Question

Anger and Coronary Heart Disease
Consider the two-way table below based on a four-year study about the relationship between anger and heart disease among a random sample of individuals. The subjects (i.e. participants in the study) were free of heart disease at the beginning of the study when they took a test that measured how prone they were to sudden anger. Their heart health was monitored over a four-year period and it was recorded whether they developed Coronary Heart Disease (CHD). In short, the study attempts to examine whether anger levels are associated with the likelihood of developing coronary heart disease. Now please answer the questions 1) to 3):

1)(4 Points)In the two-way table below, report the marginal distributions and the total sample size, in counts and percents.

2) (3 Points)In the two-way table below, report the conditional distributions of coronary heart disease in percents. Note that the conditional distributions of coronary heart disease refer to the distributions of coronary heart disease given each anger level.

3) (2 Points)With reference to your calculations above as well as our discussions in class (on how to detect association between two categorical variables), explainwhether there is potential association between anger and Coronary Heart Disease. (Note: An answer of only “Yes” or “No” without any explanation will receive no credit.)

#Individuals	Coronary Heart Disease	NO Coronary Heart Disease
Low Anger	530	3,057
Moderate Anger	1,100	4,621
High Anger	270	606

Answer 1

1)(4 Points)In the two-way table below, report the marginal distributions and the total sample size, in counts and percents.

the marginal distribution in counts

#Individuals	Coronary Heart Disease	NO Coronary Heart Disease	total
Low Anger	530	3,057	3587
Moderate Anger	1,100	4,621	5721
High Anger	270	606	876
total	1900	8284	10184

the marginal distribution in percent

#Individuals	Coronary Heart Disease	NO Coronary Heart Disease
Low Anger	0.0520	0.3002	0.3522
Moderate Anger	0.1080	0.4538	0.5618
High Anger	0.0265	0.0595	0.0860
	0.1866	0.8134	1.0000

2) (3 Points)In the two-way table below, report the conditional distributions of coronary heart disease in percents. Note that the conditional distributions of coronary heart disease refer to marginal the distributions of coronary heart disease given each anger level.

the conditional distribution is given as

#Individuals	Coronary Heart Disease	NO Coronary Heart Disease
Low Anger	0.1478	0.8522
Moderate Anger	0.1923	0.8077
High Anger	0.3082	0.6918

3) (2 Points)With reference to your calculations above as well as our discussions in class (on how to detect association between two categorical variables), explainwhether there is potential association between anger and Coronary Heart Disease. (Note: An answer of only “Yes” or “No” without any explanation will receive no credit.)

here we use chi-square test and chi-square=sum((O-E)2/E=122.2564 with (r-1)(c-1)=(3-1)(2-1)=2 df

critical chi-square(0.05,2)=5.99 is less than calcuated chi-square=122.2564, so we fail to accept null hypothesis of independence between the anger and coronary heart disease and conclude that there is potential association between anger and Coronary Heart Disease.

Observed(O)	Expected	E	(O-E)	(O-E)2/E
530	3587*1900/10184	669.2164	-139.216	28.96105
1100	5721*1900/10184	1067.351	32.64925	0.99871
270	876*1900/10184	163.4328	106.5672	69.48763
3057	3587*8284/10184	2917.784	139.2164	6.642443
4621	5721*8284/10184	4653.649	-32.6493	0.229062
606	876*8284/10184	712.5672	-106.567	15.93753
10184	0	10184	2.56E-13	122.2564