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1.Describe the characteristics of the people included in the sample at the baseline examination.

2. Characterize the people who had casual serum glucose >200 mg/dL at the baseline examination and compare them to people who had ≤200 mg/dL casual serum glucose at the baseline examination in terms of age, body mass index (BMI), education and whether they were taking blood pressure medication at the time of the baseline examination.

3. 3.Are the results from the bivariate comparisons above (point 2) different if the actual casual serum glucose level at baseline examination is analysed, rather than the dichotomized glucose variable?

4.Considering only individuals with casual serum glucose level at baseline below 200 mg/dL, which of these variables (age, BMI, education and whether they were taking blood pressure medication) are significantly associated with casual serum glucose level at baseline in a multivariable analysis? Describe their relationship with casual serum glucose level, including which variables explain the most variation in casual serum glucose level. Report the ‘minimum model’ obtained. Explain any differences you observe between the results of the bivariate analysis in point 3 above and multivariable analysis.

Baseline Examination Data

At the baseline examination, data from 3950 people were collected in terms of sex, education level, age, Serum total cholesterol, Systolic blood pressure, Diastolic blood pressure, Current cigarette smoking, Number of cigarettes smoked each day, Body mass index, use of anti-hypertensive medication, Casual serum glucose. Out of 3950, 1725 are male and 2225 are female. 41.1 % people are education level 0-11 years where as 28.6% are diploma holder.  49.1 % people are currently smoker at baseline examination whereas 50.1% are not currently smoker. Only 3.1% people use anti hyper tension mediation. At baseline examination, mean serum total cholesterol is 237.41mmg/dL with standard deviation 44.779.  Mean age of people at baseline examination is 49.95 years with standard deviation 8.644 years. Mean systolic blood pressure is 132.838 mmHg with standard deviation 22.3993. Mean systolic blood pressure is 83.047 mm/Hg with standard deviation 12.0522. People averagely smoke 8.87 cigarettes every day with standard deviation 11.844. At baseline examination people have average BMI 25.8523 Kg/m2 with standard deviation 4.07827. Mean casual serum glucose is observed as 82.18 mmg/dL with standard deviation 24.485.

2. We group the variable in two categories:

1: casual serum glucose >200 mg/dL at the baseline examination

2 : casual serum glucose   200 mg/dL at the baseline examination

Following table shows the descriptive statistics for the group 1 and 2 for age and BMI

Descriptive Statistic

Age at baseline

exam (years)

Body Mass Index

at baseline exam (kg/m^2)

Group 1

Group 2

Group 1

Group 2

Mean

55.71

49.94

28.3565

25.8425

Size

31

3556

31

3556

Median

56

49

28.5

25.425

Variance

45.28

74.613

31.245

16.388

Std. Deviation

6.729

8.638

5.58969

4.04821

Minimum

43

32

17.17

15.54

Maximum

67

70

43.67

56.8

Range

24

38

26.5

41.26

Interquartile Range

10

14

7.39

4.99

Skewness

-0.249

0.199

0.407

0.961

Kurtosis

-0.79

-1.014

0.76

2.507

We have 31 people having casual serum glucose >200 mg/dL at the baseline examination and 3556 people having casual serum glucose 200 mg/dL at the baseline examination. Mean age of people having casual serum glucose >200 mg/dL at the baseline examination is 55.71 (6.729) years whereas mean age of people having casual serum glucose   200 mg/dL at the baseline examination is 49.94(8.638) years. BMI of group 1 is higher than group 2. One can observed the difference between other statistic from above table.

64.51 % people having casual serum glucose >200 mg/dL at the baseline examination has education 0-11 years whereas for other group this percentage is 42.28%. In Group 1 19.35% people are diploma holder whereas in Group 2 29.33% people are diploma holders. There is no one in Group 1 which has college degree or more whereas in Group 2 about 12% people have college degree or more.

9% People in group 1 taking mediation whereas only 3% people in Group 2 are taking medication for controlling the blood pressure.

3 No, the results from the bivariate comparisons above (point 2) different if the actual casual serum glucose level at baseline examination is analysed, rather than the dichotomized glucose variable. 

Grouping of Variables and Descriptive Statistics

4. We considered the individuals with casual serum glucose level at baseline below 200 mg/dL. There are 3568 people having casual serum glucose level at baseline below 200 mg/dL. To test whether there is any significant relation between the casual serum glucose level at baseline and independent variables (age, BMI, education and whether they were taking blood pressure medication). We run the multiple regression analysis. In the independent variables Education and whether they were taking blood pressure medication are categorical variables, we need to create dummy variables for testing the above hypothesis, we create four dummy variables (3 for education and 1 for whether they were taking blood pressure medication. We take 1-11 years education and not taken any medication as a reference variable.

Following table shows the ANOVA of multiple regression analysis:

Source of Variation

Sum of Squares

df

Mean Square

F

P- Value

Regression

16607.05

6

2767.842

12.84

0

Residual

765023.7

3549

215.56

Total

781630.7

3555

The P-value = 0 suggest that there is  significant relation between the casual serum glucose level at baseline and independent variables (age, BMI, education and whether they were taking blood pressure medication). That is at least one of the coefficient is non zero. From following table we can see that which coefficient are significant or not.

Independent Variable

Coefficient

Std. Error

t

P Value

(Constant)

63.485

2.197

28.899

0.000

Age at baseline exam (years)

0.192

0.030

6.471

0.000

Body Mass Index at baseline exam (kg/m^2)

0.289

0.062

4.640

0.000

HighSchoolDiploma

-0.097

0.612

-0.159

0.873

Some College and Vocation

-0.399

0.729

-0.547

0.584

degree and more

-0.087

0.822

-0.106

0.916

taken or not

-0.772

1.423

-0.542

0.588

We can see that only age and BMI are significant whereas other variables education and whether they were taking blood pressure medication are found to be non-significant for predicting the casual serum glucose level at baseline. Both age and BMI have positive correlation with casual serum glucose level at baseline.

