Question

One hundred and fourteen people are eligible to participate in a clinical trial. The trial will have two arms (‘treatment’ and ‘control’), and we want an equal number of people in each arm. Gender and activity status (both of which may be related to the outcome measured in the trial) are recorded for the 114 people; the results are in the table below.

	Female	Male
Active	24	16	40
Inactive	36	38	74
	60	54	114

Explain how you would decide who gets what treatment. You do not have to go into intricate detail but hit on the important topic(s) of the assignment of treatments to individuals. Note that each person can be in only one of the two arms.

Answer 1

We have to find a relationship between gender and activity status in order to decide who gets what treatment.

The hypothesis being tested is:

H0: There is no relationship between gender and activity status

Ha: There is a relationship between gender and activity status

		Female	Male	Total
Active	Observed	24	16	40
	Expected	21.05	18.95	40.00
	O - E	2.95	-2.95	0.00
	(O - E)² / E	0.41	0.46	0.87
Inactive	Observed	36	38	74
	Expected	38.95	35.05	74.00
	O - E	-2.95	2.95	0.00
	(O - E)² / E	0.22	0.25	0.47
Total	Observed	60	54	114
	Expected	60.00	54.00	114.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	0.64	0.71	1.34
		1.34	chi-square
		1	df
		.2467	p-value

The p-value is 0.2467.

Since the p-value (0.2467) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is a relationship between gender and activity status.

Since a significant relationship is not found between gender and activity status, we cannot say which group will receive what treatment.