Hi,I need help on this Friday’s statistics exam. This course used SPSS software, which means you need to understand the graphs and forms from SPSS. This course mainly about statistics, such as Chi-Square test (Goodness-of-fit test, r*c contingency table, Mantel-Haenszel test), ANOVA (one-way, Kruskal-Wallis test; RBD two-way, Friedman-Kendall-Smith test), Correlation Analysis, Linear Regression, Logistic Regression, Survival Analysis, Proportional Hazards. You also need to be familiar with the basic knowledge of statistics, such as p-value, t-test, z-test, paired samples, Independent samples(common variance&unequal variances), Sample size estimation, Wilcoxon signed rank test, Wilcoxon rank sum test, population proportion, odds ratio. And also a chapter of Prevalence. I upload the example test with answer, but due to switch to the online test, the questions should be all multiple choice questions.Please check. Thanks for your help ! !

practice_final_answerkey.pdf

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December 6, 2017

Fall 2017: Final

Instructions:

1. Write your name in the blank.

2. Circle your instructor’s name.

3. There are 6 questions. All questions have several parts.

4. Spaces for answers are provided below the questions in this single-sided 19-page document. Please put

all answers on this exam sheet in the spaces provided. Answers recorded elsewhere will not be considered.

5. If you need more room for calculations than what is provided in the answer blanks, you may use the back

of the previous page; make a note in the answer blank if you do so.

6. For all tests, use a significance level of = 0.05 unless otherwise indicated.

7. For the statistical test questions, you must plug in the appropriate numbers for the test statistic to get full

credit. For example, on the line that says “Work” do not simply write the formula for the test statistic

again; you must plug in the appropriate numbers into the correct places in the formula.

8. Try to answer all questions, as you will not be penalized for wrong answers.

9. Be aware that not all questions are of equal value, so time yourself accordingly.

GOOD LUCK!

Page 2/19

December 6, 2017

Fall 2017: Final

A. (4 points each; 20 points total). For the following scenarios, identify the best statistical procedure the

researchers should use and briefly explain your choice.

• Independent (2-sample) t-test (equal

variances)

• Wilcoxon signed rank test

• Pearson’s χ2-test

• Goodness-of-fit χ2-test

• r × c contingency table χ2-test

• Fisher’s Exact Test

• ANOVA F-test for completely randomized

designs (one-way ANOVA)

• Kruskal-Wallis test

• Pearson correlation coefficient

• Simple linear regression analysis

• Independent (2-sample) t-test (Welch)

• Paired (matched) t-test

• Wilcoxon rank sum test

• McNemar’s χ2-test

• Mantel-Haenszel χ2-test

• ANOVA F-test for randomized blocks

design

• Friedman-Kendall-Smith test

• Spearman correlation coefficient

• Logistic regression

• Log-rank test

• Cox proportional hazards regression

A.1. A study was conducted to follow overweight males, aged 20–40 years of age for a period of 18 months.

During the study, three different methods of weight loss were assessed: calorie restriction alone, exercise

alone, and calorie restriction plus exercise. Participants were grouped into blocks defined by age-group.

Each block experienced all three weight loss programs, assigned in a random order within the block.

Total change in body weight was measured for each subject after 6 months. The investigators want to

test for differences in total change in body weight across the three weight loss programs. Histograms

revealed departure from normality for total change in body weight.

The best statistical procedure is: Friedman-Kendall-Smith test

(2 points)

Briefly explain choice of test: Test of differences in median for a continuous but non-normally distributed

response variable (change in body weight) and a categorical treatment variable (method of weight loss).

Participants were grouped into blocks (age)

(2 points)

A.2. In Nepal, a study was conducted to investigate whether exposure to indoor air pollution due to cooking

stove was associated with increased risk of cataract among rural women. Both the exposure and outcome

was measured as dichotomous variables (yes/no). In total, 128 women were recruited into the study, 34

with cataracts and 94 without cataracts.

The best statistical procedure is: Pearson’s χ2-test

(2 points)

Briefly explain choice of test: Both the dependent and independent variables are dichotomous variables

and we are testing for association between the two variables. Number of cases and controls suggest

unmatched data.

