# Part I: Identifying Appropriate Statistical Tests Directions: For each of the following scenarios, you are to read the scenario and determine which statistical analysis procedure best fits the described scenario. You are to choose from the analyses we have covered in this class (i.e., independent t-test, repeated measures/

Final Examination – Part II

This part of the Final Examination will be completed in this document and uploaded on Blackboard using the appropriate turn-in link. Be sure to answer all parts of each question. Part I and Part II (this part) of the examination are due by 11:59 pm on December 11, 2023.

Part I: Identifying Appropriate Statistical Tests
Directions: For each of the following scenarios, you are to read the scenario and determine which statistical analysis procedure best fits the described scenario. You are to choose from the analyses we have covered in this class (i.e., independent t-test, repeated measures/paired samples t-test, independent one-way ANOVA, repeated measures one-way ANOVA, multifactorial ANOVA, multivariate ANOVA, Pearson’s correlation, Spearman’s correlation, biserial correlation, point-biserial correlation, partial correlation, semi-partial correlation, simple regression, and multiple regression). Note, you are not conducting any analyses for this exercise, you are only discussing which analysis would be the best to conduct in each situation and why.

Scenario 1
Carlos, a doctoral student in physical therapy, is interested in exploring the relationship between leg strength and running speed. In particular, he believes that individuals who have greater leg strength will demonstrate faster running speed. Carlos recognizes, however, that an individual’s level of physical activity could have an effect on the relationship between leg strength and running speed. With this in mind, Carlos collects data on these three variables from a group of 75 individuals. Using appropriate tools, numerical scores on a scale of 1-100 are collected for physical activity and leg strength (higher numbers represent more strength or activity). Running speed over a fixed distance is recorded in seconds. Carlos will explore the relationship between leg strength and running speed, controlling for differences in physical activity levels among the study participants. Considering the statistical analyses we’ve studied, what is the most appropriate statistical test to employ, and why? Most appropriate statistical test:

Multiple Regression
Why you chose this test:

In this scenario, Carlos is interested in predicting a continuous outcome variable (running speed) from two predictor variables (leg strength and level of physical activity). He also wants to control for the effect of physical activity levels while examining the relationship between leg strength and running speed. This situation calls for multiple regression analysis as it allows us to predict the value of one variable based on the values of two or more other variables. It accounts for interactions among independent variables and can determine how much unique variance each predictor contributes to the outcome. Therefore, a multiple regression analysis would be best suited to address his research question.
Scenario 2
Martin is interested in conducting a study to determine if individuals become sad when they are exposed to people who are visibly depressed. Martin creates two social situations that each of the study participants will experience. During one social situation, all participants will interact with people who are visibly depressed. At the conclusion of the interaction, participants will complete the Measure of Sadness Rating Scale (higher scores represent more sadness). Each participant will, on a second occasion, participate in a social situation during which they will interact with people who do not display any signs of depression. The participants will complete the Measure of Sadness Rating Scale after this experience as well. Martin will compare the Measure of Sadness Ratings completed after each situation to determine if there is a significant difference. Considering the statistical analyses we’ve studied, what is the most appropriate statistical test to employ, and why? Most appropriate statistical test:

Paired t-test
Why you chose this test:

The paired t-test is the most appropriate for Martin’s study because it compares the means of two related groups to determine if there is a statistically significant difference between these means. In this case, each participant is exposed to both conditions (interacting with depressed individuals and non-depressed individuals) and their sadness levels are measured after each condition. These measurements are dependent on each other as they come from the same individual, making them paired observations.
Scenario 3
Thavi wants to study three methods of notetaking and their effects on college students’ GPAs. Thavi secures 30 student volunteers, 15 men and 15 women. All students in the sample will be assigned to 1 of three note-taking strategies that they will implement throughout the semester. At the same time, Thavi wonders if the effects on GPA might be different for men and women, so she wants to include gender in the analysis as well. This will also allow her to consider how note-taking strategies and gender might combine to impact college GPAs. Considering the statistical analyses we’ve studied, what is the most appropriate statistical test to employ, and why? Most appropriate statistical test:

