RCH 8303, Quantitative Data Analysis 1
Course Learning Outcomes for Unit IV
Upon completion of this unit, students should be able to:
1. Perform statistical tests using software tools.
1.1 Upload an appropriate data file.
1.2 Perform correlation using appropriate menu options.
1.3 Explain the purpose of the Spearman rank-order correlation.
2. Explain results of statistical tests.
2.1 Describe the differences between unstandardized and standardized data.
2.2 Discuss the differences between alternative hypotheses.
2.3 Elaborate on the effects of outliers on the correlation coefficient.
2.4 Describe the assumptions for correlation.
2.5 Contrast the differences between a paired sample t-test and an independent sample t-test.
3. Judge whether null hypotheses should be rejected or maintained.
3.1 Explain the differences between the null and alternative hypotheses, and perform option
selection.
3.2 Discuss what effect size is and how it is calculated.
Course/Unit
Learning Outcomes
Learning Activity
1.1, 1.2, 1.3, 3.1
Unit Lesson
Chapter 6, pp. 127–129
Unit IV Assignment 2
2.1, 2.2, 2.3, 2.4, 2.5,
3.2
Unit Lesson
Unit IV Assignment 1
Required Unit Resources
Chapter 6: Simple Statistical Tests, pp. 127–129
Unit Lesson
Unit IV Plan
The Unit IV assignment will be in two parts. Part 1 of your assignment requires you to complete modules of
the CITI Program EOSA that relate directly to the reading in this unit. Each of the modules has a final quiz
that must be completed and successfully passed, demonstrating your knowledge of basic statistics and the
research process.
For Part 2, you will review how to conduct a correlation and determine whether the test is statistically
significant or not.
There are two topics in the Unit IV CITI EOSA course.
Correlations (ID 17632): This module describes and explains the extent of relationships between two
variables. It explains in detail the two different types of tests: Pearson product-moment correlation for
parametric data and Spearman rank-order correlation for nonparametric data.
UNIT IV STUDY GUIDE
Correlation
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Comparing Correlation Coefficients (ID 17633): This module describes how to conduct the appropriate
analysis to compare two correlation coefficients. This module is important to understanding the different types
of comparisons.
What is Correlation?
Unit IV starts with a different type of outcome form of testing. The focus of Unit IV is correlation, which is a
methodology that tests to determine whether there is a relationship between variables. An example of this
could be whether there is a relationship between the two variables—cigarette smoking and the rate of throat
cancer incidence. A research question could be framed; Is cigarette smoking related to likelihood of throat
cancer?
With correlation, you are trying to find out if there is any relationship between your variables. Typically, you
will have two variables, and you will want to see if there is any relationship between the two. This can be a
positive or even a negative relationship. Important to note, though, that this is not a causal relationship. For
this test, our research question and hypotheses could be written as:
RQ: What is the relationship between a person’s weight and a person’s runtimes?
H0: There is no relationship between a person’s weight and a person’s runtimes.
HA: There is a relationship between a person’s weight and a person’s runtimes.
R and R Commander make it very easy to conduct simple statistical tests. If you are not comfortable utilizing
R and R commander you may use whatever statistical software program you choose. The answers you
submit for your assignment must be correct regardless of the software you choose.
As noted in Unit III, once data are collected, a researcher needs to be able to describe, summarize, and,
potentially, detect patterns in the data they have recorded with meaningful numerical scales such as
histograms. After reviewing the data, decisions must be made regarding whether the assumptions of the
particular test have been met. If they have, then conducting of the test can proceed. Reviewing these two
tutorials, Homogeneity of Variances and Testing for Normality, will be very helpful to you.
Prior to conducting any statistical test though, the researcher must first meet the assumptions of the particular
test.
For an example of a correlation test, make sure when you access R that you also load R Commander. Type
in library(Rcmdr) or see Unit I for a refresher on how to gain access to R Commander. Once R and R
Commander have been loaded, the next step is to load the data set wtruntime that will be used (Figure 1).