As the education and whether they were taking blood pressure medication are found to be non-significant for predicting the casual serum glucose level at baseline, we fit the model again using age and BMI variables only. Following is the equation of multiple regression analysis for predicting the casual serum glucose level at baseline using age and BMI as a predictor variables.

Casual serum glucose level at baseline = 63.35 + 0.192 × Age + 0.29 × BMI

Each incline in age results in 0.192 incline in casual serum glucose level whereas each unit of BMI incline results in 0.29 incline in casual serum glucose level.

From bivariate analysis, we observed that mean age and BMI for person having casual serum glucose >200 mg/dL at the baseline examination is more than the person having casual serum glucose   200 mg/dL at the baseline examination. And from the multivariate analysis we observed that each icline in age and BMI results in incline in the casual serum glucose level.  

Multiple Regression Analysis

5. We carry the paired t test for the testing whether there is casual serum glucose level change significantly between the baseline examination and the follow-up examination. We observed t statistics is -1.854 and P- value is 0.064 < 0.1 suggest that there is significant change in the casual serum glucose level change significantly between the baseline examination and the follow-up examination at 10% level of significance.

We now group the people having casual serum glucose >200 mg/dL and casual serum glucose 200 mg/dL. After that we used paired t test for both the groups.

We observed t statistics is 3.124 and P- value is 0.008 < 0.1 suggest that there is significant change in the casual serum glucose level >200 mg/dL  change significantly between the baseline examination and the follow-up examination at 10%.

We observed t statistics is -2.675 and P- value is 0.008 < 0.1 suggest that there is significant change in the casual serum glucose level 200 mg/dL  change significantly between the baseline examination and the follow-up examination at 10%.

From the test statistics we can observed that glucose level increases for people having casual serum glucose level >200 mg/dL at baseline examination and glucose level decreases for people having casual serum glucose level <= 200 mg/dL at baseline examination.

SPSS Output: 

Sex

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

Male

1725

43.7

43.7

43.7

Female

2225

56.3

56.3

100.0

Total

3950

100.0

100.0

Education level

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

0-11 years

1625

41.1

42.2

42.2

High school diploma

1131

28.6

29.4

71.6

Some college, vocational school

638

16.2

16.6

88.2

College degree or more

456

11.5

11.8

100.0

Total

3850

97.5

100.0

Missing

System

100

2.5

Total

3950

100.0

Current cigarette smoking at baseline exam

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

Not current smoker

2009

50.9

50.9

50.9

Current smoker

1941

49.1

49.1

100.0

Total

3950

100.0

100.0

Use of anti-hypertensive medication at baseline exam

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

Not currently used

3771

95.5

96.8

96.8

Current use

124

3.1

3.2

100.0

Total

3895

98.6

100.0

Missing

System

55

1.4

Total

3950

100.0

casual serum at baseline exam

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

1

3568

90.3

99.1

99.1

2

32

.8

.9

100.0

Total

3600

91.1

100.0

Missing

System

350

8.9

Total

3950

100.0

Descriptive Statistics

N

Mean

Std. Deviation

Age at baseline exam (years)

3950

49.95

8.644

Systolic blood pressure at baseline exam (mmHg)

3950

132.838

22.3993

Diastolic blood pressure at baseline exam (mmHg)

3950

83.047

12.0522

Number of cigarettes smoked each day at baseline exam

3920

8.87

11.824

Body Mass Index at baseline exam (kg/m^2)

3932

25.8523

4.07827

Serum total cholesterol at baseline exam (mmg/dL)

3904

237.41

44.779

Casual serum glucose at baseline exam (mg/dL)

3600

82.18

24.485

Valid N (listwise)

3552

Case Processing Summary

NewVar

Cases

Valid

Missing

Total

N

Percent

N

Percent

N

Percent

Age at baseline exam (years)

1

31

96.9%

1

3.1%

32

100.0%

2

3556

99.7%

12

.3%

3568

100.0%

Body Mass Index at baseline exam (kg/m^2)

1

31

96.9%

1

3.1%

32

100.0%

2

3556

99.7%

12

.3%

3568

100.0%

Education level * NewVar Crosstabulation

Count

NewVar

Total

1

2

Education level

0-11 years

20

1470

1490

High school diploma

6

1020

1026

Some college, vocational school

5

572

577

College degree or more

0

415

415

Total

31

3477

3508

Use of anti-hypertensive medication at baseline exam * NewVar Crosstabulation

Count

NewVar

Total

1

2

Use of anti-hypertensive medication at baseline exam

Not currently used

29

3402

3431

Current use

3

113

116

Total

32

3515

3547

Case Processing Summary

casual serum at baseline exam

Cases

Valid

Missing

Total

N

Percent

N

Percent

N

Percent

Age at baseline exam (years)

1

3556

99.7%

12

.3%

3568

100.0%

2

31

96.9%

1

3.1%

32

100.0%

Body Mass Index at baseline exam (kg/m^2)

1

3556

99.7%

12

.3%

3568

100.0%

2

31

96.9%

1

3.1%

32

100.0%

Descriptives

casual serum at baseline exam

Statistic

Std. Error

Age at baseline exam (years)

