BIOENG_2525_Homework2_solut
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BIOENG 2525: Applied Biostatistics
Homework #2
Assigned: 9/18/23
Due: 9/25/2023 by 11:59 PM EST
1) The dataset for this question, SurveyData2011.sav, is found in Canvas -> Modules -> Week 4.
This dataset is from the CD to
Statistical Methods for Health Care Research
by Barbara Hazard
Munro. Students in her course distributed questionnaires to a variety of individuals and collected
the data found in this file. You can use the variable view in SPSS to investigate what the various
columns are. First, examine the correlation between the number of years of education an
individual has and their degree of depression.
a. At what level of scale is each of these variables measured? (2 points)
number of years of education an individual has is ratio and their degree of depression
is intervall.
b. Which correlational analysis is appropriate for these variables? Justify your answer. (4
points) Pearsons,
Kendalls Tau is most appropriate because the variables represent non parametric data.
c. The SPSS correlation outputs can be found below. Based on your answer to part b,
interpret the correct output(s) to answer the following questions.
i. What is the correlation between the number of years of education an individual has
and their degree of depression? (2 points)
There is a signifigant negetive correlation
ii. Is the correlation significant (include the p-value in your answer)? (2 points)
Yes, the P value is .001
iii. What can you conclude about the relationship between the number of years of
education an individual has and their degree of depression? (2 points)
The degree of depression is slightly decreaced as the number of years of
education increase.
2) A survey of 100 first year graduate students in the Bioengineering Department at Statistics
University was conducted to assess 1) how much students were exercising during the week and 2)
the average number of coffees they consume per week. The results from this survey can be found
in Canvas -> Modules -> Week 4. Use SPSS to answer the following questions and be sure to
include screenshots of your work along with your written answers.
a. Use the methods learned in class, 1 graphical and 1 statistical test, to determine whether
the total hours spent exercising per week and the average number of coffees consumed per
week are normally distributed. (6 points)
Using the K-S test we can not assume that either are normally distributed because both of the
p-values are less than 0.05 but using the Histograms we can see that the total hours spent
exercising per week is not normally distributed but, the average number of coffees
consumed
per
week
isnormally
distributed.
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b. Is there a significant correlation between the total hours spent exercising per week and the
average number of coffees consumed per week? (4 points)
Yes there is a signifigaant positive correlation. The p-value is less than 0.05, giving it
significance and the pearsons coefficient is 0.829 to give it a strong positive correlation.
3) Professor Scott is interested in assessing the relationship between the time spent practicing parallel
parking and the time it takes to parallel park a car during a driving exam. The data from 10
students
is summarized in the table below. Note: Excel, Mathematica, Matlab, or any other
software can be used to analyze the data however you must describe the mathematical operations
that were programmed into the software. Specifically, you must write out the formulas you used
to complete the calculations for the best fit line, hypothesis test, and correlation coefficient (you
may not use
the line fitting features of these or other software packages to make these
calculations). You may, however, use statistical software packages to check your answers.
a. Determine the best fit equation using the least squares method. (4 points)
y = -0.214285714 x + 50.92857143
b. State the null and alternative hypotheses for a two-tailed test on the slope (where the null
indicates no relationship between the variables). (2 points)
The Null Hypothosis is that there is no correlation between the time spent practicing parallel
parking and the time it takes to parallel park a car during a driving exam.
The Alternative Hypothesis is that there is a correlation between the time spent practicing
parallel parking and the time it takes to parallel park a car during a driving exam.
c. Test the hypothesis that you developed in part b. (5 points)
We fail to reject the null hypothesis because the t-value is not significantly different from zero
(given our 8 degrees of freedom).
d. Calculate the Pearson correlation coefficient (r) based on this data set. (3 points)
r = -0.136
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Time training with novel training
tool (hours)
Time spent performing intubation
procedure (seconds)
13
46
14
41
15
57
18
44
12
50
16
52
10
47
20
49
11
51
17
41
4) Compare and contrast correlation analysis and regression analysis. (4 points)
Correlation and regression both seek to find linear relationships between variables. Regression looks
for that linear relationships by using a predictor variable (or variables if multiple regression) to
predict an outcome variable. This involves the creation of an equation with the output being the
predicted value of the outcome variable. Regression is based on causality, it shows the effect one (or
more) variable has on another. Correlation differs in that it dies not imply causation, instead it shows
how interrelated (or unrelated) the variables are.