Measures of Association: OR, RR, ANOVA, and Correlations

Measures of Association
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Measures of Association
Measures of association are used to draw causal relationships between two or more variables and further go ahead to quantify the relationship. There exist various measures of association, a majority of which are used in fields of research. Some of the measures of the association include the Odds Ratio (OR), Analysis of Variances (ANOVA), Risk Ratio (RR), also referred to as Relative Ratio, and Correlations.
The Odds Ratio as a measure of association is a measurement that examines the quality of the relationship between two events. The two events, in this case, being exposure and an outcome. More specifically, the OR measures the probability that a given outcome will occur given a certain exposure. Additionally, the Odds ratio also measures the probability of a certain outcome occurring even without exposure. Odds ratios are primarily used in case-control experiments but can also analyze cross-sectional data (Frick et al., 2011). Unlike the odds ratio, the risk ratio compares the probability of an event within an exposed group to the probability of the same event within an unexposed group. Therefore, RR is a probabilities ratio between two groups; one group has been exposed, and the other has not been exposed.
Correlations is another measure of association that is used to measure the linear relationship between two variables. However, in a correlation model, both variables are assumed to be changing correspondingly and at a constant rate (Wilson, 2021). On the other hand, the Analysis of Variance is used to examine whether the results of a study are significant. ANOVA points to how strongly or the extent to which the study's findings can be relied upon. ANOVA forms the basis upon which to either reject or accept the null or alternative hypotheses (Introduction | Statistics Tutorial #25 | MarinStatsLectures, 2018).
An example of a study that uses the OR, RR, ANOVA, and correlations
To analyze how the measures of association can be examined, we consider a study about a rare illness that has just come up, one that is nerve-racking and affects a large proportion of the adult population. We further assume that individuals who have a history of smoking or are current smokers are more likely to attack the disease. To begin with, we begin by analyzing the risk extent among the adult population. The most effective measure of association, in this case, would be the Risk Ratio. The RR will help determine which proportion of the population is at a higher risk for contracting the disease based on their exposure to smoking. Subsequently, the study can also use the odds ratio to determine the probability of an individual contracting the disease regardless of whether they have been exposed to smoking or not. Consider the table below:

Disease-Infected
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