July 30, 2021
By Bill Osmulski
The MacIver Institute set out to answer a simple question. Is COVID-19 activity decreasing as vaccination rates increase?
To answer this question, we collected data from 72 counties in Wisconsin from February to June 2021. We then compared the percentage of residents fully vaccinated on the first of each month and the level of COVID-19 activity per 100,000. residents about two weeks later. It takes two weeks for the vaccine to work. All data was from the Wisconsin Department of Health Services.
We arranged the data on a series of scatter plots to perform a first visual analysis. Each point represents a county at a given time. None of the graphs appeared to show a linear relationship. The residues also suggested no relationship. Finally, the correlation coefficients showed no correlation.
For there to be a correlation between two sets of data, the correlation coefficient (r-value) must be close to 1 or -1. The closer it is to zero, the weaker the correlation. The mean r value was -0.05.
The r-value is usually squared when working with linear regressions, as we are in this study. The r2-value is between 0 and 1. The closer it is to 1, the stronger the correlation. The closer it is to zero, the weaker the correlation. The average r2-value was 0.04.
Based on this evidence, we determined that there was no correlation between vaccination rates and the level of COVID-19 activity.
We also took into account potential hidden variables that could affect the data. First, we calculated and removed the outliers. This produced similar results. This gave an average r-value of -0.07 and an average r2-value of 0.03.
We then considered the effect that population density could have on the results. Using data from the most recent month (June), we grouped counties based on their population density in 2021. One group included population densities of 0 to 25 individuals per square mile. The second group included counties between 25 and 100 individuals per square mile. The latter group included counties with a population density greater than 100 individuals per square mile.
Again, there was no correlation between vaccination rates and the level of COVID-19 activity. For counties with a population density of less than 25 individuals per square mile, the r-value was -0.22 and the r2-value was 0.04. For counties with a population density between 25 and 100 individuals per square mile, the r-value was -0.22 and the r2-value was 0.05. For counties with a population density greater than 100 individuals per square mile, the r-value was -0.18 and the r2-value was 0.03.
None of the graphics produced an r2-value greater than 0.049.
This simple study does not prove that vaccinations do not impact disease activity levels. However, this shows that there is no correlation between the two. Policy makers should take this conclusion into account when making future public health decisions.
Finally, it should be noted that for all counties, regardless of vaccination rates, the level of COVID-19 activity fell below 100 cases per 100,000 population in June. This was the lowest rate of the year at that time.