Is ANCOVA correct here?

Question

I am analyzing data from a mindfulness intervention in which 60 participants took part in an ipod-based intervention listening to meditation tracks. Outcome measures on anxiety, depression, stress, health etc. were collected pre and post intervention. There was no control group.

I have been advised to use an ANCOVA to answer my research question-- (Does listening to meditation tracks reduce stress/anxiety/depression?) Where the independent variable is Total Time Spent Listening (varies per participant from 0 minutes to 1000 minutes depending on their interest and level of participation) and the dependent variable is post-intervention outcome measure scores with the covariate as the pre-intervention scores.

1. I'm wondering if this is the best way to analyze this data--as we are interested in seeing a potential dose-response effect for those who listening to more tracks and simply looking at t-tests wouldn't allow for this analysis.

2. I have read that an assumption of ANCOVA is that the DV and covariate are independent (not correlated) which would obviously be violated in this design, although I have seen plenty of papers published anyways. Is this an issue I need to be aware of?

Thanks!

Answer 1

In your question, the research question and the independent variable you mention strictly speaking don't match up.

Your research question is: "Does listening to meditation tracks reduce stress/anxiety/depression?"

Your independent variable is the time spent listening. There's no mention of time in your research question.

What I assume you're trying to get at is whether listening to meditation tracks reduce stress/anxiety/depression, and whether the length of time you spend listening moderates this. That is, whether there's a difference between listening once for five minutes, or listening for an hour every day for a week.

This question may be better addressed using a multiple regression framework. In particular, the regression equation is:

$\text{Stress/anxiety/depression score} = \text{Listened to track} \times \text{Time spent listening}$

The first predictor here will be whether the score comes from before or after the person has listened to the track (e..g, coded as 0 before, and 1 as after). The second, as the name implies, is how long they spend listening. This regression will allow you to address two questions:

1. Does listening to meditation tracks have an effect on stress/anxiety/depression scores?

2. Does the length of time spent listening to meditation tracks moderate their effect?

Before interpreting these results, please familiarise yourself with regression coding, and its consequences for how you interpret the resulting coefficient. In particular, think about whether or not it's meaningful for zero in your time spent variable to be zero minutes(/hours/days) spent listening. I'd suspect that it probably isn't, so you may want to transform time.

Now, as this is a repeated measures design (you have a pre/post score from everyone) you'll need to use a mixed effects regression. This is similar in some senses to a related samples t-test or repeated measures ANOVA. This will allow you to take into account that fact that all of your participants will have different baseline scores, and that all of them may respond differently to meditation tracks.

Some reading:

https://en.wikipedia.org/wiki/Linear_regression#Simple_and_multiple_regression

https://en.wikipedia.org/wiki/Mixed_model

https://cran.r-project.org/web/packages/lme4/index.html

Gelman, A., & Hill, J. (2006). Data analysis using regression and multilevel/hierarchical models. Cambridge University Press.

Answer 2

No. ANCOVA is not appropriate here because you appear to have 3 continuous variables. ANCOVA is a model which regresses one continuous dependent variable on a categorical variable and one or more other continuous variables, to determine whether the means of the response are equal across the different categories of the categorical variable, which adjusting for the other continuous variables. Since you don't have a categorical variable, you can't run an ANCOVA model.

As an aside, ANCOVA is not a good way to analyse change from baseline (where you do have a categorical "treatment" variable) unless the baseline values are balanced across the treatment categories. If effective randomisation is not achieved then estimates may be biased. See:

Blance A, Tu YK, Baelum V, Gilthorpe MS. Statistical issues on the analysis of change in follow-up studies in dental research. Commun Dent Oral Epidemiol 2007; 35(6): 412-20 http://www.ncbi.nlm.nih.gov/pubmed/18039282

@Ian_Fin has given some good advice about how to proceed.