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Statistics Exercises: ANOVA, Correlation, Chi-square

## Task 1: Effects of Different Study Strategies on College Students' Knowledge

A cognitive psychologist is interested in the effects of different study strategies used by college students. One group of students uses practice tests, one group uses distributed practice, and the third group uses highlighting. When the semester ends, the cognitive psychologist tests each student to obtain a measure of their overall knowledge of the course material. Please show your work to receive full credit.

G = 48

ΣX2 = 272

A. (9 POINTS) Fill in all the missing values in the table below. (HINT: Start with the df column)

B. (2 POINTS) What are the degrees of freedom needed to locate the F critical value?

C. (1 POINT) Using α = 0.05, what is the F critical value?

D. (1 POINT) Based on the results of Parts A through C, would you reject the null hypothesis or fail to reject the null hypothesis?

E. (1 POINT) Compute η2 to determine the percentage of variance accounted for by the treatments.

F. (13 POINTS) Following the steps below, compute Tukey’s HSD, then complete the table below to determine exactly which study methods were significantly different.

1. What is the mean of Practice Tests?

2. What is the mean of Distributed Practice?

3. What is the mean of Highlighting?

4. What is the k (number of treatments) value?

5. What is the df error term (dfwithin) value?3

6. What is the q value of Tukey’s HSD?

7. What is Tukey’s HSD value?

A researcher is interested in the effects on sleep related to the number of hours playing video games (1 hour, 3 hours, or 5 hours) and the time of day (morning or evening). The table below is a summary of results from a two-factor independent-measures ANOVA with 2 levels of factor A (time of day: morning or evening), 3 levels of factor B (hours playing video games: 1 hour, 3 hours, or 5 hours) and n = 8 participants in each treatment condition.

A. (15 POINTS) Fill in all missing values in the table below. (HINT: Start with the df column)

B. (1 POINT) What are the degrees of freedom needed to locate the F critical value for Factor A?

C. (1 POINT) What are the degrees of freedom needed to locate the F critical value for Factor B?

## Task 2: Effects on Sleep Related to Number of Hours Playing Video Games and Time of Day

D. (1 POINT) What are the degrees of freedom needed to locate the F critical value for A x B?

E. (1 POINT) Using α = 0.05, what is the F critical value for Factor A?

F. (1 POINT) Using α = 0.05, what is the F critical value for Factor B?

G. (1 POINT) Using α = 0.05, what is the F critical value for A x B?

H. (1 POINT) Based on the results of Parts A through G, would you reject the null hypothesis or fail to reject the null hypothesis for Factor A?

I. (1 POINT) Based on the results of Parts A through G, would you reject the null hypothesis or fail to reject the null hypothesis for Factor B?5

J. (1 POINT) Based on the results of Parts A through G, would you reject the null hypothesis or fail to reject the null hypothesis for A x B?

K. (3 POINTS) Compute η2 (the percentage of variance accounted for):

1. Main effect of Factor A:

2. Main effect of Factor B:

3. Interaction of A x B:6

A researcher is interested in the relationship between hours practicing parkour (X) and the quantity of Red Bull beverages consumed (Y). Fill in the table below and compute the Pearson correlation for the following data.

A. (20 POINTS) Fill in the table below.

B. (1 POINT) What is the X value?

C. (1 POINT) What is the Y value?

D. (1 POINT) What is the mean of X?

E. (1 POINT) What is the mean of Y?

F. (1 POINT) What is the SSX value?

G. (1 POINT) What is the SSY value?

H. (1 POINT) What is the SP value?

I. (1 POINT) What is the r value?

J. (1 POINT) What are the degrees of freedom needed to locate the Critical value?

K.(1 POINT) Using α = 0.05, what is the critical value?

L. (1 POINT) Based on the results of Parts A through K, would you reject the null hypothesis or fail to reject the null hypothesis?

M. (1 POINT) Based on the results of Parts A through K, calculate the coefficient of determination.

A behavioral psychologist is interested in whether there is a consistent, predictable relationship between diet and cholesterol level. A sample of 200 adults is obtained, and each participant is classified based on diet type (vegetarian or omnivore) and cholesterol level (high or low). The results of the observed frequencies are summarized in the following table:

A. (1 POINT) What are the degrees of freedom needed to locate the "2 critical value?

B. (1 POINT) Using α = 0.05, what is the "2 critical value?

C. (4 POINTS) What are the expected frequencies?

D. (5 POINTS) What is the "2 value?

E. (1 POINT) Based on the results of Parts A through D, would you reject the null hypothesis or fail to reject the null hypothesis?

F. (1 POINT) Compute the phi-coefficient to measure the strength of the relationship.

G. (1 POINT) Is the phi-coefficient a small, medium, or large effect?8

3. (1 EXTRA CREDIT POINT) A hypothesis test involves a comparison of which two elements?

a. research results from a sample and a hypothesis about a population

b. research results from a population and a hypothesis about a sample

c. research results from a population and a hypothesis about the population

d. research results from a sample and a hypothesis about the sample

4.  (1 EXTRA CREDIT POINT) Although the t statistic and the F-ratio have the same general structure, the formulas are based on different measures. What measure does the t statistic use? What measure does the F-ratio use?

5. (1 EXTRA CREDIT POINT) (TRUE/FALSE): When your data has many outliers, it is often the case that correlation will imply a causal relationship between two variables.