Examining the Effectiveness of a Weight-Loss Program

The nutrition expert evaluated the effectiveness of a weight-loss program by analyzing mean age, systolic BP, and diastolic BP of 10 randomly selected subjects. Results showed that those on antihypertensive had higher mean systolic and diastolic BP than those not on antihypertensive. The average age for those on antihypertensive was significantly higher than those not on antihypertensive. Further investigation is suggested to control for time and see how the results behave.

Biostatistics and Informatics
Student Name:
Instructor Name:
Course Number:
19th September 2018
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1. A group of 10-year-old boys were first ascertained in a camp for diabetic boys.
They had their first weight measured at baseline and again when they returned to
camp one year later. Each time, a serum sample was obtained from which a
determination of haemoglobin A1c (HgbA1c) was made. HgbA1c (also called
glycosylated haemoglobin) is routinely used to monitor compliance with taking
insulin injections. Usually, the poorer the compliance, the higher the HgbA1c
level. The hypothesis is that the level of HgbA1c is related to the weight. The
data are entered into an SPSS file called “assignment2_diabetes2018.sav”.
Download this file and use SPSS to answer the following questions:
a) Is HgbA1c a useful predictor for weight at baseline? Run a regression analysis
with wgt1 as the dependent and HgbA1c_1 as the independent. Does HgbA1c
significantly predict weight? Give the statistical evidence for your conclusion.
How well does HgbA1c explain the variability in weight in these data? Give the
statistical evidence for your conclusion. Write a one-sentence summary of this
analysis.
Answer
Model Summary
Model R R Square Adjusted R
Square
Std. Error of the
Estimate
1 .204a .042 -.032 4.29418
a. Predictors: (Constant), HgbA1c_1
The value of R-Squared is 0.042; this implies that only 4.2% of the variation in
weight is explained by HgbA1c.
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ANOVAa
Model Sum of Squares df Mean Square F Sig.
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Regression 10.429 1 10.429 .566 .465b
Residual 239.720 13 18.440
Total 250.149 14
a. Dependent Variable: wgt1
b. Predictors: (Constant), HgbA1c_1
The coefficients table below shows that the p-value for the HgbA1c is 0.465; this
value is higher than the 5% level of significance. The null hypothesis is not rejected
suggesting that HgbA1c does not significantly predict weight.
Coefficientsa
Model Unstandardized Coefficients Standardized
Coefficients
t Sig.
B Std. Error Beta
1 (Constant) 33.218 6.227 5.334 .000
HgbA1c_1 .553 .735 .204 .752 .465
a. Dependent Variable: wgt1
In summary, only a small proportion of variation (4.2%) in weight is explained by
HgbA1c and also results showed that the independent variable (HgbA1c) does not
significantly predict weight.
b) Repeat the above analysis for HgbA1c one year later. Giving the statistical
evidence, do your conclusions change?
Answer
Model Summary
Model R R Square Adjusted R
Square
Std. Error of the
Estimate
1 .217a .047 -.026 5.76184
a. Predictors: (Constant), HgbA1c_2
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ANOVAa
Model Sum of Squares df Mean Square F Sig.
1
Regression 21.405 1 21.405 .645 .436b
Residual 431.585 13 33.199
Total 452.989 14
a. Dependent Variable: wgt2
b. Predictors: (Constant), HgbA1c_2
Coefficientsa
Model Unstandardized Coefficients Standardized
Coefficients
t Sig.
B Std. Error Beta
1 (Constant) 52.987 13.773 3.847 .002
HgbA1c_2 -1.370 1.706 -.217 -.803 .436
a. Dependent Variable: wgt2
One year later the results do not significantly change. Only 4.7% of the variation in
weight is explained by HgbA1c. Again, the p-value for the HgbA1c is found to be
0.436; this value is higher than the 5% level of significance leading acceptance of the
null hypothesis hence implying that HgbA1c does not significantly predict weight.
c) Using transform -> compute, calculate 2 new variables: wgtdiff = wgt2 – wgt1,
which measures the change in weight from baseline to one year follow-up, and
HgbA1cDiff = HgbA1c_2 – HgbA1c_1, which measures the change in HgbA1c
from baseline to one year follow-up. Use regression analysis to investigate
whether or not the change in HgbA1c predicts the change in weight. What is the
statistical significance of the relationship? How well does change in HgbA1c
explain change in weight? What is the direction of the relationship?
