Stats 95 Assignment #3 ANOVA 1 Way, Correlation, Chi-Square 1. Draw a scatterplot and compute the Pearson correlation coefficient for the following set of data. Table: Scatterplot X 3 2 1 6 Y 4 5 9 2 2. Is a movie's earnings related to its ratings? Data on the top ten grossing movies in the United States for the weekend of July 13, 2007, were extracted from the Internet Movie Database (IMDB). These data included the weekend earnings and the average rating from users of IMDB. The rating system used by IMDB is a 10-star rating system. The following table shows the data. Using these data, determine whether there is a relation between a movie's earnings and its ratings. Calculate the values by hand (Excel is permitted) and produce an SPSS table of the results. Table: Top Ten Movies Movie Harry Potter and the Order of the Phoenix Transformers Ratatouille Live Free or Die Hard License to Wed 1408 Evan Almighty Knocked Up Sicko Ocean's Thirteen Average Rating 7.9 8.0 8.6 8.0 5.2 7.6 6.0 8.1 8.5 7.3 Page 1 Earnings (in millions) 77.1 37 18 11.3 7.31 4.93 4.9 3.68 2.6 1.98 3. Does the average IQ for residents of a state vary with the amount that the state spends on education? Seven of the 50 U.S. states were randomly selected. The amount that each spent per student (in thousands of dollars) and the average IQ for its residents were recorded. The data appear in the following table. Use SPSS to produce a correlation box along with a scatterplot (no regression line necessary) on the data to calculate the correlation coefficient to determine whether IQ varies with state spending on education. Table: Average IQ by State State Maryland Idaho Florida New Hampshire New York Texas North Dakota Spending per Student 7.25 4.21 5.72 5.86 9.62 5.22 4.78 Average IQ 97.20 99.90 96.10 101.00 97.80 97.20 101.40 4. Research out of the Alameda County Human Population Laboratory has revealed a positive correlation between eating breakfast and longevity, such that those who eat breakfast tend to live longer. State three different hypotheses about the causal relationship creating this correlation, one for each possible causal relationship in the ABC model: AB; BA; CA; and CB. 5. Does a baseball player's salary depend on the position that he plays? The following data depict the 2005 season salaries (in millions of dollars) for players randomly selected from all players in their respective positions in the National Baseball League. Perform the six steps of hypothesis testing on this set of data. Do this by hand. You can use Excel. Table: Baseball Salaries and Positions Pitcher Catcher 0.600 0.650 6.050 3.000 3.000 0.750 0.750 3.133 1.600 0.324 Outfielder 1.350 7.750 0.575 3.100 2.325 Page 2 Shortstop 0.322 8.250 0.445 3.400 0.318 6. Stat 95 SPSS Assignment: Comparing Three Means using One-Way ANOVA and Post-Hoc Tests Using SPSS Scenario: Dr. Olson is interested in the effects of three different methods for losing weight in longdistance truck-drivers. He tested a sample of 60 truck drivers. Participants were randomly assigned to one of three groups of 20 people each. Participants in the Diet-Only group followed a low-calorie diet but did not exercise. Participants in the Exercise-only group followed an exercise regimen but did not change their diet. Participants in the Diet + Exercise group followed both a low-calorie diet and an exercise regimen. Dr. Olson measured the number of pounds each individual lost after 6 months. Diet-Only Group 5 7 10 10 13 6 5 17 13 11 9 10 7 11 14 12 15 17 18 9 Exercise-Only Group 9 10 8 11 3 5 3 10 11 15 9 8 7 14 13 8 6 7 5 12 Questions (Be sure to use complete sentences): a) In this study, what was the independent and dependent variable? Page 3 Diet+Exercise Group 15 18 20 22 16 18 12 25 20 21 10 15 14 22 21 18 17 23 30 26 b) Describe the center of each distribution: What is the mean for each group? c) Describe the variability in each distribution: What is the standard deviation for each group? What does this measure tell us about the dispersion of scores in each group? d) What would the overall null hypothesis state (in everyday language)? e) What would the overall alternative hypothesis state (in everyday language)? f) Were the results of the ANOVA statistically significant? Explain how you arrived at this decision. g) What was the mean difference between each group? What does this value tell us about the effects of each weight-loss condition compared to the other conditions? h) Were the differences between each group statistically significant, as revealed by the post-hoc tests? Explain how you arrived at your decisions. i) Describe eta2 for this study. What does it tell us about the strength of the