1

Mean

49.94

.145

95% Confidence Interval for Mean

Lower Bound

49.66

Upper Bound

50.22

5% Trimmed Mean

49.82

Median

49.00

Variance

74.613

Std. Deviation

8.638

Minimum

32

Maximum

70

Range

38

Interquartile Range

14

Skewness

.199

.041

Kurtosis

-1.014

.082

2

Mean

55.71

1.209

95% Confidence Interval for Mean

Lower Bound

53.24

Upper Bound

58.18

5% Trimmed Mean

55.81

Median

56.00

Variance

45.280

Std. Deviation

6.729

Minimum

43

Maximum

67

Range

24

Interquartile Range

10

Skewness

-.249

.421

Kurtosis

-.790

.821

Body Mass Index at baseline exam (kg/m^2)

1

Mean

25.8425

.06789

95% Confidence Interval for Mean

Lower Bound

25.7094

Upper Bound

25.9756

5% Trimmed Mean

25.6369

Median

25.4250

Variance

16.388

Std. Deviation

4.04821

Minimum

15.54

Maximum

56.80

Range

41.26

Interquartile Range

4.99

Skewness

.961

.041

Kurtosis

2.507

.082

2

Mean

28.3565

1.00394

95% Confidence Interval for Mean

Lower Bound

26.3061

Upper Bound

30.4068

5% Trimmed Mean

28.1757

Median

28.5000

Variance

31.245

Std. Deviation

5.58969

Minimum

17.17

Maximum

43.67

Range

26.50

Interquartile Range

7.39

Skewness

.407

.421

Kurtosis

.760

.821

Use of anti-hypertensive medication at baseline exam * NewVar Crosstabulation

Count

NewVar

Total

1

2

Use of anti-hypertensive medication at baseline exam

Not currently used

29

3402

3431

Current use

3

113

116

Total

32

3515

3547

Descriptives

NewVar

Statistic

Std. Error

Age at baseline exam (years)

1

Mean

55.71

1.209

95% Confidence Interval for Mean

Lower Bound

53.24

Upper Bound

58.18

5% Trimmed Mean

55.81

Median

56.00

Variance

45.280

Std. Deviation

6.729

Minimum

43

Maximum

67

Range

24

Interquartile Range

10

Skewness

-.249

.421

Kurtosis

-.790

.821

2

Mean

49.94

.145

95% Confidence Interval for Mean

Lower Bound

49.66

Upper Bound

50.22

5% Trimmed Mean

49.82

Median

49.00

Variance

74.613

Std. Deviation

8.638

Minimum

32

Maximum

70

Range

38

Interquartile Range

14

Skewness

.199

.041

Kurtosis

-1.014

.082

Body Mass Index at baseline exam (kg/m^2)

1

Mean

28.3565

1.00394

95% Confidence Interval for Mean

Lower Bound

26.3061

Upper Bound

30.4068

5% Trimmed Mean

28.1757

Median

28.5000

Variance

31.245

Std. Deviation

5.58969

Minimum

17.17

Maximum

43.67

Range

26.50

Interquartile Range

7.39

Skewness

.407

.421

Kurtosis

.760

.821

2

Mean

25.8425

.06789

95% Confidence Interval for Mean

Lower Bound

25.7094

Upper Bound

25.9756

5% Trimmed Mean

25.6369

Median

25.4250

Variance

16.388

Std. Deviation

4.04821

Minimum

15.54

Maximum

56.80

Range

41.26

Interquartile Range

4.99

Skewness

.961

.041

Kurtosis

2.507

.082

DATASET COPY  Q4.

DATASET ACTIVATE  Q4.

FILTER OFF.

USE ALL.

SELECT IF (NewVar=2).

DATASET ACTIVATE  DataSet1.

EXECUTE.

DATASET ACTIVATE Q4.

DATASET ACTIVATE DataSet1.

SAVE OUTFILE='C:UsersRaju ChavanDownloadsassignment stats.sav' /COMPRESSED.

DATASET ACTIVATE Q4.

SAVE OUTFILE='C:UsersRaju ChavanDesktopRR.xlsx' /COMPRESSED.

DATASET ACTIVATE DataSet1.

DATASET ACTIVATE DataSet1.

DATASET CLOSE Q4.

DATASET COPY  Q4.

DATASET ACTIVATE  Q4.

FILTER OFF.

USE ALL.

SELECT IF (NewVar=2).

DATASET ACTIVATE  DataSet1.

EXECUTE.

DATASET ACTIVATE Q4.

RECODE educ (2=1) (ELSE=0) INTO Edu1.

VARIABLE LABELS  Edu1 'HighSchoolDiploma'.

EXECUTE.

RECODE educ (3=1) (ELSE=0) INTO Vocation.

VARIABLE LABELS  Vocation 'Some College and Vocation'.

EXECUTE.

RECODE SEX (4=1) (ELSE=0) INTO Degree.

VARIABLE LABELS  Degree 'College Degree and more'.

EXECUTE.

RECODE BPMEDS.1 (1=1) (ELSE=0) INTO Meditation.

VARIABLE LABELS  Meditation 'taken or not'.

EXECUTE.

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

taken or not, HighSchoolDiploma, Body Mass Index at baseline exam (kg/m^2), degree and more, Age at baseline exam (years), Some College and Vocationa

.

