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Association, Measures of
Measuring association between variables is very relevant for investigating causality, which is, in turn, the sine qua non of scientific research. However, an association between two variables does not necessarily imply a causal relationship, and the research design of a study aimed at investigating an association needs to be carefully considered in order for the study to obtain valid information. Knowledge of measures of association and the related ideas of correlation, regression, and causality are cornerstone concepts in research design. This entry is directed at researchers disposed to approach these concepts in a conceptual way.
Measuring Association
In scientific research, association is generally defined as the statistical dependence between two or more variables. Two variables are associated if some of the variability of one variable can be accounted for by the other, that is, if a change in the quantity of one variable conditions a change in the other variable.
Before investigating and measuring association, it is first appropriate to identify the types of variables that are being compared (e.g., nominal, ordinal, discrete, continuous). The type of variable will determine the appropriate statistical technique or test that is needed to establish the existence of an association. If the statistical test shows a conclusive association that is unlikely to occur by random chance, different types of regression models can be used to quantify how change in exposure to a variable relates to the change in the outcome variable of interest.
Examining Association between Continuous Variables with Correlation Analyses
Correlation is a measure of association between two variables that expresses the degree to which the two variables are rectilinearly related. If the data do not follow a straight line (e.g., they follow a curve), common correlation analyses are not appropriate. In correlation, unlike regression analysis, there are no dependent and independent variables.
When both variables are measured as discrete or continuous variables, it is common for researchers to examine the data for a correlation between these variables by using the Pearson product-moment correlation coefficient (r). This coefficient has a value between − 1 and +1 and indicates the strength of the association between the two variables. A perfect correlation of ± 1 occurs only when all pairs of values (or points) fall exactly on a straight line.
A positive correlation indicates in a broad way that increasing values of one variable correspond to increasing values in the other variable. A negative correlation indicates that increasing values in one variable corresponds to decreasing values in the other variable. A correlation value close to 0 means no association between the variables. The r provides information about the strength of the correlation (i.e., the nearness of the points to a straight line). Figure 1 gives some examples of correlations, correlation coefficients, and related regression lines.
A condition for estimating correlations is that both variables must be obtained by random sampling from the same population. For example, one can study the correlation between height and weight in a sample of children but not the correlation between height and three different types of diet that have been decided by the investigator. In the latter case, it would be more appropriate to apply a regression analysis.
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