Question

Now that you have a better idea about what differentiates a one sample chi square from an independent samples (two factor) chi square, I want you to come up with one study idea that would use a one sample chi square and one study that would use an independent samples (two factor) chi square.

Answer 1

One sample Chi square

Suppose a University conducted a survey of its recent graduates to collect demographic and health information for future planning purposes as well as to assess students' satisfaction with their undergraduate experiences. The survey revealed that a substantial proportion of students were not engaging in regular exercise, many felt their nutrition was poor and a substantial number were smoking. In response to a question on regular exercise, 60% of all graduates reported getting no regular exercise, 25% reported exercising sporadically and 15% reported exercising regularly as undergraduates. The next year the University launched a health promotion campaign on campus in an attempt to increase health behaviors among undergraduates. The program included modules on exercise, nutrition and smoking cessation. To evaluate the impact of the program, the University again surveyed graduates and asked the same questions. The survey was completed by 500 graduates and the following data were collected:

	No regular exercise	Sporadic exercise	Regular exercise	Total
Number of Students	265	135	100	500

Based on the data, We can find " is there evidence of a shift in the distribution of responses to the exercise question following the implementation of the health promotion campaign on campus ?".

Independent sample chi square

Suppose that students in grades 4-6 were asked whether good grades, athletic ability, or popularity was most important to them. A two-way table separating the students by grade and by choice of most important factor is shown below:

	Grade
	4	5	6	Total
Grades	53	61	58	172
Popular	24	36	38	98
Sports	28	15	24	67
Total	105	112	120	337

We can investigate whether Student's choices are independent of the grade using the Independent samples Chi square.