Biostatistics

Answer the following questions. Copy and paste any required data charts or summaries into this Word document. Use additional space as needed. Be sure to include your name on the document and use the

file naming convention. This exam is open book and open notes.

I. Descriptive Statistics: (20 pts)

Download the data set gerstman1.sav. Complete the following:

1) List the level of measurement for the variables, AGE, SEX, AGEGRP, SBP1 in the data set and describe the appropriate numerical and descriptive statistics based on these. 4 pts

2) Calculate (by hand) the mean and standard deviation for age based on the first 20 records in the data set. Use the table below to do your calculations. 4 pts

Record Number AGE Observed

Mean Difference Difference

Squared

1 3

2 11

3 15

4 46

5 14

6 35

7 46

8 35

9 40

10 29

11 22

12 16

13 31

14 42

15 22

16 45

17 24

18 1

19 28

20 25

Sum

3) Generate numerical and graphical descriptive statistics for each of the variables, namely, AGE, SEX, AGEGRP and SBP1. 8 pts

4) Interpret the output you generated in part 3 for each of the variables in the data set. 4 pts

II. Paired and Independent t tests: (20 pts)

Using the data set gerstman 1.sav and use SPSS to complete the following calculations. Be sure to include interpretation of the SPSS output in your responses.

1) Use the 5-step approach to hypothesis testing and the calculation of the 95% confidence intervals to answer the following research question: Did you observe a significant difference in Systolic Blood

Pressure (SBP) over the course of the study? (10 pts)

2) Use the 5-step approach to hypothesis testing and the calculation of the 95% confidence intervals to answer the following research question: Is there a difference in SBP1 based on HIV status? (10 pts)

III. Cross-Tabulation: (20pts)

Download the data set alcohol_Bladder.sav and use SPSS to complete the following calculations. Be sure to include interpretation of the SPSS output in your responses.

1) Use the 5-step approach to hypothesis testing to answer the following research question: In the sample provided in alcohol_Bladder.sav, are the variables income and Bladder Cancer independent of each

other? (Note: The question could also be asked: Is there an association between the variables because the lack of independence implies an association)? (10 pts)

2) Answer the following based on the cross-tabulation of alcohol consumption and Bladder Cancer: (10 pts)

Alcohol consumption * Bladder Cancer Crosstabulation

Count

Bladder Cancer Total

No Yes

Alcohol consumption “Less than 1 drink per week” 30 54 84

4 or more drinks per month 22 115 137

Total 52 169 221

• Calculate the odds ratio. 4 pts

• Describe how the odds ratio differs from the relative risk or risk ratio and why you would chose it here. 2 pts

• Interpret the odds ratio and how it might impact the practice of public health practitioners. 2 pts

• If you wanted to know whether this relationship was statistically significant what test(s) could you use? 2 pts

IV. ANOVA: 20pts

Download the data set inc-pov-hlthins.sav and use SPSS to complete the following calculations. Be sure to include interpretation of the SPSS output in your responses.

1) Produce box plots of income for each region of the US in the data set and interpret them. Based on the box plots do you expect to find a difference between any of the groups? 4 pts

2) Create descriptive statistics for each region, using the variable income. 4 pts

• Include skewness and kurtosis in the output. 2 pts

• Create a histogram for each group. 2 pts

3) Run the ANOVA for income based on region. Include the ANOVA table and the test for Homogeneity of Variance. Interpret the results. 6 pts

4) Conduct post hoc analysis using Bonferroni and LSD methods to control for multiple testing. 6 pts

• Provide the output. 2 pts

• Interpret your results. 3 pts

• Why do you need to use methods like Bonferroni and LSD with the ANOVA? 1 pt

V. Regression: 20pts

1) Download the data set Gender_BMI.sav and use SPSS to complete the following calculations.

Use an independent t test and simple linear regression to identify whether a relationship exists between gender and BMI. (10 pts)

• Run the appropriate t test in SPSS, report the significance of the difference in means and the confidence interval, and interpret the results. 4 pts

• Run the simple linear regression in SPSS, report the significance of the variable gender and the overall fit of the model (using r2). Interpret the results. 4 pts