Two-way ANOVA
Why you chose this test:

A two-way ANOVA is most appropriate for this study because it will allow Thavi to examine the main effects of both note-taking strategies and gender on college GPAs, as well as the interaction effect between these two independent variables. This type of analysis compares the mean differences between groups that have been split on two independent variables.
Scenario 4
Darlene is interested in investigating whether students who do well in math and science also tend to do well in the social sciences and humanities. Darlene collects student grades in four classes and compiles a math & science GPA and social sciences & humanities GPA for the 80 students in her sample. Darlene then conducts a statistical analysis to explore the relationship between the two GPA variables. Considering the statistical analyses we’ve studied, what is the most appropriate statistical test to employ, and why? Most appropriate statistical test:

Correlation analysis
Why you chose this test:

MATH and science score by averaging the two grades, as well as a social sciences and humanities score in the same way. She then uses correlation analysis to see if there is a relationship between high scores in math and science and high scores in social sciences and humanities.
Scenario 5
Stacy’s school has a limited budget for school programming each year. As the school principal, Stacy has to decide which combination of intervention programs (not counting what takes place as a part of classroom teaching) and extracurricular activities will have the best chance of improving student learning outcomes overall. She knows that student absences, student tardiness, school climate, quality of lunch, participation in social clubs, participation in academic clubs, school field trips, extracurricular sports, extracurricular drama, and extracurricular music can all impact student learning to some extent. Stacy is not sure, however, which areas have greater impact on student outcomes, and wishes to conduct a study to explore the issue so that she can be better informed about her budgeting choices. As a result of her analysis, Stacy wants to be able to determine which of these 10 variables work best together to significantly predict student learning outcomes. Considering the statistical analyses we’ve studied, what is the most appropriate statistical test to employ, and why? Most appropriate statistical test:

Multiple Regression Analysis
Why you chose this test:

The multiple regression analysis allows for the examination of the relationship between a dependent variable (student learning outcomes) and multiple independent variables (the ten factors Stacy is considering).
Scenario 6
William, a graduate student in psychology, is interested in exploring if there is a significant association between two variables of concern among graduate students in his program, meditation and mood, given that studies suggest that certain forms of meditation can result in improved mood. William asks 80 students to complete a brief survey on which they indicated if during the week they meditated (yes or no), and what their average mood was for the week (low/negative mood, average mood, or high/positive mood). William will explore the association between these two variables using a statistical analysis procedure. Considering the statistical analyses we’ve studied, what is the most appropriate statistical test to employ, and why? Most appropriate statistical test:

Chi-Square Test
Why you chose this test:

The Chi-Square Test of Independence is used when we want to see if there is a relationship between two categorical variables. In this case, both the variables ‘meditation’ (yes or no) and ‘mood’ (low/negative mood, average mood, or high/positive mood) are categorical.
Scenario 7
Rochelle is interested in the effect of coffee drinking on cigarette smoking. After securing the participation of 40 men women who smoke (at least 20 cigarettes per day) and drink coffee (at least 2 cups per day), she decides to set up an experiment whereby the participants watch TV for 45 minutes, during which they can drink the provided coffee for the first 35 minutes and smoke the provided cigarettes for the last 10 minutes. Rochelle records the number of cups of coffee drank and the millimeters of cigarettes smoked (based on video records and the measurement of the length the remaining cigarette butts). Rochelle is interested in running a statistical analysis that will explore how much variance in cigarette smoking can be attributed to variance in coffee drinking. Rochelle is also interested in arriving at a model that will allow her to predict how much cigarette smoking can be expected to occur based on the amount of coffee drank. Considering the statistical analyses we’ve studied, what is the most appropriate statistical test to employ, and why? Most appropriate statistical test:

Regression Analysis
Why you chose this test:

Rochelle is interested in understanding the relationship between two variables – coffee drinking and cigarette smoking. She wants to see how changes in one variable (coffee drinking) can predict changes in another variable (cigarette smoking). This is precisely what regression analysis does – it explores the relationship between a dependent variable and an independent variable, allowing us to predict outcomes based on specific inputs.
Scenario 8
Victor is interested in whether fathers of children with disabilities feel competent in parenting their children. Victor identifies 60 participants for her study; 20 fathers of children with no disabilities, 20 fathers of children with physical disabilities; and 20 fathers of children with cognitive disabilities. Victor collects data from all fathers in the study using 3 different measures of parenting competence: Instrumental Parental Competence, which assess caretaking responsibilities; Emotional Parental Competence, which evaluates the quality of emotional support provided to the child; and Play Parental Competence, which measures the quality of recreational time spent with the child. Each measure produces a numerical score on a scale of 1-75 where higher scores represent better outcomes. Victor will conduct a statistical analysis that will allow him to explore if there are any significant differences in competence scores based on child disability group for each of the 3 measures, and if there is a significant relationship between the fathers’ competence scores on the 3 measures. Considering the statistical analyses we’ve studied, what is the most appropriate statistical test to employ, and why? Most appropriate statistical test:

Two-Way ANOVA
Why you chose this test:

A Two-Way ANOVA is the most suitable in this case because Victor’s study has two independent variables (type of child disability and type of parenting competence) and one dependent variable (competence scores). A Two-Way ANOVA can analyze the main effects of each independent variable on the dependent variable, as well as any possible interaction effect between the two independent variables.

Part II: Statistical Analysis
1. Required:
An experimenter wanted to investigate simultaneously the effects of two types of reinforcement schedules and three types of reinforcers on the arithmetic problem-solving performance of second-grade students. A sample of 66 second graders were identified. The SPSS data file includes 66 cases and three variables: one representing two types of reinforcement schedules (random or spaced), a second variable representing three types of reinforcers (token, money, or food), and the dependent variable, each student’s score on an arithmetic problem-solving test. You will conduct a multifactorial ANOVA to analyze the data according to the steps below. The data is found in the following dataset:

A. Exploration of the Variables.
i. What are the independent variables? Be sure to describe each independent variable including the groups that represent them.

The independent variables are the types of reinforcement schedules and the types of reinforcers.

-Reinforcement Schedules: This variable has two groups, random and spaced.

-Types of Reinforcers: This variable has three groups – token, money, and food.

ii. Name and describe the dependent variable.

The dependent variable is the student’s score on an arithmetic problem-solving test. This variable will be used to measure the effect of different reinforcement schedules and types on second-grade students math problem-solving performance.

B. Exploration of Assumptions.
Given the variables you described, address each assumption for an independent multifactorial ANOVA. Be sure to provide written statements as well the related numeral data where needed, as usual. It is important to remind you that datasets are rarely perfect. This means that violation of some assumptions does not always rule out the use of an intended statistical analysis, specifically given the robust nature of the ANOVA test. We should, however, acknowledge assumptions violations when we interpret the results of our analysis.

C. Line Graph. Use SPSS to produce a line graph appropriate for this analysis.

(Paste the graph here)

i. Looking at the graph, do there appear to be any potentially significant main effects? How do you know?

ii. Looking at the graph, do there appear to be any potentially significant interaction effects? How do you know?

D. Analysis of Variance. Conduct the independent multifactorial ANOVA in the following steps.
i. Based on the SPSS output, can we conclude that there are any significant main effects? (Support your results with the appropriate statistical values using the appropriate format).

ii. Are there any significant interaction effects (support your results with the appropriate statistical values using the appropriate format)?

E. Source of the Difference. Conduct appropriate additional analyses to indicate where the differences are (if there were any) for main effects as well as interaction effects. Be sure to justify your response by reporting the statistics in the accepted format.

F. The Results. Write up the results of the analysis. Use the sample from class as a basic model. Be sure to add statements of caution if any of the assumptions were violated.