Enter

a. All requested variables entered.

b. Dependent Variable: Casual serum glucose at baseline exam (mg/dL)

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.146a

.021

.020

14.682

a. Predictors: (Constant), taken or not, HighSchoolDiploma, Body Mass Index at baseline exam (kg/m^2), degree and more, Age at baseline exam (years), Some College and Vocation

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

16607.050

6

2767.842

12.840

.000a

Residual

765023.664

3549

215.560

Total

781630.714

3555

a. Predictors: (Constant), taken or not, HighSchoolDiploma, Body Mass Index at baseline exam (kg/m^2), degree and more, Age at baseline exam (years), Some College and Vocation

b. Dependent Variable: Casual serum glucose at baseline exam (mg/dL)

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

63.485

2.197

28.899

.000

Age at baseline exam (years)

.192

.030

.112

6.471

.000

Body Mass Index at baseline exam (kg/m^2)

.289

.062

.079

4.640

.000

HighSchoolDiploma

-.097

.612

-.003

-.159

.873

Some College and Vocation

-.399

.729

-.010

-.547

.584

degree and more

-.087

.822

-.002

-.106

.916

taken or not

-.772

1.423

-.009

-.542

.588

a. Dependent Variable: Casual serum glucose at baseline exam (mg/dL)

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

16477.435

2

8238.717

38.257

.000a

Residual

765153.279

3553

215.354

Total

781630.714

3555

a. Predictors: (Constant), Body Mass Index at baseline exam (kg/m^2), Age at baseline exam (years)

b. Dependent Variable: Casual serum glucose at baseline exam (mg/dL)

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

63.350

2.009

31.526

.000

Age at baseline exam (years)

.192

.029

.112

6.679

.000

Body Mass Index at baseline exam (kg/m^2)

.290

.061

.079

4.727

.000

a. Dependent Variable: Casual serum glucose at baseline exam (mg/dL)

Paired Samples Statistics

Mean

N

Std. Deviation

Std. Error Mean

Pair 1

Casual serum glucose at baseline exam (mg/dL)

81.04

2824

20.073

.378

Casual serum glucose at follow-up exam (mg/dL)

81.83

2824

22.270

.419

Paired Samples Correlations

N

Correlation

Sig.

Pair 1

Casual serum glucose at baseline exam (mg/dL) & Casual serum glucose at follow-up exam (mg/dL)

2824

.438

.000

Paired Samples Test

Paired Differences

t

df

Sig. (2-tailed)

Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference

Lower

Upper

Pair 1

Casual serum glucose at baseline exam (mg/dL) - Casual serum glucose at follow-up exam (mg/dL)

-.785

22.513

.424

-1.616

.045

-1.854

2823

.064

Paired Samples Statistics

Mean

N

Std. Deviation

Std. Error Mean

Pair 1

Casual serum glucose at baseline exam (mg/dL)

271.36

14

69.373

18.541

Casual serum glucose at follow-up exam (mg/dL)

211.00

14

64.709

17.294

Paired Samples Correlations

N

Correlation

Sig.

Pair 1

Casual serum glucose at baseline exam (mg/dL) & Casual serum glucose at follow-up exam (mg/dL)

14

.420

.135

Paired Samples Test

Paired Differences

t

df

Sig. (2-tailed)

Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference

Lower

Upper

Pair 1

Casual serum glucose at baseline exam (mg/dL) - Casual serum glucose at follow-up exam (mg/dL)

60.357

72.298

19.322

18.613

102.101

3.124

13

.008

Paired Samples Statistics

Mean

N

Std. Deviation

Std. Error Mean

Pair 1

Casual serum glucose at baseline exam (mg/dL)

80.10

2810

14.186

.268

Casual serum glucose at follow-up exam (mg/dL)

81.19

2810

19.887

.375

Paired Samples Correlations

N

Correlation

Sig.

Pair 1

Casual serum glucose at baseline exam (mg/dL) & Casual serum glucose at follow-up exam (mg/dL)

2810

.231

.000

Paired Samples Test

Paired Differences

t

df

Sig. (2-tailed)

Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference

Lower

Upper

Pair 1

Casual serum glucose at baseline exam (mg/dL) - Casual serum glucose at follow-up exam (mg/dL)

-1.090

21.598

.407

-1.889

-.291

-2.675

2809

.008

References:

Abbott, M. L. (2016). Using Statistics in the Social and Health Sciences with SPSS and Excel. John Wiley & Sons.

Bickel, P. J., & Doksum, K. A. (2015). Mathematical statistics: basic ideas and selected topics, volume I (Vol. 117). CRC Press.

Chatterjee, S., & Hadi, A. S. (2015). Regression analysis by example. John Wiley & Sons.

Darlington, R. B., & Hayes, A. F. (2016). Regression analysis and linear models: Concepts, applications, and implementation. Guilford Publications.

Draper, N. R., & Smith, H. (2014). Applied regression analysis (Vol. 326). John Wiley & Sons.

Fox, J. (2015). Applied regression analysis and generalized linear models. Sage Publications.

Glantz, S. A., Slinker, B. K., & Neilands, T. B. (2016). Primer of applied regression & analysis of variance. McGraw-Hill Medical Publishing Division.

Paired T-test for Glucose Level Change

Larson-Hall, J. (2015). A guide to doing statistics in second language research using SPSS and R. Routledge.

Pett, M. A. (2015). Nonparametric statistics for health care research: Statistics for small samples and unusual distributions. Sage Publications.

Pett, M. A. (2015). Nonparametric statistics for health care research: Statistics for small samples and unusual distributions. Sage Publications.

Rasch, D., & Schott, D. (2018). Basic Ideas of Mathematical Statistics. Mathematical Statistics, 1-38.

Schroeder, L. D., Sjoquist, D. L., & Stephan, P. E. (2016). Understanding regression analysis: An introductory guide (Vol. 57). Sage Publications.

Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics. Allyn & Bacon/Pearson Education.

