Descriptive Statistics

Using the provided dataset in Excel, calculate the appropriate descriptive statistics for the
following variables comparing diabetes with no diabetes status: gender, race, salary, education,
height, weight, BMI, allergies, family history diabetes, family history allergies. For chi-square
tests, report the chi-square value and the p-value (if p-value < 0.05, then the test is significant).
For t-tests, report the t-test value and the p-value. Include a 2-3 page description of the
descriptive statistics including tables of the summarized data, similar to a “Results” section in a
published manuscript or journal article.

Descriptive Statistics
Using the provided dataset in Excel, descriptive statistics that are appropriate for variables
concerning to diabetes including gender, race, salary, height, weight, as well as BMI. The
descriptive statistics calculated using the provided dataset specifically include mean, standard
deviation, variance as well as media. These descriptive statistics are mainly concerned with
analysis of measurement of central tendency i.e. mean and median as well as measurement of
variation i.e. standard deviation and variance.
Table 1: Descriptive Statistics

Age Salary Height Weight BMI

To feel
depressed
during the
winter
To
exercise
during
the
summer

To overeat
when
stressed out

Mean 50 \$54,498 66.98333 159.1133 24.63867 2.993333 3.373333 2.77
Standard
Deviation

20 28923.783 3.750102 31.66517 2.231375 1.226773 1.227046 1.315116638

Variance 401 836585199 14.06327 1002.683 4.979035 1.504972 1.505641 1.729531773
Median 50 \$50,012 67 161 25 3 4 3

In particular, this SLP assignment will be analyzed the provided dataset using chi-square tests
and t-test. For the chi-square tests apart from the descriptive statistics, the report will also include
chi-square value as well as the p-value. On the other hand, for the t-tests the report will include
the t-test value as well as the p-value.
In addition, the specific numbers of people in the provided the dataset within their specific
category i.e. diabetes and no diabetes are determined in order to enable the data analysis to be
carried out. A summary of those statistics is presented in the table shown below:
Table 2: Data Summary

Diabetes No Diabetes Total Percentages
Female 56 103 159 53%
Male 53 88 141 47%
Total 109 191 300
Percentages 36.3% 63.7% 100%

Based on the statistics presented in the above table concerning the chi-square obtained from the
VassarStats website which is used for statistical computation, particularly in the context of Chi-
Square for Categorical Data and specifically using Chi-Square, Cramer’s V, and Lambda in a 2 x

2 table; there are some inferences that can already be done. Some of the inferences based on
percentages include:
There are significantly more women (53%) who have diabetes than men (47%).
Additionally, the results of the chi-square test show that the chi-square value is 0.09 and the p-
value is <0.0001 an indication that the test is significant meaning that there a significant
difference between the number of women who are diabetic compared to men who are diabetic.

T-Tests for Continuous Data
The t-test was used to compare the two groups i.e. Sample A (no diabetes) and Sample B
(diabetes) and the t-test reported the t-test value as well as p-value. The t-test values for variables
such as age, height, weight as well as BMI are reported in the table shown below. In addition, the
two-tailed p-values are also shown and the are all below <0.05 and indication that the tests are
significant which means there are significant differences between the two groups (i.e. Sample A
and Sample B) with regards to the considered variables.
Table 3: Data Summary

A B Total t-test
value

Two-
tailed p-
value

N 191 109 300

Age Mean 39.0052 70.5229 50.4567 -20.69 <0.0001

Height Mean 65.0209 70.422 66.9833 -16.63 <0.0001
Weight Mean 142.7016 187.8716 159.1133 -16.33 <0.0001
BMI Mean 23.5628 26.5239 24.6387 -14.35 <0.0001

The average age of those without diabetes is 39 years and for those with diabetes is 70.5 years.
Those with diabetes were significantly older/younger (p<0.05).
The average height of those without diabetes is 65.02 centimeters and for those with diabetes is
70.4 centimeters. Those with diabetes were significantly shorter/taller (p<0.05).
The average weight of those without diabetes is 132.7 lbs and for those with diabetes is 187.8
lbs. Those with diabetes were significantly heavier/lighter (p<0.05).
The BMI of those without diabetes is 23.6 and for those with diabetes BMI is 26.5. The BMI for
those with diabetes is significantly higher/lower (p<0.05).

References

Corder, G. W. & Foreman, D. I. (2014). Nonparametric Statistics: A Step-by-Step Approach.
New York, NY: Wiley.
Greenwood, P. E. & Nikulin, M. S. (1996) A guide to chi-squared testing. New York, NY:
Wiley.
Markowski, C. A. & Markowski, E. P. (1990). Conditions for the Effectiveness of a Preliminary
Test of Variance. The American Statistician, 44(4), 322–326.
Sawilowsky, S. S. (2005). Misconceptions Leading to Choosing the t Test over the Wilcoxon
Mann–Whitney Test for Shift in Location Parameter. Journal of Modern Applied
Statistical Methods, 4(2), 598–600.
VassarStats (2015). Procedures Applicable to Categorical Frequency Data.
VassarStats (2015). t-Tests & Procedures.

Zimmerman, D. W. (1997). A Note on Interpretation of the Paired-Samples t Test. Journal of
Educational and Behavioral Statistics, 22(3), 349–360.

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