The measures of association refer to a wide variety of coefficients that measure the strength of the relationship that has been described in several ways. The word ‘association’ in measures of association measures the strength of association in which there is at least one of the variables that is dichotomous in nature, generally nominal or ordinal.
There are certain terminologies that a researcher should know to understand the measures of association.
First, the researcher should know that measures of association and the measures of significance are not at all equivalent to each other. Compared to the measures of association, the measures of significance test has a null hypothesis that states that there is no significant difference between the strength of an observed relationship and the strength of an expected relationship by means of simple random sampling. Therefore, there is a possibility of having a relationship that depicts strong measures of association but is insignificant, and a relationship that depicts weak measures of association but is very significant.
The coefficient of the measures of association that has a value of zero signifies no relationship. The coefficient of the measures of association that has a value as one signifies a perfect relationship. The coefficient of the measures of association that has a value of negative one signifies a perfect negative relationship.
The linear definitions of the perfect relationships in the measures of association are those which deal with strictly monotonic, ordered monotonic, predictive monotonic and weak monotonic relationships. The researcher should note that if the relationships in measures of association are perfect due to strict monotonicity, then it should be perfect by other conditions as well. However, in measures of association, one cannot have perfect ordered and perfect predictive monotonicity at the same time. The researcher should note that the linear definitions of perfect relationships in measures of association are inappropriate for curvilinear relationships or discontinuous relationships.
The measures of association define the strength of the linear relationship in terms of the degree of monotonicity. This degree of monotonicity used by the measures of association is based on the counting of various types of pairs in a relationship. There are basically four types of pairs in the measures of association. These are concordant pairs (i.e. the pairs that agree with each other), discordant pairs (i.e. the pairs that do not agree with each other), the tied pair on one variable, and the tied pair on the other variable. The researcher should note that as the concordant pair increases, all the linear definitions of perfect relationships in measures of association increases the coefficient of association towards +1.
There are certain assumptions that are made on the measures of association. These assumptions are as follows:
The measures of association assume nominal, ordinal and interval types of level of data. The measures of association assume a symmetrical or asymmetrical type of causal direction.
The measures of association that define an ideal relationship in terms of the strict monotonicity will attain the value of one only if the two variables have evolved from the same marginal distribution. The measures of association also ignore those rows and columns which have null values.
If the non square table of measures of association that do not contain any null rows and columns have ties in their variables, they will have a comparatively smaller number of classes. If the rows variables in the measures of association have fewer number of classes, then ties will definitely exist in those row variables. Thus, such a type of table cannot have perfect measures of association under the condition of predictive or weak monotonicity.
Measures of Association Resources
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