What are the best effect size measures for your MANOVA analysis?

1 Why use effect size?

Effect size is important for several reasons. First, it helps you to evaluate the practical significance of your findings, beyond the statistical significance. Statistical significance depends on the sample size, the alpha level, and the variance of the data, but it does not tell you how large or meaningful the difference is. Effect size, on the other hand, is independent of these factors and reflects the actual impact of the independent variable on the dependent variables. Second, effect size allows you to compare the results of different studies or different dependent variables, even if they use different scales or units of measurement. Third, effect size enables you to conduct meta-analysis, which is a systematic way of combining and synthesizing the results of multiple studies on the same topic.

2 How to calculate effect size?

When calculating effect size for MANOVA, there are several methods to consider. Partial eta-squared (η2p) is the proportion of variance in the dependent variables that is explained by the independent variable, after accounting for other independent variables. This ranges from 0 to 1, with higher values indicating larger effects. Wilks' lambda (λ) is a ratio of the variance in the dependent variables not explained by the independent variable to the total variance in the dependent variables. This also ranges from 0 to 1, with lower values indicating larger effects. Lastly, Cohen's f2 is a standardized measure of effect size based on the ratio of the variance in the dependent variables that is explained by the independent variable to that which isn't. This ranges from 0 to infinity, with higher values indicating larger effects. Each method has its own strengths and weaknesses, so it's important to understand them before making a decision.

3 How to report effect size?

When reporting effect size for MANOVA, it is important to include the name and value of the effect size measure, the degrees of freedom, and the p-value of the MANOVA test. For example, "The effect of treatment on the three outcome variables was significant, F(6, 144) = 4.52, p < .001, η2p = .16." This implies that treatment accounted for 16% of the variance in the outcome variables which is a large effect according to Cohen's (1988) guidelines. Additionally, this effect size is comparable to the one reported by Smith and Jones (2010), who found η2p = .18 for the same treatment and outcome variables.

4 How to choose effect size?

When deciding which effect size measure is best for MANOVA, it is important to take into account the purpose and scope of your study, the characteristics and assumptions of your data, as well as the availability and feasibility of the calculation. For instance, if you want to assess practical significance, compare results with other studies or variables, or conduct meta-analysis, then Cohen's f2 might be a good option. On the other hand, if you have a large sample size, a balanced design, and a single independent variable, then eta-squared might be more appropriate. Furthermore, if you have access to a statistical software or formula that can easily calculate the desired effect size measure, then this might be the most feasible choice. Ultimately, it is important to consider all these criteria when choosing an effect size measure for MANOVA.

5 How to improve effect size?

Effect size is influenced by many factors, some of which are under your control and some of which are not. To increase the effect size of your MANOVA, you should select and measure dependent variables that are relevant, reliable, and valid for your research question and hypothesis. Additionally, you should use appropriate scales, units, and methods to measure them, and avoid measurement errors or outliers. Furthermore, the independent variable should have a clear and strong operationalization that is applied consistently and accurately to the groups or conditions. Random or matched assignment should also be used to reduce confounding or extraneous variables. Lastly, a sample size that is large enough to detect the effect size that you expect or want to find should be used based on a power analysis or a previous study. Missing data or attrition should also be avoided as it can reduce the effective sample size or introduce bias.