2. Optional (Bonus – 6 points) (***All other parts of the final must be completed in order to be eligible for bonus points.***)

A group of art students were asked to rate the level of beauty they associated with an art display at various levels of dim light. The goal was for the art department to set the lighting at an optimal level for the upcoming exhibition. Students rated the images on a scale of 0-100 (less beautiful to more beautiful) at 4 levels of dim lighting where level 4 was the dimmest, and level 1 was the brightest. The data is available in the following dataset:

For this exercise, you need to determine if there is a significant difference in the levels of perceived beauty of the art display at the different levels of dim light. No predictions have been made.

a. What would the null and alternative hypotheses be for this situation?

b. You wish to determine if there is a significant difference in the levels of perceived beauty of the art display at the different levels of dim light. No predictions have been made. What statistical test should be used in this case?

c. Testing assumptions. Demonstrate that the statistical test you selected is mainly an appropriate test to use to explore the difference described by addressing all the appropriate assumptions.

d. Use SPSS to conduct the statistical test you selected to explore the difference described. (For the purpose of this exercise, run the test even if the normality for either variable is questionable; include this observation in your result as a caution if normality is a concern). Be sure to report your outcome appropriately. Be sure to describe any significant differences found (i.e., the source of the difference).

3. Optional (Bonus – 6 points): (***All other parts of the final must be completed in order to be eligible for bonus points.***)

A local newspaper reports that the number of violent crimes committed in a region is strongly related to the outdoor air temperature in that region. Sara, a sociologist interested in crime prevention, elects to investigate the relationship. She believes that the relationship between violent crimes and outdoor air temperature may be spurious, and that a third variable, the amount of beer purchased (and presumably drunk), could explain this relationship. She collects data on the number of violent crimes committed, the average daily high temperatures for the month of July in 30 U.S. cities, and the amount of beer purchased (in hundreds of gallons) in the related region. The data is available in the following data set:

a. What is the correlation between amount of beer purchased and violent crimes? Investigate the assumptions and choose the appropriate correlation to address this question. Appropriately discuss the results of the correlation.

b. Conduct a partial correlation between amount of beer purchased and violent crimes, controlling for temperature. Based on the results of the partial correlation, what should Sara conclude about the relationship between the amount of beer purchased and the number of violent crimes committed?

4. Optional (Bonus-12 points) (***All other parts of the final must be completed in order to be eligible for bonus points.***)
Alex is interested in conducting a multiple regression analysis to explore which strength-related predictor variables significantly contribute to the overall injury index level among a group of older women patients. The data related to this investigation are found in the following file:

The following table describes the 5 predictor variables (quads, gluts, abdoms, arms, and grip) and the outcome variable (injury) to be used for this regression analysis (they collected additional data that they will use for other analyses).

a. Exploration of Assumptions. Given the variables as described, address each assumption for multiple linear regression. It is important to remind you that datasets are rarely perfect. This means that violation of some assumptions (especially when there are several) does not always rule out the use of an intended statistical analysis. We should, however, acknowledge assumptions violations when we interpret the results of our analysis. For instance, if we discover potential violations of multi-collinearity, we would appropriately add a statement to our discussion of the results such as: “These results may need to be viewed with some caution, as there was evidence of multi-collinearity between some predictor variables.” As part of your consideration of each assumption, provide the relevant evidence from SPSS to justify your responses. Be sure to discuss each assumption as outlined in the PowerPoint.

b. The Regression Analysis. Run the multiple regression analysis, using ‘injury’ as the outcome variable, and the 5 predictor variables indicated above using the ‘Enter’ method (as we did in class). Be sure to address the three essential considerations for the analysis (How much variance was explained by this model? Was the model significant? Which of the predictors were significant?)

c. The Results. Write up the results of the analysis. Use the sample we discussed in class as a basic model. Be sure to add statements of caution if any of the assumptions were violated.

d. The Model. Using the appropriate beta values, provide the equation for the regression model for this situation.