Statistics for bivariate analyses

Here are two statistics for bivariate (two variable) analyses:

Chi-square χ2 tests of association

The chi-square χ2 test is a commonly used statistic for nominal/categorical data. We use it to examine the distribution of cases across categories. Essentially, it compares the distribution of cases you actually see to the distribution of cases you would expect to see from normal variation.

Here is one example of a chi-square χ2 test for a recent resident project. The question is whether gender (male/female) makes a statistically significant difference in whether patients need three or more dose changes of bivalirudin before they reach a therapeutic goal.

#d <- read.csv("data/bivalirudin.csv") # load data
#table_dosechgs_gender <- xtabs(~d$d_Male + d$DV_3DoseChanges, data=d) # crosstabulate 
#knitr::kable(table_dosechgs_gender, align = "l")
#summary(table_dosechgs_gender) # calculate chi-square

The chi-square χ2 value of 1.9421 with one degree of freedom has a p-value of 0.1634. It is not statistically significant, suggesting that gender makes no significant difference in reaching therapeutic goal.

t tests

The t test is a commonly used statistic for comparing two groups on a continuous outcome.