relationship between the independent and dependent variables? j) Which of the three weight-loss techniques was most effective; which one was least effective? Explain your answers. k) From all of this information, can you conclude that the different weight-loss techniques caused the truck drivers to lose weight? Explain your answer. Based on materials developed by Frank Payne, Ph.D. and Nancy Da Silva, Ph.D.Modified 08/2008 by Sean Laraway, Ph.D. and Mike Abrams, Ph.D. 7. A social psychologist is interested in whether the type of music a college student is listening to will have any effect on the number of beers the student drinks. Fifteen college students were randomly assigned to one of three listening conditions and each student's beer consumption was covertly recorded during trips to three different taverns that played the type of music to which the student was assigned. The data is shown in the following table. List each of the assumptions for performing an ANOVA and for each assumption evaluate whether the described study meets the assumption. Table: Music and Drinking Rock & Roll 4 3 5 3 4 Acid Rock 8 4 6 4 5 Easy Listening 2 4 2 2 3 Page 4 8. Imagine that you have performed a \"beer goggling\" experiment and have randomly assigned 21 participants to drink either 0, 1, or 3 beers, and then had all participants rate the attractiveness of the same fellow college student on a scale from 0 to 50, with higher scores indicating greater perceived attractiveness. Here is the ANOVA source table and the group means. Use this information to answer the following questions. Table: Beer and Attractiveness Source Between Within Total SS 720.096 300.857 1020.950 df 2 18 20 MS 360.048 16.714 F 21.54 Table: Beer and Attractiveness, Group Means Group 0 beer 1 beer 2 beers M 21.5714 26.5714 35.7143 a. Is it appropriate to run a post-hoc analysis for this experiment? Why or why not? 9. A researcher is interested in whether herbal remedies are effective in relieving allergies, and if so, which ones are most effective. The researcher takes a group of 20 allergy sufferers and randomly assigns each one to receive either herbal tea, a homeopathic administration of allergens, a traditional antihistamine, or a placebo pill. The dependent measure is the number of allergy complaints by patients during weeks 2-3 of the treatments. Use SPSS to determine statistical significance and explicitly state your conclusions, and if applicable do a post-hoc analysis and identify which of these conditions differ. Table: Herbal Remedies Herbal Tea 2 4 0 2 3 Homeopathy 3 2 2 1 1 Antihistamine 2 1 0 3 4 Page 5 Placebo 5 3 7 4 8 10. A study by Jackman-Cram, Dobson, and Martin (2006) investigated the communication behavior of married couples during problem-solving discussions. The researchers first classified participant couples according to their level of marital distress (distressed, nondistressed). They then classified the couples on the basis of whether one of the spouses was suffering depression (depressed, nondepressed). All couples were videotaped during problem-solving discussions, and all videotapes were then coded by the researchers using the Marital Interaction Coding System. Among the dependent measures was the proportion of communications that were \"facilitative\" in nature. The following fictional data reproduce the pattern of results obtained for the women partners in the original research. Distressed, Depressed: 0.45, 0.15, 0.22, 0.30, 0.25 Nondistressed, Depressed: 0.60, 0.32, 0.49, 0.39, 0.41 Distressed, Nondepressed: 0.31, 0.18, 0.42, 0.20, 0.17 Nondistressed, Nondepressed: 0.52, 0.45, 0.61, 0.36, 0.42 a. Use SPSS, and determine if there were main effects or interactions. b. Please interpret the graph below in terms of main effects and interactions. Figure: Gender and SciFi Page 6 11. In a 2006 study, Gortmake and colleagues surveyed 80 lesbian and gay students at a large Midwestern state university to assess their experiences and their perceptions of the campus climate regarding lesbians and gays. One of the questions the researchers were interested in was whether a person's \"outness\" depended on his or her class in school. All participants were classified as closeted or as out. The following table depicts the number of students who were closeted or out as a function of their class. Table: Closeted or Out by Class Closeted Out Freshman Sophomore 2 8 7 4 Junior 6 3 Senior 25 7 Grad Student 3 15 a. Perform the appropriate hypothesis test to determine whether a person's \"outness\" depends on his or her class. b. Calculate the appropriate measure of effect size for these data. Is this a small, medium, or large effect? Page 7