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Figure 1
Data Set Wtruntime Successfully Uploaded
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Viewing the data set allows a user to examine the type of category information and numeric values (Figure 2).
Figure 2
Visual Representation of Wtruntime Data Set
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The next step is to view the data set in a graphical form. This will allow us the opportunity to view the data set
in graphical display. Select Graphs and then Histogram (Figure 3).
Figure 3
Histogram Selection Menu
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Next step is to select which variable (Figure 4) to view in a histogram. Since we have two in this data set, we
will do this for each one.
Figure 4
Variable Selection Menu: Weight Selection
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Variable Weight Histogram (Figure 5) is shown below.
Figure 5
Variable Weight Histogram
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Variable Runtimes Histogram (Figure 6) is shown below.
Figure 6
Variable Runtimes Histogram
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Our next step is to view the numerical summaries of our data (Figure 7).
Figure 7
Numerical Summaries of Data Selection Menu
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Next, since we have two variables, selecting both of them will summarize both data sets (Figure 8).
Figure 8
Variable Selection Menu
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Selecting the Statistics tab displays options available to user. Selecting Skewness and Kurtosis will display
these numbers as well (Figure 9).
Figure 9
Numerical Display Options Menu
Figure 1
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Numerical display output (Figure 10) is shown below.
Figure 10
Numerical Display Output
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The next step is to determine whether the data are normally distributed. Assessing a variable’s distribution
can help determine which of the correlation tests can be used (Figure 11).
Figure 11
Testing for Normality Selection
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This displays a menu (Figure 12) of which variables to use. Since we will check each variable, we will start
with the Weight variable first and use the Anderson-Darling Test of Normality.
Figure 12
Weight Variable Test of Normality Options Menu
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Weight Variable Test of Normality output display (Figure 13) is shown below.
Figure 13
Weight Variable Test of Normality Output
Since we have failed to reject the null hypothesis, this indicates there is no difference between the data’s
distribution and a theoretical normal distribution. For more information, please review the tutorials located in
the dissertation center about this topic.
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Runtimes Variable Test of Normality selection menu (Figure 14) is shown below.
Figure 14
Runtimes Variable Test of Normality Selection Menu
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Runtimes Variable Test of Normality output display (Figure 15) is shown below.
Figure 15
Runtimes Variable Test of Normality Output Display
Since we have failed to reject the null hypothesis indicating there is no difference, the data are normally
distributed. For more information, please review the tutorials Homogeneity of Variances and Testing for
Normality.
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The next graph to view is a scatterplot of both variables to see how well they fit the line (Figure 16).
Figure 16
Scatterplot Selection Menu
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Next, select which will be the x and y variables (Figure 17).
Figure 17
Scatterplot Variable Selection Menu
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Scatterplot results (Figure 18) are shown below.
Figure 18
Scatterplot Results
The scatterplot results in a good display of the data points. There are six that are clearly not on the line.
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Our next step is to run the correlation to determine the strength of the relationship between the weight and
runtimes variables (Figure 19).
Figure 19
Correlation Selection Menu
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Since our data are normally distributed and are continuous variables, we can use the Pearson productmoment test. Selecting both variables and checking to make sure the Two-sided test is selected will allow us
to run the test (Figure 20).
Figure 20
Correlation Test Options menu
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Figure 21
Correlation Test Output Display
The results of the test are statistically significant (p-value = 0.000001806). The test has a Pearson r of
.8525839 indicating a positive relationship. One could write these results as:
A test of the relationship between a person’s weight and their runtimes was performed. Both variables
were considered normally distributed. The Pearson Product-Moment Correlation Coefficient (r) was
selected as the test statistic. The result of the test was significant, r(18) = .853, 95% CI (.659, .940), p
< .001.
In conclusion, the correlation test discussed in this unit is used to determine whether there is a relationship
between variables. Unit V will focus on t-tests and the different types of t-tests and the type of data needed to
run the analyses.
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Learning Activities (Nongraded)
Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit
them. If you have questions, contact your instructor for further guidance and information.
When studying APA formatting, pay particular attention to the sections that pertain to formatting for research
and statistics.

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