Answer
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Model Summary
Model R R Square Adjusted R
Square
Std. Error of the
Estimate
1 .461a .213 .152 2.20266
a. Predictors: (Constant), HgbA1cDiff
The value of R-Squared is 0.213; this means that 21.3% of the variation in difference
in weight is explained by difference in HgbA1c.
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1
Regression 17.061 1 17.061 3.517 .083b
Residual 63.072 13 4.852
Total 80.133 14
a. Dependent Variable: wgtdiff
b. Predictors: (Constant), HgbA1cDiff
Coefficientsa
Model Unstandardized Coefficients Standardized
Coefficients
t Sig.
B Std. Error Beta
1 (Constant) -3.874 .590 -6.569 .000
HgbA1cDiff .934 .498 .461 1.875 .083
a. Dependent Variable: wgtdiff
The p-value for the difference in HgbA1c is 0.083 (a value less than 10% level of
significance), hence we can say that difference in HgbA1c significantly predicts
difference weight at 10% level of significance.
d) Using the results from all three of the analyses above, write a paragraph giving
your conclusions, suitable for the conclusions/ discussions section of a paper.
What further investigations would you suggest, based on these data?
Answer
The results obtained showed that HgbA1c does not significantly predict weight.
This is true even after one year. However, when we obtain the difference in
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weight and the difference in HgbA1c for the two periods we saw some
improvements. The difference in HgbA1c was able to significantly predict the
difference in weight though at 10% level of significance. Further investigation
should focus on controlling for time and seeing how the results behave.
2. Use the Framingham data set, with period = 1, to answer the following questions.
a) Does mean age (AGE) differ between those on antihypertensives (BPMEDS = 1)
and those not on antihypertensives (BPMEDS = 0)?
Answer
Group Statistics
BPMeds N Mean Std.
Deviation
Std. Error
Mean
age
Not on antihypertensive 603 53.9088 8.07358 .32878
On antihypertensive 41 57.6341 5.99481 .93623
Independent Samples Test
Levene's Test for
Equality of
Variances
t-test for Equality of Means
F Sig. t df Sig. (2-
tailed)
Mean
Differen
ce
Std.
Error
Differen
ce
95% Confidence
Interval of the
Difference
Lower Upper
age
Equal variances
assumed
7.330 .007 -2.900 642 .004 -3.7254 1.28470 -6.248 -1.203
Equal variances
not assumed
-3.754 50.423 .000 -3.7254 .99228 -5.718 -1.733
We performed an independent t-test was in order to compare the average age for those
on antihypertensive (BPMEDS = 1) and those not on antihypertensive (BPMEDS =
0). Results showed that the average age for those on antihypertensive (M = 57.63, SD
= 5.99, N = 41) was significantly different with the average age (M = 53.90, SD =
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8.07, N = 603), t (642) = -2.900, p < .05, two-tailed. Those on antihypertensive were
significantly older than those not on antihypertensive.
b) Does mean systolic BP (SYSBP) differ between those on antihypertensives
(BPMEDS = 1) and those not on antihypertensive (BPMEDS = 0)?
Answer
Group Statistics
BPMeds N Mean Std. Deviation Std. Error Mean
sysBP
Not on antihypertensive 603 141.6924 25.34485 1.03212
On antihypertensive 41 171.9512 30.08463 4.69843
Independent Samples Test
Levene's Test for
Equality of
Variances
t-test for Equality of Means
F Sig. t df Sig. (2-
tailed)
Mean
Differen
ce
Std.
Error
Differen
ce
95% Confidence
Interval of the
Difference
Lower Upper
sysBP
Equal variances
assumed
2.625 .106 -7.305 642 .000 -30.259 4.14235 -38.393 -22.125
Equal variances
not assumed
-6.290 43.947 .000 -30.259 4.81046 -39.954 -20.564
We performed an independent t-test was in order to compare the mean systolic BP for
those on antihypertensive (BPMEDS = 1) and those not on antihypertensive
(BPMEDS = 0). Results showed that the mean systolic BP for those on
antihypertensive (M = 171.95, SD = 30.08, N = 41) was significantly different with
the mean systolic BP (M = 141.69, SD = 25.34, N = 603), t (642) = -7.305, p < .05,
two-tailed. Those on antihypertensive had higher mean systolic BP than those not on
antihypertensive.
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c) Does mean diastolic BP (DIABP) differ between those on antihypertensives
(BPMEDS = 1) and those not on antihypertensive (BPMEDS = 0)?
