Question

1) Suppose patients were recruited into a clinical trial from three different clinical sites. Use the following data to test for differences in the proportion of hypertensive patients across the three sites.

	Site 1	Site 2	Site 3
Hypertensive	10	14	12
Not Hypertensive	68	56	40

Step 4.             In the table below the upper number in each cell is the observed frequency (O) and the lower number (in parentheses) is the expected frequency (E). Compute the observed  χ² using the following formula

Observed freq. (Expected freq.)	Site 1	Site 2	Site 3	Total
Hypertensive	10 (14.0)	14 (12.6)	12 (???)	36
Not Hypertensive	68 (64.0)	56 (57.4)	40 (42.6)	164
Total	78	70	52	200

What is the obtained x² value? (Hint: you need to first calculate the expectancy frequency of hypertensive patients in Question 3 if you haven't already.)

a) 1.14

b)2.46

c)0.16

d) 0.25

2) Suppose patients were recruited into a clinical trial from three different clinical sites. Use the following data to test for differences in the proportion of hypertensive patients across the three sites.

	Site 1	Site 2	Site 3
Hypertensive	10	14	12
Not Hypertensive	68	56	40

Step 4.       In the table below the upper number in each cell is the observed frequency (O) and the lower number (in parentheses) is the expected frequency (E). Compute the observed  χ² using the following formula

Observed freq. (Expected freq.)	Site 1	Site 2	Site 3	Total
Hypertensive	10 (14.0)	14 (12.6)	12 (???)	36
Not Hypertensive	68 (64.0)	56 (57.4)	40 (42.6)	164
Total	78	70	52	200

Step 5: Which one of the following conclusions is correct?

A)There is a statistically significant relationship between proportion of hypertensive patients and site.

b)There is a statistically significant difference between proportions of hypertensive patients across sites.

  

c) Proportions of hypertensive patients and site are dependent.

d) Proportions of hypertensive patients are not statistically different across sites.

Answer 1

Firstly, the missing expected frequency = 36 - (14.0 + 12.6) = 9.4
The obtained chi-square value = 2.46

Correct conclusion -> Proportions of hypertensive patients are not statistically different across sites.