• How are these two approaches different? 1 pt

• Are your conclusions the same using both tests? 1 pt

2) Answer the following questions using the provided output: 10 pts

• Multiple Linear Regression 5 pts

Researchers looked at the Emergency Department Records of 60 adults ages 22 to 46 years who arrived in the ED complaining of chest pain during a 6 month period of time. They did not use a random

sample as they wanted 30 males and 30 females in the study. They collected information on BMI (a measure of overweight/obesity), Age, SBP (Systolic Blood Pressure) and the diagnosis of Diabetes. Their

first hypothesis (alternative) was that the dependent variable SBP is associated with BMI, Age, Diabetes, and Gender. They conducted a multiple linear regression to test their hypothesis. Here are the results

(note that they had two models and chose to use the second one):

Model Summaryc

Model R R Square Adjusted R Square Std. Error of the Estimate

1 .796a .634 .608 5.443

2 .792b .627 .607 5.445

a. Predictors: (Constant), Diabetes, Age, Gender, BMI

b. Predictors: (Constant), Age, Gender, BMI

c. Dependent Variable: SBP

ANOVAc

Model Sum of Squares df Mean Square F Sig.

1 Regression 2824.968 4 706.242 23.839 .000a

Residual 1629.408 55 29.626

Total 4454.376 59

2 Regression 2794.222 3 931.407 31.418 .000b

Residual 1660.155 56 29.646

Total 4454.376 59

a. Predictors: (Constant), Diabetes, Age, Gender, BMI

b. Predictors: (Constant), Age, Gender, BMI

c. Dependent Variable: SBP

Coefficientsa

Model Standardized Coefficients t Sig. 95.0% Confidence Interval for B

Beta Lower Bound Upper Bound

1 (Constant) 8.092 .000 57.471 95.309

Gender -.189 -2.100 .040 -6.381 -.149

BMI .557 6.130 .000 1.213 2.392

Age .507 6.067 .000 .426 .847

Diabetes -.089 -1.019 .313 -4.752 1.549

2 (Constant) 8.885 .000 55.243 87.407

Gender -.173 -1.950 .056 -6.054 .081

BMI .574 6.413 .000 1.276 2.436

Age .517 6.243 .000 .441 .859

a. Dependent Variable: SBP

1) Which variables in model 1 are significant? 1 pt

2) Which variables in model 2 are significant? 1 pt

3) Why did they choose model 2? 1 pt

4) What is the “fit” of model 2 (the one they chose to use)? 1 pt

5) Is this a good model, why or why not? 1 pt

• Multiple Logistic Regression 5 pts

The Emergency Department Researchers selected another 60 adults and again looked at Age, SBP, BMI, Gender, and Diabetes. This time however, they also collected information on whether the chest pain

was diagnosed as an MI (aka Heart Attack) or something else. Now their alternative hypothesis was that gender was related to the diagnosis of an MI, after controlling for Age, SBP, BMI, and Diabetes. They

used multiple logistic regression to test their hypothesis and these are their results (note that there are multiple models and they chose to use the final one):

Model Fitting Information

Model Model Fitting Criteria Likelihood Ratio Tests

-2 Log Likelihood Chi-Square df Sig.

Intercept Only 74.995

Final 16.398 58.598 5 .000

Pseudo R-Square

Cox and Snell .623

Nagelkerke .866

McFadden .767

Parameter Estimates

Heart Attacka B Std. Error Wald df Sig. Exp(B)

No Intercept 115.037 43.679 6.936 1 .008

BMI -1.400 .572 5.995 1 .014 .247

Age .037 .116 .099 1 .753 1.037

Diabetes .811 1.471 .304 1 .581 2.251

SBP -.469 .213 4.849 1 .028 .626

[Gender=1] -11.866 4.695 6.389 1 .011 7.025E-6

[Gender=2] 0b . . 0 . .

Parameter Estimates

Heart Attacka 95% Confidence Interval for Exp(B)

Lower Bound Upper Bound

No Intercept

BMI .080 .756

Age .826 1.303

Diabetes .126 40.193

SBP .412 .950

[Gender=1] 7.088E-10 .070

[Gender=2] . .

1) Is the final model significant? 2 pts

2) What are the odds ratios for each of the significant variables, and what do they mean? 2 pts

3) Will this model help the researchers, why or why not? 1 pt

Answer Summary

I would appreciate that you include a summary of answers or answers to each question in this table. You can hit “Enter” key to increase the space in each cell.

Please do not add rows or columns.

Please post supporting SPSS tables and graphs below the table.