(2 points)

Page 3/19

December 6, 2017

Fall 2017: Final

A.3. A study was conducted in Wales relating blood pressure and lead levels in the blood. It was reported

that 40 out of 455 men with low lead levels (≤ 11μg/100mL) had elevated systolic blood pressure (SBP

≥ 160 mmHg), while 160 out of 410 men with high blood-lead levels had elevated SBP. For women, 60

out of 663 women with low blood-lead levels had elevated SBP, while 10 out of 192 women with high

blood-lead levels had elevated SBP. The researchers want to test the hypothesis that there is an

association between blood pressure and blood lead, while controlling for gender.

The best statistical procedure is: Mantel-Haenszel χ2-test

(2 points)

Briefly explain choice of test: The investigators are comparing two continuous variables that have been

converted to dichotomous categorical variables, while controlling for a third categorical variable.

(2 points)

A.4. A group of 12 hemophiliacs, all 40 years of age or younger at HIV seroconversion, was followed from

the time of primary AIDS diagnosis (between 1984 and 1989) until either death or the end of the study

in 1991. Another group of 10 hemophiliacs—all of whom were older than 40 years of age at the time of

seroconversion—was followed independently in the same way. For all subjects, transmission of HIV

had occurred through infected blood products. The researchers would like to determine if the subjects

who were younger at seroconversion tended to live longer than the subjects who were older than 40 at

seroconversion.

The best statistical procedure is: Log-rank test (Cox regression also works)

(2 points)

Briefly explain choice of test: The data are time-to-event with censoring and the investigators want to

compare the two groups.

(2 points)

Page 4/19

December 6, 2017

Fall 2017: Final

A.5. The following table contains results looking at difference in baseline characteristics between people with

or without age-related macular degeneration (AMD). Name the statistical procedure that was used to

get the p-values marked by A.5.1, A.5.2, A.5.3 and A.5.4. (Assume normality for both age and diastolic

blood pressure, equal variances for age, and unequal variances for diastolic blood pressure.)

Variables

No AMD

Incident AMD

(N = 3808)

(N = 100)

Socio-demographic Characteristics

Age (years)

p-value

54.3 (±10.1)

60.8 (±12.2)

<0.001 (A.5.1)
40–49
1660 (38.2%)
23 (23.0%)
<0.001 (A.5.2)
50–59
1218 (32.0%)
25 (25.0%)
60–69
771 (20.2%)
23 (23.0%)
70–79
313 (8.2%)
21 (21.0%)
46 (1.2%)
8 (8.0%)
2285 (59.9%)
58 (58.0%)
Age group (years)
80+
Sex: female
0.57 (A.5.3)
Diastolic BP (DBP)
75.8 (±10.8)
76.0 (±10.7)
0.92 (A.5.4)
Data are presented as mean (SD) or frequency (%); BP = Blood Pressure;
A.5.1: Independent (2-sample) t-test (equal variances)
(1 point)
A.5.2: r × c contingency table χ2-test
(1 point)
A.5.3: Pearson’s χ2-test (Fisher’s Exact Test also acceptable)
(1 point)
A.5.4: Independent (2-sample) t-test (Welch)
(1 point)
Page 5/19
December 6, 2017
Fall 2017: Final
B. (11 points) Myopia (near-sightedness) seems to be more common in people with higher education. In a
recent study looking at the possible association between education status and myopia severity, education
was categorized as high (>12 years) or low (≤ 12 years) and myopia was categorized into three groups by

severity (mild, moderate, and severe). The SPSS output below summarizes the results.

Case Processing Summary

Cases

Valid

N

Education Status * Myopia

Missing

Percent

1518

N

Total

Percent

99.7%

5

N

0.3%

Percent

1523

Severity

Education Status * Myopia Severity Crosstabulation

Count

Myopia Severity

mild

Education Status

moderate

severe

Total

low

61

221

46

328

high

152

822

216

1190

213

1043

262

1518

Total

Chi-Square Tests

Asymptotic

Significance (2Value

Pearson Chi-Square

8.862a

df

sided)

B.2

B.2

Likelihood Ratio

8.576

2

.014

Linear-by-Linear Association

8.159

1

.004

N of Valid Cases

1518

a. 0 cells (0.0%) have expected count less than 5. The minimum expected

count is 46.02.