At the baseline examination, data from 3950 people were collected in terms of sex, education level, age, Serum total cholesterol, Systolic blood pressure, Diastolic blood pressure, Current cigarette smoking, Number of cigarettes smoked each day, Body mass index, use of anti-hypertensive medication, Casual serum glucose. Out of 3950, 1725 are male and 2225 are female. 41.1 % people are education level 0-11 years where as 28.6% are diploma holder.  49.1 % people are currently smoker at baseline examination whereas 50.1% are not currently smoker. Only 3.1% people use anti hyper tension mediation. At baseline examination, mean serum total cholesterol is 237.41mmg/dL with standard deviation 44.779.  Mean age of people at baseline examination is 49.95 years with standard deviation 8.644 years. Mean systolic blood pressure is 132.838 mmHg with standard deviation 22.3993. Mean systolic blood pressure is 83.047 mm/Hg with standard deviation 12.0522. People averagely smoke 8.87 cigarettes every day with standard deviation 11.844. At baseline examination people have average BMI 25.8523 Kg/m2 with standard deviation 4.07827. Mean casual serum glucose is observed as 82.18 mmg/dL with standard deviation 24.485.

  1. Characterize the people who had casual serum glucose >200 mg/dL at the baseline examination and compare them to people who had ≤200 mg/dL casual serum glucose at the baseline examination in terms of age, body mass index (BMI), education and whether they were taking blood pressure medication at the time of the baseline examination.

We group the variable in two categories:

1: casual serum glucose >200 mg/dL at the baseline examination

2 : casual serum glucose   200 mg/dL at the baseline examination

Following table shows the descriptive statistics for the group 1 and 2 for age and BMI

Descriptive Statistic

Age at baseline

exam (years)

Body Mass Index

at baseline exam (kg/m^2)

Group 1

Group 2

Group 1

Group 2

Mean

55.71

49.94

28.3565

25.8425

Size

31

3556

31

3556

Median

56

49

28.5

25.425

Variance

45.28

74.613

31.245

16.388

Std. Deviation

6.729

8.638

5.58969

4.04821

Minimum

43

32

17.17

15.54

Maximum

67

70

43.67

56.8

Range

24

38

26.5

41.26

Interquartile Range

10

14

7.39

4.99

Skewness

-0.249

0.199

0.407

0.961

Kurtosis

-0.79

-1.014

0.76

2.507

We have 31 people having casual serum glucose >200 mg/dL at the baseline examination and 3556 people having casual serum glucose 200 mg/dL at the baseline examination. Mean age of people having casual serum glucose >200 mg/dL at the baseline examination is 55.71 (6.729) years whereas mean age of people having casual serum glucose   200 mg/dL at the baseline examination is 49.94(8.638) years. BMI of group 1 is higher than group 2. One can observed the difference between other statistic from above table.

64.51 % people having casual serum glucose >200 mg/dL at the baseline examination has education 0-11 years whereas for other group this percentage is 42.28%. In Group 1 19.35% people are diploma holder whereas in Group 2 29.33% people are diploma holders. There is no one in Group 1 which has college degree or more whereas in Group 2 about 12% people have college degree or more.

9% People in group 1 taking mediation whereas only 3% people in Group 2 are taking medication for controlling the blood pressure.

  1. Are the results from the bivariate comparisons above (point 2) different if the actual casual serum glucose level at baseline examination is analysed, rather than the dichotomized glucose variable?

No, the results from the bivariate comparisons above (point 2) different if the actual casual serum glucose level at baseline examination is analysed, rather than the dichotomized glucose variable.

  1. Considering only individuals with casual serum glucose level at baseline below 200 mg/dL, which of these variables (age, BMI, education and whether they were taking blood pressure medication) are significantly associated with casual serum glucose level at baseline in a multivariable analysis? Describe their relationship with casual serum glucose level, including which variables explain the most variation in casual serum glucose level. Report the ‘minimum model’ obtained. Explain any differences you observe between the results of the bivariate analysis in point 3 above and multivariable analysis.

We considered the individuals with casual serum glucose level at baseline below 200 mg/dL. There are 3568 people having casual serum glucose level at baseline below 200 mg/dL. To test whether there is any significant relation between the casual serum glucose level at baseline and independent variables (age, BMI, education and whether they were taking blood pressure medication). We run the multiple regression analysis. In the independent variables Education and whether they were taking blood pressure medication are categorical variables, we need to create dummy variables for testing the above hypothesis, we create four dummy variables (3 for education and 1 for whether they were taking blood pressure medication. We take 1-11 years education and not taken any medication as a reference variable.

Following table shows the ANOVA of multiple regression analysis:

Source of Variation

Sum of Squares

df

Mean Square

F

P- Value

Regression

16607.05

6

2767.842

12.84

0

Residual

765023.7

3549

215.56

Total

781630.7

3555

The P-value = 0 suggest that there is  significant relation between the casual serum glucose level at baseline and independent variables (age, BMI, education and whether they were taking blood pressure medication). That is at least one of the coefficient is non zero. From following table we can see that which coefficient are significant or not.

Independent Variable

Coefficient

Std. Error

t

P Value

(Constant)

63.485

2.197

28.899

0.000

Age at baseline exam (years)

0.192

0.030

6.471

0.000

Body Mass Index at baseline exam (kg/m^2)

0.289

0.062

4.640

0.000

HighSchoolDiploma

-0.097

0.612

-0.159

0.873

Some College and Vocation

-0.399

0.729

-0.547

0.584

degree and more

-0.087

0.822

-0.106

0.916

taken or not

-0.772

1.423

-0.542

0.588

We can see that only age and BMI are significant whereas other variables education and whether they were taking blood pressure medication are found to be non-significant for predicting the casual serum glucose level at baseline. Both age and BMI have positive correlation with casual serum glucose level at baseline.

