This is going to be a quick analysis where I attempt to answer a question in what basically looks like the first pass I’d do for a larger research project. The goal is not to conclusively answer the question I pose, but rather to show how you could go start exploring a question like this and get at least some evidence and see if this is worth exploring further. I’ve previously done a similar analysis looking at commute times and housing prices.
Research question: how do income and exercise relate to one another?
Hypothesis: There is a non-linear relationship between income and physical activity levels. As with my previous quick research blog, I got this idea from a newsletter that was looking at physical activity in different countries. One thing that jumped out at me when I saw the rankings was how there didn’t seem to be any relationship between how rich a country was and how active it was. My intuition based on living in the U.S. would be that income and exercise would be much more closely related.
The question that follows for me is whether this trend holds at the national level. Do we see a similar non-linear trend between income and physical activity if we just look at data from one country, or are there indeed broader cultural trends that make some low-income countries more active than some wealthy countries?
Methods
I will be looking at the Center for Disease Control’s Behavioral Risk Factor Surveillance System (BRFSS). This is the largest health survey conducted in the U.S. each year, and in particular it asks respondents some basic demographic questions (including their household income) as well as a few relevant questions about the amount of physical activity they report.
There are two outcome questions we will look at: a binary variable for whether or not a respondent reported exercising enough to meet the recommendation for the amount of aerobic exercise they should be doing and a categorical variable for whether a respondent is classified as highly active, active, insufficiently active, or inactive. Both of our dependent variables are calculated based on respondents' answers to other questions about their type and frequency of their exercise. These are not self-reported measures, so we don’t need to worry about how people interpret things like “highly active.”
We will use an ANOVA (analysis of variance) model to test whether there is some impact. The reason we are going to use ANOVA to start is because I am curious if there is a non-linear relationship between income and exercise. By treating each income category separately rather than assuming that physical activity increases or decreases at a constant rate with income, ANOVA allows us to identify differences between income groups that a simple linear regression might miss.
Results
The first thing we see when we look at the responses is that if there is an effect, it is almost certainly linear. Table 1 reports the percentage of respondents in each income group that meet their aerobic exercise recommendation, as well as the average response category for the categorical variable about total activity level. This variable is coded such that one is associated with highly active and four is associated with inactive, so smaller numbers mean more physical activity on average.
Table 1: Higher income respondents are more active than lower income respondents
The ANOVA results back for both variables both conclusively suggest that there is a relationship between these income categories and both of the response variables, with both p-values coming out to essentially zero. We can in both cases reject the null hypothesis that there is no relationship between income and exercise level.
Limitations
I have not really gone far enough to fully understand the relationship between income and amount of physical activity. We found by looking at these data that there is some relationship, and the clear order of these averages suggests that it is quite likely linear. More work is needed to demonstrate more strongly that the relationship is indeed linear, and what the strength of the relationship is.
Preliminary conclusions and next steps
There certainly is some relationship between income and the amount of physical activity respondents participate in, and we have plenty of evidence to dispute the original hypothesis that it is non-linear. The connection between income and exercise appears to be positively correlated, meaning higher income is correlated with higher likelihood of being physically active, though the exact strength of this relationship is still open to further research. The next steps to fully understand this relationship would be to look for potential confounders and account for those as well.
