Dichotomous association is that type of association in which the coefficients have been designed for 2 by 2 tables in such a way that it can measure the strength of relationships.
The percent difference, which is denoted by %d, is a type of dichotomous association. Percent difference is the simplest way of measuring the strength of the relationship of 2 by 2 tables. This type of Dichotomous association is the subtraction between the percentage based values in the first and second column of a 2 by 2 table. This type of Dichotomous association explains the perfect association under the given condition of strict monotonicity. The percent difference explains the null relation under the statistical independence. This measure of the Dichotomous association is an asymmetrical type of measure. This measure of the Dichotomous association can handle the nominal type of data level.
Yule’s Q is another type of Dichotomous association. Yule’s Q is a symmetric measure. If the value reaches 1 under weak monotonicity, then Yule’s Q defines the perfect association. Under statistical independence, Yule’s Q defines the null relationship. Yule’s Q is a type of gamma measure in cases of ordinal association. Generally, the measure of Yule’s Q is higher than the gamma measure when the data is in dichotomized and non dichotomized forms.
Another type of Dichotomous association called the Yule’s Y is a variant of Yule’s Q. Yule’s Y is computed by utilizing the diagonal and the off diagonal discordant and concordant pairs. If the value of this measure of the Dichotomous association reaches the value of 1 under weak monotonicity, then this Dichotomous association defines the perfect association. The null relationship in this type of Dichotomous association is defined under the condition of statistical independence. The nature of Yule’s Y is symmetrical. The level of the data in Yule’s Y is either nominal or higher level. The value of Yule’s Y is lower than Yule’s Q under the condition of less than perfect weak monotonicity. Yule’s Y is less sensitive than Yule’s Q to the differences in the marginal distributions of the two variables.
The risk that is also denoted as RR is a common measure of association for the dichotomous type of variables. The risk measure is used in medical disciplines that deal with risk factors. The risk measure is applicable in those situations where the independent or the predictor variable is a treatment for the disease and the dependent variable or the predicted variable is the outcome or the effect of the disease. The risk measure becomes high when the treatment approaches the value of zero. The level of data in this type of the Dichotomous association is generally nominal or a higher level. Unlike the other measures of Dichotomous association, this type of Dichotomous association does not vary between the range of 0 or +- 1. The term relative risk reduction is one minus the relative risk. This terminology of risk indicates the percentage the risk of a particular disease has reduced if a particular treatment is being applied.
The next measure of dichotomous association is the odds ratio. Odd ratio is also related to the relative risk. If an odd ratio is one, it means that the two variables under consideration are independent. The larger the value of the odd ratio, the greater the effect of the independent variable on the dependent ones. The odd ratio is an asymmetric measure.