As the education and whether they were taking blood pressure medication are found to be non-significant for predicting the casual serum glucose level at baseline, we fit the model again using age and BMI variables only. Following is the equation of multiple regression analysis for predicting the casual serum glucose level at baseline using age and BMI as a predictor variables.

Casual serum glucose level at baseline = 63.35 + 0.192 × Age + 0.29 × BMI

Each incline in age results in 0.192 incline in casual serum glucose level whereas each unit of BMI incline results in 0.29 incline in casual serum glucose level.

From bivariate analysis, we observed that mean age and BMI for person having casual serum glucose >200 mg/dL at the baseline examination is more than the person having casual serum glucose   200 mg/dL at the baseline examination. And from the multivariate analysis we observed that each icline in age and BMI results in incline in the casual serum glucose level.

  1. Did the casual serum glucose level change significantly between the baseline examination and the follow-up examination? Is this result the same when casual serum glucose level is categorised according to the clinical threshold of >200 mg/dL versus ≤200 mg/dL?

We carry the paired t test for the testing whether there is casual serum glucose level change significantly between the baseline examination and the follow-up examination. We observed t statistics is -1.854 and P- value is 0.064 < 0.1 suggest that there is significant change in the casual serum glucose level change significantly between the baseline examination and the follow-up examination at 10% level of significance.

We now group the people having casual serum glucose >200 mg/dL and casual serum glucose 200 mg/dL. After that we used paired t test for both the groups.

We observed t statistics is 3.124 and P- value is 0.008 < 0.1 suggest that there is significant change in the casual serum glucose level >200 mg/dL  change significantly between the baseline examination and the follow-up examination at 10%.

We observed t statistics is -2.675 and P- value is 0.008 < 0.1 suggest that there is significant change in the casual serum glucose level 200 mg/dL  change significantly between the baseline examination and the follow-up examination at 10%.

From the test statistics we can observed that glucose level increases for people having casual serum glucose level >200 mg/dL at baseline examination and glucose level decreases for people having casual serum glucose level <= 200 mg/dL at baseline examination.

SPSS Output:

Sex

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

Male

1725

43.7

43.7

43.7

Female

2225

56.3

56.3

100.0

Total

3950

100.0

100.0

Education level

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

0-11 years

1625

41.1

42.2

42.2

High school diploma

1131

28.6

29.4

71.6

Some college, vocational school

638

16.2

16.6

88.2

College degree or more

456

11.5

11.8

100.0

Total

3850

97.5

100.0

Missing

System

100

2.5

Total

3950

100.0

Current cigarette smoking at baseline exam

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

Not current smoker

2009

50.9

50.9

50.9

Current smoker

1941

49.1

49.1

100.0

Total

3950

100.0

100.0

Use of anti-hypertensive medication at baseline exam

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

Not currently used

3771

95.5

96.8

96.8

Current use

124

3.1

3.2

100.0

Total

3895

98.6

100.0

Missing

System

55

1.4

Total

3950

100.0

casual serum at baseline exam

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

1

3568

90.3

99.1

99.1

2

32

.8

.9

100.0

Total

3600

91.1

100.0

Missing

System

350

8.9

Total

3950

100.0

Descriptive Statistics

N

Mean

Std. Deviation

Age at baseline exam (years)

3950

49.95

8.644

Systolic blood pressure at baseline exam (mmHg)

3950

132.838

22.3993

Diastolic blood pressure at baseline exam (mmHg)

3950

83.047

12.0522

Number of cigarettes smoked each day at baseline exam

3920

8.87

11.824

Body Mass Index at baseline exam (kg/m^2)

3932

25.8523

4.07827

Serum total cholesterol at baseline exam (mmg/dL)

3904

237.41

44.779

Casual serum glucose at baseline exam (mg/dL)

3600

82.18

24.485

Valid N (listwise)

3552

Q2

Case Processing Summary

NewVar

Cases

Valid

Missing

Total

N

Percent

N

Percent

N

Percent

Age at baseline exam (years)

1

31

96.9%

1

3.1%

32

100.0%

2

3556

99.7%

12

.3%

3568

100.0%

Body Mass Index at baseline exam (kg/m^2)

1

31

96.9%

1

3.1%

32

100.0%

2

3556

99.7%

12

.3%

3568

100.0%

Education level * NewVar Crosstabulation

Count

NewVar

Total

1

2

Education level

0-11 years

20

1470

1490

High school diploma

6

1020

1026

Some college, vocational school

5

572

577

College degree or more

0

415

415

Total

31

3477

3508

Use of anti-hypertensive medication at baseline exam * NewVar Crosstabulation

Count

NewVar

Total

1

2

Use of anti-hypertensive medication at baseline exam

Not currently used

29

3402

3431

Current use

3

113

116

Total

32

3515

3547

Q3:

Case Processing Summary

casual serum at baseline exam

Cases

Valid

Missing

Total

N

Percent

N

Percent

N

Percent

Age at baseline exam (years)

1

3556

99.7%

12

.3%

3568

100.0%

2

31

96.9%

1

3.1%

32

100.0%

Body Mass Index at baseline exam (kg/m^2)

1

3556

99.7%

12

.3%

3568

100.0%

2

31

96.9%

1

3.1%

32

100.0%

Descriptives

casual serum at baseline exam

Statistic

Std. Error

Age at baseline exam (years)

