# Two-way repeated measures ANOVA for 2 independant and 1 dependant with heart rate

I've been trying to find someone with a similar question for hours now, so sorry if this is a duplicate:

I've got music (independent variable no. 1)-three different types (so 3 levels), emotion (independent variable no. 2) -measured through 3 self-assess scales & change in heart-rate (total 4 levels of emotion). Dependent variable is performance.
I assume a two-way repeated measures ANOVA is the correct way to analyse, as each participant was tested under each condition. No idea how to work this in SPSS.

Independent variables:

• Music (3 levels)
• Emotion (3 levels + heart rate)

Dependent variables:

• Performance

My understanding is that you wish to gauge whether music and emotional intensity (measured according to several ordinal or interval metrics) are predictive of your performance measure. In this regard your description was unclear – specifically, if you have three self-report measures of emotion plus heart rate, this would not represent four levels of a single variable but rather four separate variables tapping into a similar construct. I will assume this to be the case for the purpose of my response. Presuming I am correct, you have two options that come to mind with an important secondary consideration (dimension reduction), which I will cover at the end.

Repeated-Measures ANOVA

This seems to be your default approach. The difficulty is that ANOVAs are not intended to deal with non-categorical predictors, so you would need to somehow dichotomize each of you emotion measures for inclusion. One popular method would be to use a median split (i.e., for each measure determine the median value and then generate a new variable which is LOW for those records scoring below the median or HIGH for those records scoring above the median). This new variable could readily be incorporated into an ANOVA. Tutorials on how to conduct repeated-measures ANOVAs using SPSS are readily available (e.g., link). Of greater concern, you would end up with a separate predictor for each of your emotion measures, which would prove to be difficult for you to interpret.

Multi-level/Mixed Linear Regression Model

As a more advanced solution, you could explore your data using a multi-level linear model in which you model individual differences as random effects (these are sometimes called mixed models). This approach is the regression equivalent to a repeated-measures ANOVA, the benefit of which being that you could include non-categorical predictor variables without dichotomizing them (for the record, treating such predictors as continuous is often recommended as superior to procedures such as a median split). This approach could also incorporate per trial predictors (e.g., if you measured emotion/heart rate for each trial). SPSS can fit these sorts of models, but you will have greater difficulty finding good tutorials. If you were at all interested in the R programming language, I could recommend the lme4 package. However, I will not develop this further at this time, because I suspect you may be looking for something more in line with a standard ANOVA.

Dimension Reduction

I mention above that one unresolved problem you face is the number of predictors in your design. You seem to have three self-report scales as well as a measure of heart rate. Even should these measures be dichotomized and fit into a single model, you would end up with a total of five predictor variables, which would be difficult to interpret. Presuming that each of your emotion measures is thought to tap into the same underlying construct (e.g., fear) you might consider combining them into a single variable. In the simplest case, you could convert them to a common scale (if needed) and then average them for each subject/condition. A more advanced approach would be to adopt something akin to principal/independent component analysis, which would use your data to estimate the latent (i.e., unobserved) variables you are tapping across the four emotion measures. Should you decide to pursue dimension reduction, I suggest that you first consider what each variable is measuring and what you hope to gain by including it in your analysis. The simplest approach to dimension reduction is to avoid including predictors that are redundant or otherwise not relevant to your theoretical question (or useful for some other statistical purpose – such as a covariate).

Now, I have for the time being ignored another topic of potential relevance (multicollinearity), but should your emotion measures be strongly correlated with your music manipulation (or each other, if included as separate predictors), any model might find it difficult to estimate the effect of these variables independently.