions of the Analysis

For the results of the analysis to be valid, certain assumptions must be met. The dependent variable must be measured on a continuous scale, that is, it should be interval or ratio, such as time, weight, or test scores. The independent variable must consist of at least two related groups or matched pairs, meaning the same participants take part in all measurements. There should be no significant outliers in the related groups, as they may distort the results. The distribution of the dependent variable within each group should be approximately normal, something that can be checked with the Shapiro-Wilk test. Finally, the assumption of sphericity must be satisfied, which means that the variances of the differences between all combinations of related groups should be equal. Violation of sphericity increases the probability of a Type I error. The last three assumptions can be tested using SPSS Statistics, while the first two depend on the study design.

Procedure in SPSS Statistics

The application of repeated measures ANOVA in SPSS involves specific steps. First, the data are entered and coded, with separate columns for each measurement. Then, from the menu, the path Analyze, General Linear Model, and Repeated Measures is selected. The independent variable, such as time, and its levels are defined. Next, the data columns are assigned to the levels, and the assumption of sphericity is tested through Mauchly’s Test. If this assumption is violated, corrections such as Greenhouse-Geisser or Huynh-Feldt are applied. Finally, the results are extracted and interpreted in terms of main effects and interactions.

Interpretation of Results

SPSS provides tables with statistical results, where the main criterion is the p-value of the f-test. When the p-value is less than 0.05, the null hypothesis is rejected, and we conclude that there are statistically significant differences among the groups. When the p-value is equal to or greater than 0.05, no evidence of differences is found. In cases where significant results are identified, additional comparisons, such as post-hoc tests or pairwise comparisons, are applied to determine which time point or condition differs from the others.

Conclusion

Repeated measures ANOVA is a powerful method that allows the analysis of data where the same participants are measured across multiple time points or conditions. With SPSS Statistics, the procedure becomes more systematic and accessible, provided that the necessary assumptions are checked and the results are interpreted carefully. Its application provides reliable conclusions and makes a significant contribution to the study of interventions, treatments, or experimental procedures, establishing it as one of the most useful tools in data analysis in social, psychological, and biomedical sciences.