Project #35301 - Statics II

Learner Course ID: 358116

Activity 4

Section 2: Assumptions and Common Statistical Strategies � Correlation, Regression, and Comparing Means

This section begins with exploring assumptions and why they are important (and what to do if your data do not meet required assumptions). Prior to conducting statistical tests, you must examine your dataset to ensure that it does not violate the assumptions upon which the intended tests are based. Using the procedures outlined in Section 1, you may already have a good idea about your dataset with regards to the necessary assumptions. However, in this section we will formalize the evaluation of these assumptions. In your dissertation, it will be expected that you both understand and acknowledge assumptions, and that you are able to make modifications in your proposed analytical strategy, as necessary.

Once a firm understanding of assumptions related to statistical tests is gleaned, we jump into actually performing and interpreting common statistical tests; now the fun really begins!

The tests covered in this section include:
Correlation: Are two variables related; If so, how? A correlation tells you how and to what extent two variables are linearly related. A correlation coefficient will always fall between -1 and +1 with 0 indicative of no relationship between the variables. Rule of thumb effect sizes are as follows: Small (+.1), Medium (+.3) and Large (+.5), although these effect sizes should always be evaluated relative to research. An important point to remember: correlation does not equal causation! 

Regression: A regression analysis is very similar to a correlation, but is the framework commonly used when one wants to predict one variable from another. For example: How much variance in happiness scores are predicted by hours of physical activity performed each week? With the simple regression framework, you have one predictor variable and one outcome variable; the outcome variable is measured on a continuous scale (soon you will learn how multiple regression can handle multiple predictor variables simultaneously). 

Logistic Regression: A logistic regression is the framework one would use for prediction when the outcome variable is categorical. For example: Do numbers of hours spent in voluntary corporate training during the first year of employment predict whether an employee is still at the company in two years (yes/no)?

Comparing Means and ANOVA: While many questions can be answered by correlation and regression, frequent questions require the comparison of mean scores. For example: Are standardized test scores higher in a school that uses one reading method compared to another? Do men or women reap a greater benefit, in terms of pounds lost, from a certain exercise program? Questions that compare two groups can be answered with a simple t-test. An Analysis of Variance (ANOVA) can handle designs that compare more than two groups, like: Does Drug A, B, or C result in better life expectancies for people diagnosed with cancer? Or does Diet A, B, C, or D result in healthier cholesterol levels?

A lot of information is covered in these chapters, so please plan accordingly. Also, pay attention to how these techniques are fundamentally similar � it seems like a ton of information, but if you master the statistical models at this level, the rest of the course will progress more smoothly. 

It will be expected that you have gained an understanding of all analyses presented in the text. That is, should you require the use of an analytical strategy covered in the text but not performed in the Activity for your dissertation, you will have the core competencies to perform these alternative techniques.


Required Reading:
Please refer to each Activity for required readings within Activity Resources.

Assignment 4   t test and ANOVA
Last week you learned how to examine relationships between variables, conduct analyses related to correlation and regression, and interpret the output associated with each. 

This week you will learn how to conduct tests that determine if there are differences between mean scores for groups. For example, you might be interested in studying whether there are mean differences in heart rate between two groups: those who exercise and those who do not (t test), or you might use a slightly more complicated design and compare mean heart rates for three groups: non-exercisers, occasional exercisers, and regular exercisers (ANOVA). 

Activity Resources
  • Field, A. (2013): Chapters 9, 10, and 11
Self-Tests
  • Smart Alex's Quizzes
SPSS Data Sets
  • Activity 4a.sav
  • Activity 4c.sav
Optional Resources
  • Interactive Multiple Choice Questions
  • Flashcards
To Prepare for this week�s Activity
Download the following SPSS Data Sets. 
  • Activity 4a.sav
  • Activity 4c.sav
Read Chapters 9, 10 and 11 in the text. It will be to your advantage to have SPSS open on your computer as you work through these chapters. While you are reading and testing the assumptions of various statistical procedures, consider various types of datasets and whether they would run the risk of violating these assumptions.

Complete the Self-Tests in the chapters. Answers are available: http://www.sagepub.com/field4e/study/selftest.htm. 

Complete Smart Alex�s Quizzes. Answers are available at: 
http://www.sagepub.com/field4e/study/smartalex.htm. 

Optional Preparation for Activity 4
After completing the above activities, if you feel you need additional instruction on the concepts covered, please choose any of the following activities that will assist you in mastering the core concepts.
Main Task
You will submit one Word document and one SPSS data file for this activity. You will create the Word document by cutting and pasting SPSS output into Word. 

Part A. Dependent t test
In this activity, we are interested in finding out whether participation in a creative writing course results in increased scores of a creativity assessment. For this part of the activity, you will be using the data file �Activity 4a.sav�. In this file, �Participant� is the numeric student identifier, �CreativityPre� contains creativity pre-test scores, and �CreativityPost� contains creativity post-test scores. A total of 40 students completed the pre-test, took the creativity course, and then took the post-test.