1

Mean

49.94

.145

95% Confidence Interval for Mean

Lower Bound

49.66

Upper Bound

50.22

5% Trimmed Mean

49.82

Median

49.00

Variance

74.613

Std. Deviation

8.638

Minimum

32

Maximum

70

Range

38

Interquartile Range

14

Skewness

.199

.041

Kurtosis

-1.014

.082

2

Mean

55.71

1.209

95% Confidence Interval for Mean

Lower Bound

53.24

Upper Bound

58.18

5% Trimmed Mean

55.81

Median

56.00

Variance

45.280

Std. Deviation

6.729

Minimum

43

Maximum

67

Range

24

Interquartile Range

10

Skewness

-.249

.421

Kurtosis

-.790

.821

Body Mass Index at baseline exam (kg/m^2)

1

Mean

25.8425

.06789

95% Confidence Interval for Mean

Lower Bound

25.7094

Upper Bound

25.9756

5% Trimmed Mean

25.6369

Median

25.4250

Variance

16.388

Std. Deviation

4.04821

Minimum

15.54

Maximum

56.80

Range

41.26

Interquartile Range

4.99

Skewness

.961

.041

Kurtosis

2.507

.082

2

Mean

28.3565

1.00394

95% Confidence Interval for Mean

Lower Bound

26.3061

Upper Bound

30.4068

5% Trimmed Mean

28.1757

Median

28.5000

Variance

31.245

Std. Deviation

5.58969

Minimum

17.17

Maximum

43.67

Range

26.50

Interquartile Range

7.39

Skewness

.407

.421

Kurtosis

.760

.821

Use of anti-hypertensive medication at baseline exam * NewVar Crosstabulation

Count

NewVar

Total

1

2

Use of anti-hypertensive medication at baseline exam

Not currently used

29

3402

3431

Current use

3

113

116

Total

32

3515

3547

Descriptives

NewVar

Statistic

Std. Error

Age at baseline exam (years)

1

Mean

55.71

1.209

95% Confidence Interval for Mean

Lower Bound

53.24

Upper Bound

58.18

5% Trimmed Mean

55.81

Median

56.00

Variance

45.280

Std. Deviation

6.729

Minimum

43

Maximum

67

Range

24

Interquartile Range

10

Skewness

-.249

.421

Kurtosis

-.790

.821

2

Mean

49.94

.145

95% Confidence Interval for Mean

Lower Bound

49.66

Upper Bound

50.22

5% Trimmed Mean

49.82

Median

49.00

Variance

74.613

Std. Deviation

8.638

Minimum

32

Maximum

70

Range

38

Interquartile Range

14

Skewness

.199

.041

Kurtosis

-1.014

.082

Body Mass Index at baseline exam (kg/m^2)

1

Mean

28.3565

1.00394

95% Confidence Interval for Mean

Lower Bound

26.3061

Upper Bound

30.4068

5% Trimmed Mean

28.1757

Median

28.5000

Variance

31.245

Std. Deviation

5.58969

Minimum

17.17

Maximum

43.67

Range

26.50

Interquartile Range

7.39

Skewness

.407

.421

Kurtosis

.760

.821

2

Mean

25.8425

.06789

95% Confidence Interval for Mean

Lower Bound

25.7094

Upper Bound

25.9756

5% Trimmed Mean

25.6369

Median

25.4250

Variance

16.388

Std. Deviation

4.04821

Minimum

15.54

Maximum

56.80

Range

41.26

Interquartile Range

4.99

Skewness

.961

.041

Kurtosis

2.507

.082

Q4:

DATASET COPY  Q4.

DATASET ACTIVATE  Q4.

FILTER OFF.

USE ALL.

SELECT IF (NewVar=2).

DATASET ACTIVATE  DataSet1.

EXECUTE.

DATASET ACTIVATE Q4.

DATASET ACTIVATE DataSet1.

SAVE OUTFILE='C:UsersRaju ChavanDownloadsassignment stats.sav' /COMPRESSED.

DATASET ACTIVATE Q4.

SAVE OUTFILE='C:UsersRaju ChavanDesktopRR.xlsx' /COMPRESSED.

DATASET ACTIVATE DataSet1.

DATASET ACTIVATE DataSet1.

DATASET CLOSE Q4.

DATASET COPY  Q4.

DATASET ACTIVATE  Q4.

FILTER OFF.

USE ALL.

SELECT IF (NewVar=2).

DATASET ACTIVATE  DataSet1.

EXECUTE.

DATASET ACTIVATE Q4.

RECODE educ (2=1) (ELSE=0) INTO Edu1.

VARIABLE LABELS  Edu1 'HighSchoolDiploma'.

EXECUTE.

RECODE educ (3=1) (ELSE=0) INTO Vocation.

VARIABLE LABELS  Vocation 'Some College and Vocation'.

EXECUTE.

RECODE SEX (4=1) (ELSE=0) INTO Degree.

VARIABLE LABELS  Degree 'College Degree and more'.

EXECUTE.

RECODE BPMEDS.1 (1=1) (ELSE=0) INTO Meditation.

VARIABLE LABELS  Meditation 'taken or not'.

EXECUTE.

Variables Entered/Removedb

Model

Variables Entered

Variables Removed

Method

1

taken or not, HighSchoolDiploma, Body Mass Index at baseline exam (kg/m^2), degree and more, Age at baseline exam (years), Some College and Vocationa

.