Problem Answers Possible points

1. Descriptive Statistics: (20 pts)

1) List the level of measurement for the variables, AGE, SEX, AGEGRP, SBP1 in the data set and describe the appropriate numerical and descriptive statistics based on these. 4 pts 4.00

2) Calculate (by hand) the mean and standard deviation. 4 pts Mean:

SD:

Please put your calculation details below the table. 4.00

3) Generate numerical and graphical descriptive statistics for each of the variables, namely, AGE, SEX, AGEGRP and SBP1. 8 pts Please post your output graphs below the end of this table. 8.00

4). Interpret the output you generated in part 3 for each of the variables in the data set 4.00

II. Paired and Independent t tests: (20 pts)

1) Use the 5-step approach to hypothesis testing and the calculation of the 95% confidence intervals to answer the following research question: Was a significant difference in Systolic Blood Pressure (SBP)

observed over the course of the study? (10 pts)

a). Establish hypotheses and determine the level of significance 2.00

b) Select the appropriate test statistic (1.5 points): 1.00

c) Set up your decision rule 2.00

d) Calculate the test statistic 2.00

e) Conclusion: Was a significant difference in Systolic Blood Pressure (SBP) observed over the course of the study? 2.00

f) 95% confidence interval of the difference 1.00

2) Use the 5-step approach to hypothesis testing and the calculation of the 95% confidence intervals to answer the following research question: Is there a difference in SBP1 based on HIV status? (10 pts)

a). Establish hypotheses and determine the level of significance: 2.00

b). Select the appropriate test statistic 1.00

c). Set up your decision rule 2.00

d). Calculate the test statistic 2.50

e). Conclusion 1.50

f). 95% Confidence interval of difference 1.00

III. Cross-Tabulation: (20pts)

1) Use the 5-step approach to hypothesis testing to answer the following research question: In the sample provided in Final_3.sav, are the variables income and Bladder Cancer independent of each other?

(Note: The question could also be asked: Is there an association between the variables because the lack of independence implies an association)? (10 pts)

a). Establish hypotheses and determine the level of significance. 2.00

b) Select the appropriate test statistic. 1.00

c) Set up your decision rule 2.00

d) Calculate the test statistic. 3.00

e) Conclusion 2.00

III. 2) Answer the following based on the cross-tabulation of alcohol consumption and Bladder Cancer: (10 pts).

a). Calculate the odds ratio. 4 pts 4.00

b) Describe how the odds ratio differs from the relative risk or risk ratio and why you would chose it here. 2 pts 2.00

c). Interpret the odds ratio and how it might impact the practice of public health practitioners. 2 pts 2.00

d). If you wanted to know whether this relationship was statistically significant what test(s) could you use? 2 pts 2.00

IV. ANOVA

Produce box plots of income for each region of the US in the data set and interpret them. Based on the box plots do you expect to find a difference between any of the groups? 4.00

Create descriptive statistics for each region, using the variable income. 4 pts

Include skewness and kurtosis in the output. 2.00

Create a histogram for each group. 2.00

Run the ANOVA for income based on region. Include the ANOVA table and the test for Homogeneity of Variance. Interpret the results. 6.00

Conduct post hoc analysis using Bonferroni and LSD methods to control for multiple testing. 6 pts

Provide the output. 2.00

Interpret your results 3.00

Why do you need to use methods like Bonferroni and LSD with the ANOVA? 1.00

V. Regression

1) Use an independent t test and simple linear regression to identify whether a relationship exists between gender and BMI. (10 pts)

a) Run the appropriate t test in SPSS, report the significance of the difference in means and the confidence interval, and interpret the results. 4 pts

i) Significance of the difference in means 1.30

ii) Report the confidence interval. 1.30

iii) Interpretation of the results. 1.40

b). Run the simple linear regression in SPSS, report the significance of the variable gender and the overall fit of the model (using r2). 2.00

Interpretation of the regression analysis results: 2.00

c). How are these two approaches different? 1 pt 1.00

d). Are your conclusions the same using both tests? 1 pt 1.00

2) Answer the questions using the provided output: 10 pts

a) Linear Regression

i) Which variables in model 1 are significant? 1 pt 1.00

ii) Which variables in model 2 are significant? 1 pt 1.00

iii) Why did they choose model 2? 1 pt 1.00

iiii) What is the “fit” of model 2 (the one they chose to use)? 1 pt 1.00

v) Is this a good model, why or why not? 1 pt 1.00

b). Multiple Logistic Regression 5 pts

i) Is the final model significant? 2 pts 2.00

ii). What are the odds ratios for each of the significant variables, and what do they mean? 2 pts 2.00

iii). Will this model help the researchers, why or why not? 1 pt 1.00

Total 100.00