Answer
Group Statistics
BPMeds N Mean Std. Deviation Std. Error Mean
diaBP
Not on antihypertensive 603 86.2736 13.72689 .55900
On antihypertensive 41 97.3902 14.43542 2.25443
Independent Samples Test
Levene's Test for
Equality of
Variances
t-test for Equality of Means
F Sig. t df Sig. (2-
tailed)
Mean
Differen
ce
Std.
Error
Differen
ce
95% Confidence
Interval of the
Difference
Lower Upper
diaBP
Equal variances
assumed
.003 .955 -5.001 642 .000 -11.117 2.22276 -15.481 -6.752
Equal variances
not assumed
-4.786 45.058 .000 -11.117 2.32270 -15.795 -6.439
We performed an independent t-test was in order to compare the mean diastolic BP
for those on antihypertensive (BPMEDS = 1) and those not on antihypertensive
(BPMEDS = 0). Results showed that the mean diastolic BP for those on
antihypertensive (M = 97.39, SD = 14.44, N = 41) was significantly different with the
mean diastolic BP (M = 86.27, SD = 13.73, N = 603), t (642) = -5.001, p < .05, two-
tailed. Those on antihypertensive had higher mean diastolic BP than those not on
antihypertensive.
3. A nutrition expert is examining a weight-loss program to evaluate its effectiveness
(i.e. whether participants lose weight on the program). Ten subjects are randomly
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selected for the investigation. Each subject’s initial weight is recorded, they
follow the program for 6 weeks, and they are weighed again. The data are;
subject Initial weight Final weight
1 180 165
2 142 138
3 126 128
4 138 136
5 175 170
6 205 197
7 116 115
8 142 128
9 157 144
10 136 130
Use SPSS to test if there is evidence of a significant weight loss. Run the
appropriate test at the 5% level of significance. Write a 1-sentence summary
of your analysis.
Answer
Paired Samples Statistics
Mean N Std. Deviation Std. Error Mean
Pair 1 Initial Weight 151.7000 10 27.42687 8.67314
Final Weight 145.1000 10 24.86162 7.86193
Paired Samples Correlations
N Correlation Sig.
Pair 1 Initial Weight & Final Weight 10 .980 .000
Paired Samples Test
Paired Differences t df
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Sig. (2-
tailed)
Mean Std.
Deviation
Std. Error
Mean
95% Confidence
Interval of the
Difference
Lower Upper
Pair 1 Initial Weight - Final
Weight
6.60000 5.81569 1.83908 2.43971 10.76029 3.589 9 .006
A paired-samples t-test was conducted to compare initial weight and final weight of
individuals after a weight-loss program. There was a significant difference in the
initial weight (M = 151.70, SD = 27.43) and final weight (M = 145.10, SD = 24.86)
conditions; t(9) = 3.589, p = 0.006. These results suggest that the weight-loss program
really does have an effect weight of individuals. Specifically, our results suggest that
before the weight-loss program, the individual’s weight more as compared after the
weight loss program.
4. The following data reflect the ages of students at completion of year 7. Test if
there is a significant difference in the mean age at completion of year 7 for rural,
suburban and urban students using SPSS. Write a 1-2 sentence summary of your
findings.
rural 14 14 14 14 13 13 13 12
suburba
n
14 14 14 13 13 13 13 13 12 12
urban 16 16 15 15 15 14 14 14 13 12
Answer
Test of Homogeneity of Variances
Age
Levene Statistic df1 df2 Sig.
2.064 2 25 .148
ANOVA
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Age
Sum of Squares df Mean Square F Sig.
Between Groups 9.254 2 4.627 4.991 .015
Within Groups 23.175 25 .927
Total 32.429 27
Multiple Comparisons
Dependent Variable: Age
Bonferroni
(I) Region (J) Region Mean Difference
(I-J)
Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
Rural Sub-Urban .27500 .45670 1.000 -.8969 1.4469
Urban -1.02500 .45670 .102 -2.1969 .1469
Sub-Urban Rural -.27500 .45670 1.000 -1.4469 .8969
Urban -1.30000* .43058 .017 -2.4049 -.1951
Urban Rural 1.02500 .45670 .102 -.1469 2.1969
Sub-Urban 1.30000* .43058 .017 .1951 2.4049
*. The mean difference is significant at the 0.05 level.
First, we checked for the homogeneity of variances where we observed the variances
to be homogenous (p = 0.148). For the ANOVA test, results showed that there is
significant difference in the mean age at completion of year 7 for at least one region.
Post-hoc test using Bonferroni showed that significance difference exists in the mean
age at completion of year 7 for the urban and Sub-Urban regions.
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