Question 3: How would a chi-squared test be used to check the propensity scores?
The propensity score is a continuous, quantitative variable. The authors have split the distribution at the four quintiles, giving five fifths. The fifth of the propensity score distribution in which a subject falls then becomes a qualitative variable with five ordered categories.
This ordered categorical variable has been cross-tabulated with the dichotomous outcome variable, death or admission to an intensive care unit. A chi-squared test for trend, either Armitage's test or the Mantel-Haenzsel test for trend, has been applied to this table.
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