Analysis Assignment #2

Analysis Assignment #2

50 points

Due: December 11^th, 2016 11:59 p.m.

Student Name: ______________________________

Submission Date: _________________

Instructions:

Rename this file as first initial_lastname_assignment2_mmddyyyy. Provide your answer underneath each question. You must upload the renamed file with your answer to the Assignment 2 tab inside the class Blackboard by the deadline.

1. In a sample of 140 hospitalized older adults, the individuals were cross-classified by their cognitive impairment status and whether they had an incidence of fall, and an association was tested between the two classification factors.(6 points)

Chi-square (df=1) = 5.25, p-value = 0.022

Answer the following questions based on the data above.

a. What percentage of elders in this sample had a fall? (2 points)

I.14.3%

II. 20.0%

III. 25.0%

IV. 85.7%

b. Is there an evidence of association between cognitive status and incidence of fall? Support your answer with a statistic.(2 points)

c. Compute expected frequency for the cell with cognitive impairment and fall.(2 points)

2. The following correlation matrix represents relationships among social variables. These data were obtained from 793 children in the third, fourth and fifth grades in 10 different elementary schools. For each of the variables a higher score indicates more of the attribute.(6 points)

Table 1: Correlation matrix (Pearson’s correlation coefficient)

a. What is the value of the Pearson’s r for the relationship between “withdrawal” and “aggression”? Interpret the value in words. (2 pts)

b. Which variable has the strongest relationship with “withdrawal”? (2 pts)

c. What is the value of the coefficient of determination for the relationship between perceived behavior conflict and social preference? (2 pts)

3. The following table shows the relationship between methyl mercury intake (ug Hg/day) and whole blood mercury values (ug/g) in 12 subjects exposed to methyl mercury through consumption of contaminated fish.(8 points)

Table 2: Linear regression of whole blood mercury on methyl mercury intake through contaminated fish

N = 12, F = 75.53 (p < 0.001), R² = 0.883

a. Write a research question for this scenario. (2 pts)

b. Write the estimated regression equation describing the linear relationship between the two variables. (2 pts)

c. Interpret the coefficient of determination value. (2 pts)

d. If someone had a methyl Mercury intake of 500 units, what would be the amount of mercury in the whole blood? (2 pts)

4. Refer to the data on cardiovascular risk factors (RISKFACT). The subjects are 250 males engaged in sedentary occupations. You wish to study the relationships among risk factors in this population. The variables included are:(7 points)

Y= oxygen consumption
X1 = systolic blood pressure (mm Hg)
X2 = total Cholesterol (mg/DL)
X3 = HDL cholesterol (mg/DL)
X4 = triglycerides (ug/DL)

Table 3: Linear regression of oxygen consumption on four independent (explanatory) variables

N = 250, F = 314.02 (p < 0.001), R² = 0.837

a. Using all the variables, write a research hypothesis for these data. (2 pts)

b. Write out the multiple regression equation for these data. (2 pts)

c. Interpret the effects of Systolic BP and total cholesterol variables. (2 pts)

d. What is the most relevant predictor in the model? (1 pt)

5. Research suggests that both maternal smoking history and maternal BMI are associated with the delivery of low birth weight infants. In the table below, birth weight (grams) and BMI are continuous variables and smoking history is a categorical variable. The research question is: Does the infant mean birth weight differ by maternal smoking status after controlling for maternal BMI? (7 points)

Table 4: Analysis of covariance results

Levene’s test p-value = 0.968

Linear relationship between infant birth weight and maternal BMI, r = -0.20, p<.001

Homogeneity of regression assumption p>.05

a. In the research question above: (3 pts)

i. What is the dependent variable?

ii. What is the independent variable?

iii. What is the covariate?

b. Is the homogeneity of regression assumption met? Provide statistical evidence. (1 pt)

c. Is there a statistical evidence of group difference? If yes, what is the evidence? (1 pt)

d. After reviewing the multiple comparisons section of the table, identify which groups differ significantly and which ones do not differ significantly from each other. In each comparison state whether the mean birth weight is higher or lower for each group. (2 pts)

6. These data are from a Prostate Cancer Study data set, with a sample of 379 men. A logistic regression model was fit to the data with capsule penetration (CAPSULE) as the dependent variable with predictor variables of age (Age), prostatic specific antigen (PSA), and tumor volume (VOL). The dependent variable is coded as 0= no capsule penetration and 1 = capsule penetration. The independent variables are all continuous variables. The data for this study are presented in the table below. (8 points)

Clinical variables that may predict capsule penetration

a. Write a research hypothesis for these data. (2 pts)

b. How would you interpret NagelkerkeR² value? (2 pts)

c. Is age a significant predictor in the model? Why or why not? Provide statistical evidence. (2 pts)

d. Interpret effect of PSA and VOL in words. (2 pts)

7. Suppose that a researcher conducted a prospective cohort study, i.e. they followed a number of participants over 10 years in which they started with known exposure (smoking status), and recorded lung cancer diagnosis (outcome) at the end of the study. They classified participants by smoking status and lung cancer diagnosis as follows: (8 points)

a. Compute risk of lung cancer in smoking group. (2 pts)

b. Compute risk of lung cancer in nonsmoking group. (2 pts)

c. Estimate relative risk. (2 pts)

d. How would you interpret the relative risk estimate? (2 pts)

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