1. Exploratory Data Analysis/Hypotheses

a. Perform exploratory data analysis on CreativityPre and CreativityPost. Using SPSS, calculate the mean and standard deviation of these two variables.

b. Construct an appropriate chart/graph that displays the relevant information for these two variables.

c. Write the null and alternative hypotheses used to test the question above (e.g., whether participation in the course affects writing scores).


2. Comparison of Means

a. Perform a dependent t test to assess your hypotheses above (note that many versions of SPSS use the term �paired samples t test� rather than �dependent t test�; the test itself is the same.

b. In APA style, write one or two paragraphs that describe the dataset, gives your hypothesis, and presents the results of the dependent sample t test.


Part B. Independent t test
We will start with the data file used in Part A (�Activity 4a.sav�). Suppose, however, you [the researcher] encountered a small problem during data collection: after the post-tests were collected, you realized that the post-test form did not ask for the students� identification number. As such, it will be impossible to match pre-test scores to post-test scores. Rather than simply give up, you start thinking about the data you do have and try to determine whether you can salvage your project. In assessing the situation, you realize that you have 40 pre-test scores and 40 post-test scores, but no way to link them. While it will result in a weaker comparison, you determine that you are still able to compare pre-test vs. post-test scores; you will use a between-subjects design rather than a within-subjects design.

1. Create the data set.

a. Using the �Activity 4a.sav� file as a starting point, create a new dataset that you can use with the between subjects design. Hint: you will no longer need the variables CreativePre and CreativeTest. Instead, you have only one variable for the score on the creativity test. A second (or grouping) variable will serve to indicate which test the student took.

b. Submit the dataset as one of the Activity 4 files.


2. Exploratory Data Analysis/Hypotheses.

a. Perform exploratory data analysis on CreativityPre and CreativityPost. Using SPSS, calculate the mean and standard deviation of these two variables.

b. Construct an appropriate chart/graph that displays the relevant information for these two variables.

c. Write the null and alternative hypotheses used to test the question above (e.g., whether participation in the course affects writing scores).


3. Comparison of Means

a. Perform an independent t test to assess your hypotheses above.

b. In APA style, write one or two paragraphs that describe the dataset, gives your hypothesis, and presents the results of the dependent sample t test.


4. Comparison of Designs

a. In this activity, you used the same dataset to analyze both a between- and within-subjects design. Create a single paragraph (using the material you wrote above), that presents both sets of results.

b. Explain, in 300-500 words, whether the two tests resulted in the same findings. Did you expect this to be the case? Why or why not? What have you learned in this activity?


Part C. ANOVA
All of us have had our blood pressure measured while at our physician�s office. How accurate are these measurements? It may surprise you to learn that there is something called �white coat syndrome��the tendency of some people to exhibit elevated blood pressure in clinical (medical) settings only. In other words, for these people, the very fact that the physician is taking their blood pressure causes it to increase In this activity, you will be using the �Activity 4c.sav� data file to determine whether you find support for the existence of white coat syndrome. In this study, 60 participants were randomly assigned to one of three groups. The �settings� variable indicates the location in which the participants� blood pressure was recorded: 1=home, 2=in a doctor�s office, and 3=in a classroom setting. The �SystolicBP� variable contains the participants� systolic pressure (the �upper� number). The �DiastolicBP� variable contains the participant�s diastolic pressure (the �lower� number).

1. Exploratory Data Analysis/Hypotheses.

a. Perform exploratory data analysis on both the SystolicBP and DiastolicBP variables. Using SPSS, calculate the mean and standard deviation of these two variables. Be sure that your analysis is broken down by setting (e.g., you will have six means, six SD�s, etc.).

b. Create two graphs�one for systolic and one for diastolic pressure. Each graph should clearly delineate the three groups.

c. Write a null and alternative hypothesis for the comparison of the three groups (note that your hypothesis will state that the three groups are equivalent; be sure to word your null hypothesis correctly).


2.ANOVA.

a. Using the �Activity 4c.sav� data file, perform two single factor ANOVAs: one using SystolicBP and one using DiastolicBP as the dependent variable.

b. If appropriate for either or both of the ANOVAs, perform post hoc analyses to determine which groups actually differ.

c. Write one paragraph for each ANOVA (be sure to use APA style). At a minimum, each paragraph should contain the three means, three SD�s, ANOVA results (F, df), post hoc tests (if applicable), effect size, and an interpretation of these results.


Submit your documents in the Course Work area below the Activity screen.

Learning Outcomes: 2, 3, 4, 5, 6, 10, 11
Assignment Outcomes
Develop appropriate null and alternative hypotheses given a research question.
Calculate and interpret descriptive statistical analysis.
Create and interpret visual displays of data.
Apply appropriate statistical tests based on level of measurement.
Determine the appropriate use of inferential statistical analysis.
Demonstrate proficiency in the use of SPSS.
Demonstrate proficiency in reporting statistical output in APA format.

Course Work

Course: BTM8107-8 Syllabus: 31479
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