Page 6/19

100.0%

December 6, 2017

Fall 2017: Final

B.1. What statistical method was used to test the association between education status and severity of myopia?

Justify your answer.

Answer: r × c contingency table χ2-test

(1 point)

Explanation: Both variables are categorical, with one having more than two categories. No stratification

was done.

(2 points)

B.2. Calculate the expected frequency for the “high education, moderate myopia” group.

Formula:

Work:

E22

E22

r2 c2

n

(1 point)

1190 1043

1518

(1 point)

Answer: 817.635

(1 point)

B.3. Calculate the values that should go in the places marked “B.2” in the SPSS output.

df: df = (r – 1)(c – 1) = (2 – 1)(3 – 1) = 2

(1 point)

p-value: 0.0119

(1 point)

B.4. Is there an association between education status and severity of myopia? Explain.

Answer: Yes, p = 0.0119 < 0.05
(1 point)
B.5. Write a conclusion based on your analyses, as written in a journal article.
Conclusion: There is a statistically significant association between amount of education and severity of
myopia (p = 0.0119).
(2 points)
Page 7/19
December 6, 2017
Fall 2017: Final
C. (18 points) A study was conducted to investigate the effects of treating cows with antibiotics to see how
much weight (in kilograms) they gained over a period of three months. On the theory that cows from the
same farm might react more similarly to each other than to cows from other farms, the investigators
selected four farms. On each farm, the investigators randomly selected one cow to receive Antibiotic 1,
one cow to receive Antibiotic 2, and one cow to receive a placebo. Investigators believed that the data
would be normally distributed with equal variances in each treatment group.
C.1. What is the appropriate statistical test for the experiment described above?
Answer: ANOVA F-test for randomized blocks design
(2 points)
C.2. The following output contains the partial, edited results from the study. Complete the table. (0.5 points
each entry, 6 points total)
Sum of Squares
df
Mean Square
F
p-value
2.122
2
1.061
0.9667
0.43259
202.200
3
67.400
61.4123
0.00007
Error
6.585
6
Total
210.907
11
Between
Treatments
Between
Farms
1.0975
C.3. Based on the results, what do you conclude?
Conclusion: There is not a statistically significant difference in weight gain among cows treated with
either placebo or the two antibiotics (p = 0.43259).
(2 points)
Assuming that the F-test from above gave a statistically significant result, the investigators were planning to
find out which (if any) of the pairwise comparisons were statistically significant.
C.4. How many pairwise comparisons would there be?
Answer:
M
3(3 1)
3
2
(1 point)
C.5. What would the Bonferroni-adjusted significance level in these comparisons be?
Answer:
A
0.05
0.0167
3
(1 point)
Page 8/19
December 6, 2017
Fall 2017: Final
C.6. Should the investigators do the multiple comparisons? Why or why not?
Answer: No, since the overall F-test was not significant, they should not check the pairwise comparisons.
(2 points)
C.7. The investigators originally assumed that cows from the same farm would react more similarly to each
other than to cows from other farms. Does their analysis indicate that was the case? Explain.
Answer: Yes, because the test for the effect of the Farms was highly significant (p = 0.00007). That says
that the choice of blocks was effective.
(2 points)
C.8. If the distribution of weight gain showed a departure from normality, what would be the preferred
statistical method of analysis?
Answer: Friedman-Kendall-Smith
(2 points)
Page 9/19
December 6, 2017
Fall 2017: Final
D. (21 points) An investigator is interested in the relationship between Body Mass Index (BMI)—a measure
of obesity—and systolic blood pressure (SBP). He utilized data from a study on 1,514 individuals that
