Home » Normal data distribution and two-variable correlation testing

Normal data distribution and two-variable correlation testing

For this three-part assessment you will create a histogram or bar graph for a data set, perform assumption and correlation tests, and interpret your graphic and test results in a 2-to-3 page paper.

In this unit we focus on whether two or more groups have important differences on a single variable of interest. For example, for the dependent variable stress score, we may want to know if there is a difference in stress between males and females, or maybe we would like to know if there is a difference in stress levels between people who drink chamomile tea and those who do not, or maybe we would like to determine if a group of expectant parents is less anxious (this is the dependent variable) about the birthing experience after a series of discussions with experienced parents. In each of these examples we have two groups (two groups being compared or the same group being compared before and after), and one dependent variable that is being compared in each group. In this unit you will begin exploring popular statistical techniques (and their assumptions) that are used to compare two or more groups.

The independent t-test, also called unpaired t-test, is typically used in health care to compare two groups of individuals that are entirely unrelated to each other (that is, independent), thus the one group cannot influence the other group. For example, we may wish to compare a drug treatment group to a control group (those not receiving drug treatment) for a specific clinical characteristic (dependent variable) that can be measured at the interval or ratio level (such as cholesterol, depression scale, or memory test).

The dependent t-test, also called paired t-test, compares two groups for a dependent variable measured at the interval or ratio level as well; however, these two groups are in reality just one group. But because they are measured before and after an intervention, we consider them as two groups for analytical purposes. This group is considered dependent because nothing is expected to vary in the nature of the individuals being measured except as a result of the intervention, as the group is composed of the same individuals.


One of the most important steps along the researcher’s path to data analysis is to become familiar with the character of the raw data collected for the project. Before weaving the strands of data into an analytical story that is related to a study’s goals, researchers typically inspect the completeness and quality of the data with various visualization techniques (graphics), summary tables, and mathematical tests of quality (assumption tests), as discussed in Assessment 2. One of these latter tests is a correlation analysis. With this approach, the researcher performs a very basic series of exploratory tests on variable pairs to identify any potentially interesting (yet unknown) relationships between groups of data (variables). Correlational analyses are often later performed as part of the predetermined data analysis plan to answer a specific research question.

Demonstration of Proficiency

By successfully completing this assessment you will address the following scoring guide criteria, which align to the indicated course competencies.

  • Competency 1: Describe underlying concepts and reasoning related to the collection and evaluation of quantitative data in health care research. 
    • Interpret the overall clinical meaning and limitations of the relationship of two variables, based on a correlation analysis and literature regarding age and stress.
  • Competency 2: Apply appropriate statistical methods using common software tools in the collection and evaluation of health care data. 
    • Create a histogram and scatter plot for variables tested for normal distribution.
    • Perform a normal distribution assumption test for two variables to determine if data is normally distributed.
    • Perform an appropriate correlation test to determine the direction and strength or magnitude of the relationship between two variables.
  • Competency 3: Interpret the results and practical significance of statistical health care data analyses. 
    • Interpret the effect size for correlation analysis results.
  • Competency 5: Address assignment purpose in a well-organized text, incorporating appropriate evidence and tone in grammatically sound sentences. 
    • Articulate meaning relevant to the main topic, scope, and purpose of the prompt. 
    • Apply APA formatting to in-text citations and references.


For this three-part assessment, complete the following, referring to Yoga Stress (PSS) Study Data Set [XLSX], which you have used previously, as needed.


The following statistical analysis software is required to complete your assessments in this course:

  • IBM SPSS Statistics Standard or Premium GradPack, version 22 or higher, for PC or Mac.

You have access to the more robust IBM SPSS Statistics Premium GradPack.

Please refer to the Statistical Software page on Campus for general information on SPSS software, including the most recent version made available to Capella learners.

Part 1: Graphic Representation of the Data from the Yoga Stress (PSS) Study Data Set
  1. Create a histogram or bar graph (according to the measurement level of the data) of the following variables: Age, Education, Pre-intervention Psychological Stress Score (PSS). 
    • Refer to the following resources as needed while creating your histogram: 
  2. Create a scatter plot of the following pair of variables: Age versus Pre-intervention Psychological Stress Score (PSS). 
    • Refer to the following resources, as needed, while creating your scatterplot: 
Part 2: Statistical Tests
  1. Perform a preanalysis assumption test for a normal distribution test to determine if the data you intend to use for the correlation tests passes the assumption of being normally distributed. 
    • You will use this test for Age and Pre-intervention Psychological Stress Score (PSS).
  2. Perform the appropriate correlation test to determine the direction and strength or magnitude of the relationship between these two variables from Step 1. 
    • Remember, we are not concerned about causation at this point and want to determine only if there is a statistical association.
Part 3: Yoga Stress (PSS) Study Paper
  • Include the histogram and scatter plot graphics you created earlier for Age and Pre-intervention Psychological Stress Score (PSS). 
    • Provide an interpretation for these graphics.
  • Report the statistical outcome of the correlation analysis using appropriate scholarly style, including a brief interpretation of the effect size of the correlation.
  • Interpret the practical, real-world meaning (and limitations of the interpretation) of the relationship of these two variables based on the correlation analysis you performed.
  • Include the SPSS “.sav” output file that shows your programming and results from Parts 1 and 2 for this assessment.
  • Provide at least one evidence-based scholarly or peer-reviewed article that supports your interpretation.

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