In a previous post, I wrote about the repeated measures (RM) ANCOVA, which is also commonly referred to as repeated measures MANCOVA. In this post, however, when I use the term repeated measures multivariate analysis of covariance (MANCOVA) I will be referring to a design with multiple dependent variables (DVs) for each of which repeated measures have been taken. It is important to know that the term

repeated measures MANCOVA is quite often also used to refer to the repeated measures ANCOVA where there is a single dependent variable for which different measurements have been taken over time. In this sense one could see it as having multiple dependent variables, one for each time point, hence the use of multivariate in the name, but in reality we are talking about one single DV. This can be really confusing because the same term is used to describe different analyses. To help clarify it I will briefly review the two parent analyses: the *repeated measures analysis of variance (ANOVA)* and the *MANCOVA*.

The RM ANOVA is used when we have a dependent variable being measured over time. Imagine that a researcher has measured performance of a group of athletes using their average pace over a six-mile run and we have measurements from each of them for 3 consecutive races. In the dataset the dependent variable will be represented by 3 columns: performance1 performance2 and performance3, one for each of the three time measurements of performance. This type of data structure is known as *wide* shape. *Long* shape refers to a data set where each repeated measure occupies an independent row. In other words, the observations corresponding to one participant occupy as many rows as the number of times the dependent variable has been measured. Therefore one single column is dedicated to the DV. In our example, the researcher is interested in knowing which training method used (A or B) has a greater impact in the athlete’s performance. This would be a classic example of a RM ANOVA with one within-subjects factor (time) and one between-subjects factor (method). The researcher may be interested in adding a covariate to the model, a variable that is related to the dependent variable performance. For instance, they may want to control for the age of the runner. In such a case, the model is named RM ANCOVA. In this type of model, the researcher is usually interested in the interaction term time*method since this interaction will determine whether one method was more effective than the other.

On the other hand, the multivariate analysis of covariance (MANCOVA) is an extension of the analysis of covariance (ANCOVA) to cases where there is more than one dependent variable and the researcher is interested in assessing the effect of an independent grouping variable (e.g. treatment) on all dependent variables as a whole while controlling for at least one variable, the covariate. Common covariates are gender, age and other socio demographic characteristics. In the medical field, current comorbidities and past medical history are important covariates to control for. Following our previous example, imagine that our researcher only has data on athletes from a single race or has access to the average over the last year races. In addition, now performance is not only measured by pace but by two additional metrics: average heart rate and time to recover after the race. The researcher still wants to compare performance by using two training methods (between-subject factor) and wants to adjust the comparison by the age of the runner (covariate). This is a classic example of a *one-way MANCOVA*.

Now, imagine that our researcher wants to use the three different metrics to measure performance (pace, heart rate, recovery time) and wants to measure them over different races. In this context, we have what we call repeated measures MANCOVA. Notice that it is multivariate in two ways: it has multiple DVs each of which has been measures multiple times. If working with a wide shape dataset, in this example the researcher would have 9 columns dedicated to the DVs since there are 3 DVs that measure performance and each one has been measured at three time points. The statistical package SPSS offers an easy user interface to conduct the repeated measures MANCOVA. In fact it is the same that is used to conduct the RM ANOVA/ANCOVA but it allows defining more than one measure or dependent variable. Stata allows repeated measures MANCOVA under the mancova command but misleadingly it only refers to the RM ANCOVA, in other words, a single DV for which repeated measures have been taken.

Check out this link I found when they offer SPSS examples for both RM ANOVA and RM MANOVA, very useful.

Reblogged this on statistics tutors.