collected data on BMI (kg/m2) and systolic blood pressure (mm Hg). The investigator wants to study the
strength of linear association and see if BMI can predict systolic blood pressure.
The partially edited SPSS outputs summarize the results of the analysis:
Descriptive Statistics
Mean
Systolic Blood Pressure
Body Mass Index
Std. Deviation
N
124.85
18.311
1514
24.56
3.520
1514
Correlations
Body Mass Index
Body Mass
Systolic Blood
Index
Pressure
Pearson Correlation
.281**
1
Sig. (2-tailed)
Systolic Blood Pressure
.000
N
1514
1514
Pearson Correlation
.281**
1
Sig. (2-tailed)
.000
N
1514
1514
**. Correlation is significant at the 0.01 level (2-tailed).
Correlations
Spearman's rho
Body Mass Index
Systolic Blood
Index
Pressure
1.000
.272**
.
.000
N
1514
1514
Correlation Coefficient
.272**
1.000
Sig. (2-tailed)
.000
.
N
1514
1514
Correlation Coefficient
Sig. (2-tailed)
Systolic Blood Pressure
Body Mass
**. Correlation is significant at the 0.01 level (2-tailed).
Page 10/19
December 6, 2017
Fall 2017: Final
Model Summaryb
Model
R
Adjusted R
Std. Error of the
Square
Estimate
R Square
.281a
1
17.579
a. Predictors: (Constant), Body Mass Index
b. Dependent Variable: Systolic Blood Pressure
Coefficientsa
Unstandardized
Standardized
95.0% Confidence Interval
Coefficients
Coefficients
for B
Model
B
Std. Error
Beta
1
(Constant)
88.951
3.185
Body Mass
1.462
.128
t
27.930
.281
D.5
Sig.
.000
D.5
Lower
Upper
Bound
Bound
82.704
95.198
1.210
1.714
Index
a. Dependent Variable: Systolic Blood Pressure
D.1. Based on the histograms of the variables, which correlation coefficient would be appropriate? Provide
a brief justification for your choice.
Answer: Pearson
(1 point)
Justification: Since at least one of the variables (BMI) appears to be normally distributed, Pearson
correlation is the better measure.
(2 points)
D.2. Is there a statistically significant linear association between the BMI and SBP? Provide a brief
justification for your conclusion.
Answer: Yes
(1 point)
Justification: The Pearson correlation is 0.281, which is not large, but the associated p-value from SPSS is
0.000, which means that the association is significant.
(2 points)
Page 11/19
December 6, 2017
Fall 2017: Final
D.3. Which of the following regression lines correctly answers the investigator’s question. (circle one only)
(1 point)
a) BMI = 1.462 + 88.95 × SBP
c) SBP = 1.462 + 88.95 × BMI
e) None of the above
b) BMI = 88.95 + 1.462 × SBP
d) SBP = 88.95 + 1.462 × BMI
D.4. Calculate the statistic that measures the goodness of fit. What is the interpretation of the value?
Answer: R2 = r2 = 0.2812 = 0.079
(1 point)
Interpretation: 7.9% of the variation in SBP is explained by its linear relationship with BMI.
(2 points)
D.5. Calculate the values that should go in the places marked “D.5” in the SPSS output.
1.462
t
11.42188
0.128
Test statistic:
p-value: <0.0001
(1 point)
(1 point)
D.6. What is the slope in this analysis? Interpret it.
Slope: 1.462
(1 point)
Interpretation: For each unit increase in BMI (kg/m2), the predicted value of SBP increases by
1.462 mm Hg.
(2 points)
D.7. What is the predicted mean value of SBP for people who have a BMI of 30?
Formula: yˆ ( x) a bx
(1 point)
Work: yˆ (30) 88.95 1.462 30
(1 point)
Answer: 132.81
(1 point)
Page 12/19
December 6, 2017
Fall 2017: Final
D.8. Calculate a 99% confidence interval for the predicted mean value from D.7.
1 (30 x )2
n (n 1)sX2
yˆ (30) t0.995,15142 se[ yˆ (30)] yˆ (30) t0.995,1512 sY∣ X
Formula:
132.81 2.58 17.579
Work:
(1 point)
1
(30 24.56) 2
1514 (1514 1) 3.5202
(1 point)
Answer: (130.6639, 134.9561)
(1 point)
E. (14 points) A group of glaucoma researchers at the Eye Institute recruited a sample of 32 cases and
18 controls to examine the association of sex (female/male) and primary angle closure glaucoma (PACG;
yes/no). People from East Asia are known to suffer disproportionately from PACG, so the investigators
