This file is part of a program based on the Bio 4835 Biostatistics class taught at
Daniel, W. W. 1999. Biostatistics: a foundation for analysis in the health sciences.
The file follows this text very closely and readers are encouraged to consult the text for further information.
D) Hypothesis testing of the difference between two population proportions
It is frequently important to test the difference between two population proportions. Generally we would test = . This permits the construction of a pooled estimate which is given by the following formula.
The standard error of the estimator is:
In a study of patients on sodium-restricted diets, 55 patients with hypertension were studied. Among these, 24 were on sodium-restricted diets. Of 149 patients without hypertension, 36 were on sodium-restricted diets. We would like to know if we can conclude that, in the sampled population, the proportion of patients on sodium-restricted diets is higher among patients with hypertension than among patients without hypertension.
Patients with hypertension: = 55 = 24 = .4364
Patients without hypertension: = 149 = 36 = .2416
: p1 p2
: p1 > p2
(4) Test statistic
The test statistic is z which is calculated as
(a) Distribution of test statistic
If the null hypothesis is true, the test statistic approximately follows the standard normal distribution.
(b) Decision rule
With = .05 the critical z score is 1.645. We reject if z > 1.645.
(5) Calculation of test statistic
(6) Statistical decision
Reject because 2.71 > 1.645
The proportion of patients on sodium restricted diets among hypertensive patients is higher than in nonhypertensive patients.
p = .0034