Question

To investigate whether bald males have a higher incidence of heart disease, researchers asked a sample of 663 male heart patients to classify their degree of baldness on a 4-point scale.They also asked a second group (not suffering from heart disease) of 772 males to do the same baldness assessment. The results are summarized in the table below.

Heart Disease No Heart Disease Total None Little Some Much 25116519552 331 | 221 185 35 582 386 380 87

(a) Identify the response and explanatory variable.

(b) Of those males who had heart disease, what proportion claimed to have little or no baldness?

(c) Is there an association between these two variables? Give be sure to calculate the conditionals and marginals to support.

Answer 1

a) Heart disease is the Response or target variable and kind/scale of baldness is the explanatory variable or predictors.

b) out of 663 males 25% of little bald male have heart disease and 38% of no bald male have heart disease.

c) There is association between the variables because the p value is less than 0.05 alpha level. so we reject null hypothesis

Reference result in R:

chi2$statistic chi2$p.value
14.510189031 0.002286883

D) Marginal and conditional distribution

Marginal distribution for Disaese class

Out of both 1435 samples 46% of people has heart disease and 54% of male has no heart disease

Marginal distribution for Bald type

None = 41%

little = 27%

some = 26%

much = 6%

conditional distribution for heart disease for all bald types:

none = 37%

little = 27%

some = 29%

much = 7%

conditional distribution for No heart disease for all bald types:

none = 43%

little = 29%

some = 24%

much = 4%