Question

Overview
Most doctors would probably agree that a Mediterranean diet, rich in vegetables, fruits, and grains, is healthier than a high-saturated fat diet. Indeed, previous research has found that the diet can lower risk of heart disease. However, there is still considerable uncertainty about whether the Mediterranean diet is superior to a low-fat diet recommended by the American Heart Association. This study is the first to compare these two diets.

The subjects, 605 survivors of a heart attack, were randomly assigned follow either (1) a diet close to the "prudent diet step 1" of the American Heart Association (control group) or (2) a Mediterranean-type diet consisting of more bread and cereals, more fresh fruit and vegetables, more grains, more fish, fewer delicatessen foods, less meat. An experimental canola-oil-based margarine was used instead of butter or cream. The oils recommended for salad and food preparation were canola and olive oils exclusively. Moderate red wine consumption was allowed.

Over a four-year period, patients in the experimental condition were initially seen by the dietician, two months later, and then once a year. Compliance with the dietary intervention was checked by a dietary survey and analyses of plasma fatty acids. Patients in the control group were expected to follow the dietary advice given by their physician.

The researchers collected information on number of deaths from cardiovascular causes e.g., heart attack, strokes, as well as number of nonfatal heart-related episodes. The occurrence of malignant and nonmalignant tumors was also carefully monitored.

Question to Answer
Is the Mediterranean diet superior to a low-fat diet recommended by the American Heart Association?

Design Issues
The strength of the design is that subjects were randomly assigned to conditions. A possible weakness is that compliance rates depended on reports rather than observation since observation is impractical in this type of research.

Descriptions of Variables

Variable	Description
Type of diet	AHA or Mediterranean
Various outcome measures of health and disease	does the patient have cancer, etc.?

Data Frequencies

	Cancers	Deaths	Nonfatal illness	Healthy	Total
AHA	15	24	25	239	303
Mediterranean	7	14	8	273	302
Total	22	38	33	512	605

Assignment

The following questions are to be answered on the Chapter 11 Quiz.

1. What percentage of people on the AHA diet had some sort of illness or death?
2. What percentage of people on the Mediterranean diet had some sort of illness or death?
3. Perform a chi-square test for independence on the above data to determine if there is any relationship between diet and outcome. Report the Chi Square value and p-value.
4. State your conclusions.

Answer 1

The percentage of people on the AHA diet had some sort of illness or death = (24 + 25)/303 =

The percentage of people on the Mediterranean diet had some sort of illness or death = (14 + 8)/302 =

The hypothesis being tested is:

H₀: There is no relationship between diet and outcome

H_a: There is a relationship between diet and outcome

		Col 1	Col 2	Col 3	Col 4	Total
Row 1	Observed	15	24	25	239	303
	Expected	11.02	19.03	16.53	256.42	303.00
	O - E	3.98	4.97	8.47	-17.42	0.00
	(O - E)² / E	1.44	1.30	4.34	1.18	8.26
Row 2	Observed	7	14	8	273	302
	Expected	10.98	18.97	16.47	255.58	302.00
	O - E	-3.98	-4.97	-8.47	17.42	0.00
	(O - E)² / E	1.44	1.30	4.36	1.19	8.29
Total	Observed	22	38	33	512	605
	Expected	22.00	38.00	33.00	512.00	605.00
	O - E	0.00	0.00	0.00	0.00	0.00
	(O - E)² / E	2.88	2.60	8.70	2.37	16.55
		16.55	chi-square
		3	df
		.0009	p-value

The test statistic is 16.55.

The p-value is 0.0009.

Since the p-value (0.0009) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a relationship between diet and outcome.