tested race (1 = East Asians, 0 = others) as a potential confounder and controlled for that.
The partially edited SPSS output of the analysis is below:
Case Processing Summary
Cases
Valid
N
sex * PACG * racial group
Missing
Percent
100
N
Total
Percent
100.0%
0
N
0.0%
Percent
100
sex * PACG * racial group Crosstabulation
Count
PACG
racial group
others
no
sex
females
22
39
5
15
20
22
37
59
females
9
18
27
males
5
9
14
14
27
41
females
26
40
66
males
10
24
34
36
64
100
Total
sex
Total
Total
sex
Total
17
males
East Asians
yes
Total
Page 13/19
100.0%
December 6, 2017
Fall 2017: Final
Chi-Square Tests
Asymptotic
racial group
others
Value
Pearson Chi-Square
Continuity
Correctionb
Likelihood Ratio
Significance (2-
Exact Sig. (2-
Exact Sig. (1-
sided)
sided)
sided)
df
1.954c
1
.162
1.240
1
.266
2.020
1
.155
Fisher's Exact Test
Linear-by-Linear Association
1
.166
.023d
1
.879
Continuity Correctionb
.000
1
1.000
Likelihood Ratio
.023
1
.879
N of Valid Cases
East Asians
1.921
Pearson Chi-Square
Linear-by-Linear Association
N of Valid Cases
1.000
.572
.023
1
.880
.970a
1
.325
.586
1
.444
.986
1
.321
.383
.223
41
Pearson Chi-Square
Continuity
.132
59
Fisher's Exact Test
Total
.255
Correctionb
Likelihood Ratio
Fisher's Exact Test
Linear-by-Linear Association
.961
N of Valid Cases
100
1
.327
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 12.24.
b. Computed only for a 2x2 table
c. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 7.46.
d. 1 cells (25.0%) have expected count less than 5. The minimum expected count is 4.78.
Tests of Homogeneity of the Odds Ratio
Asymptotic
Significance (2Chi-Squared
df
sided)
Breslow-Day
1.064
1
.302
Tarone's
1.064
1
.302
Page 14/19
December 6, 2017
Fall 2017: Final
Tests of Conditional Independence
Chi-Squared
df
Asymptotic Significance (2-sided)
Cochran's
.970
1
.325
Mantel-Haenszel
.573
1
.449
Mantel-Haenszel Common Odds Ratio Estimate
Estimate
1.551
ln(Estimate)
.439
Standard Error of ln(Estimate)
.450
Asymptotic Significance (2-sided)
.329
Asymptotic 95% Confidence
Common Odds Ratio
Interval
ln(Common Odds Ratio)
Lower Bound
.642
Upper Bound
3.749
Lower Bound
-.443
Upper Bound
1.322
The Mantel-Haenszel common odds ratio estimate is asymptotically normally distributed
under the common odds ratio of 1.000 assumption. So is the natural log of the estimate.
Based on the output above answer the questions:
E.1. What statistical method was used to test the association between sex and PACG? Why was that method
used?
Answer: Mantel-Haenszel χ2-test
(1 point)
Explanation: The investigators were comparing two categorical variables while controlling for a third.
(2 points)
E.2. Is there an association between sex and PACG, ignoring race?
Answer: No
(1 point)
Explanation: From the “Chi-Square Tests” table, the Pearson Chi-Square for the total racial group is 0.970
with a p-value of 0.325.
(2 points)
Page 15/19
December 6, 2017
Fall 2017: Final
E.3. Is there an association between sex and PACG, after controlling for race?
Answer: No
(1 point)
Explanation: From the “Tests of Conditional Independence” table, the Mantel-Haenszel Chi-Squared is
0.573 with a p-value of 0.449.
(2 points)
E.4. Is there any evidence of a statistically significant difference between the stratum-specific odds ratios?
Answer: No
(1 point)
Explanation: From the “Tests of Homogeneity of the Odds Ratio” table, the Breslow-Day p-value is 0.302,
indicating that the odds ratios in the strata are not significantly different.
(2 points)
E.5. Write a conclusion based on your analyses, as written in a journal article.
Conclusion: After controlling for race, there is not a statistically significant association between sex and
PACG (p = 0.449).
(2 points)
Page 16/19
December 6, 2017
Fall 2017: Final
F. (16 points) Investigators were testing a new drug for treating ...
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