Enter

a. All requested variables entered.

b. Dependent Variable: Casual serum glucose at baseline exam (mg/dL)

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.146a

.021

.020

14.682

a. Predictors: (Constant), taken or not, HighSchoolDiploma, Body Mass Index at baseline exam (kg/m^2), degree and more, Age at baseline exam (years), Some College and Vocation

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

16607.050

6

2767.842

12.840

.000a

Residual

765023.664

3549

215.560

Total

781630.714

3555

a. Predictors: (Constant), taken or not, HighSchoolDiploma, Body Mass Index at baseline exam (kg/m^2), degree and more, Age at baseline exam (years), Some College and Vocation

b. Dependent Variable: Casual serum glucose at baseline exam (mg/dL)

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

63.485

2.197

28.899

.000

Age at baseline exam (years)

.192

.030

.112

6.471

.000

Body Mass Index at baseline exam (kg/m^2)

.289

.062

.079

4.640

.000

HighSchoolDiploma

-.097

.612

-.003

-.159

.873

Some College and Vocation

-.399

.729

-.010

-.547

.584

degree and more

-.087

.822

-.002

-.106

.916

taken or not

-.772

1.423

-.009

-.542

.588

a. Dependent Variable: Casual serum glucose at baseline exam (mg/dL)

ANOVAb

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

16477.435

2

8238.717

38.257

.000a

Residual

765153.279

3553

215.354

Total

781630.714

3555

a. Predictors: (Constant), Body Mass Index at baseline exam (kg/m^2), Age at baseline exam (years)

b. Dependent Variable: Casual serum glucose at baseline exam (mg/dL)

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

63.350

2.009

31.526

.000

Age at baseline exam (years)

.192

.029

.112

6.679

.000

Body Mass Index at baseline exam (kg/m^2)

.290

.061

.079

4.727

.000

a. Dependent Variable: Casual serum glucose at baseline exam (mg/dL)

 Q5

Paired Samples Statistics

Mean

N

Std. Deviation

Std. Error Mean

Pair 1

Casual serum glucose at baseline exam (mg/dL)

81.04

2824

20.073

.378

Casual serum glucose at follow-up exam (mg/dL)

81.83

2824

22.270

.419

Paired Samples Correlations

N

Correlation

Sig.

Pair 1

Casual serum glucose at baseline exam (mg/dL) & Casual serum glucose at follow-up exam (mg/dL)

2824

.438

.000

Paired Samples Test

Paired Differences

t

df

Sig. (2-tailed)

Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference

Lower

Upper

Pair 1

Casual serum glucose at baseline exam (mg/dL) - Casual serum glucose at follow-up exam (mg/dL)

-.785

22.513

.424

-1.616

.045

-1.854

2823

.064

For Group 1:

Paired Samples Statistics

Mean

N

Std. Deviation

Std. Error Mean

Pair 1

Casual serum glucose at baseline exam (mg/dL)

271.36

14

69.373

18.541

Casual serum glucose at follow-up exam (mg/dL)

211.00

14

64.709

17.294

Paired Samples Correlations

N

Correlation

Sig.

Pair 1

Casual serum glucose at baseline exam (mg/dL) & Casual serum glucose at follow-up exam (mg/dL)

14

.420

.135

Paired Samples Test

Paired Differences

t

df

Sig. (2-tailed)

Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference

Lower

Upper

Pair 1

Casual serum glucose at baseline exam (mg/dL) - Casual serum glucose at follow-up exam (mg/dL)

60.357

72.298

19.322

18.613

102.101

3.124

13

.008

For Group 2:

Paired Samples Statistics

Mean

N

Std. Deviation

Std. Error Mean

Pair 1

Casual serum glucose at baseline exam (mg/dL)

80.10

2810

14.186

.268

Casual serum glucose at follow-up exam (mg/dL)

81.19

2810

19.887

.375

Paired Samples Correlations

N

Correlation

Sig.

Pair 1

Casual serum glucose at baseline exam (mg/dL) & Casual serum glucose at follow-up exam (mg/dL)

2810

.231

.000

Paired Samples Test

Paired Differences

t

df

Sig. (2-tailed)

Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference

Lower

Upper

Pair 1

Casual serum glucose at baseline exam (mg/dL) - Casual serum glucose at follow-up exam (mg/dL)

-1.090

21.598

.407

-1.889

-.291

-2.675

2809

.008

References:

Abbott, M. L. (2016). Using Statistics in the Social and Health Sciences with SPSS and Excel. John Wiley & Sons.

Bickel, P. J., & Doksum, K. A. (2015). Mathematical statistics: basic ideas and selected topics, volume I (Vol. 117). CRC Press.

Chatterjee, S., & Hadi, A. S. (2015). Regression analysis by example. John Wiley & Sons.

Darlington, R. B., & Hayes, A. F. (2016). Regression analysis and linear models: Concepts, applications, and implementation. Guilford Publications.

Draper, N. R., & Smith, H. (2014). Applied regression analysis (Vol. 326). John Wiley & Sons.

Fox, J. (2015). Applied regression analysis and generalized linear models. Sage Publications.

Glantz, S. A., Slinker, B. K., & Neilands, T. B. (2016). Primer of applied regression & analysis of variance. McGraw-Hill Medical Publishing Division.

Larson-Hall, J. (2015). A guide to doing statistics in second language research using SPSS and R. Routledge.

Pett, M. A. (2015). Nonparametric statistics for health care research: Statistics for small samples and unusual distributions. Sage Publications.

Pett, M. A. (2015). Nonparametric statistics for health care research: Statistics for small samples and unusual distributions. Sage Publications.

Rasch, D., & Schott, D. (2018). Basic Ideas of Mathematical Statistics. Mathematical Statistics, 1-38.

Schroeder, L. D., Sjoquist, D. L., & Stephan, P. E. (2016). Understanding regression analysis: An introductory guide (Vol. 57). Sage Publications.

Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics. Allyn & Bacon/Pearson Education.

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