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 ! !
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December 6, 2017
Fall 2017: Final
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.
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
• 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
• 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
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)
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
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
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
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.
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
The best statistical procedure is: Log-rank test (Cox regression also works)
Briefly explain choice of test: The data are time-to-event with censoring and the investigators want to
compare the two groups.
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.)
(N = 3808)
(N = 100)
<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
Education Status * Myopia
Education Status * Myopia Severity Crosstabulation
N of Valid Cases
a. 0 cells (0.0%) have expected count less than 5. The minimum expected
count is 46.02.
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
Explanation: Both variables are categorical, with one having more than two categories. No stratification
B.2. Calculate the expected frequency for the “high education, moderate myopia” group.
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
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 ... Purchase answer to see full attachment
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