EXERCISE #3: ANOVA Test for Independent Samples Invoke the analyze/compare means/One-Way ANOVA sequence to invoke the ANOVA test to complete this exercise. This exercise compares the responses of freshmen, sophomores, juniors, seniors, and graduate students to test for significant differences in the importance placed on several movie theater items. For the ANOVA test, SPSS calls the variable in which means are being computed the independent variable and the variable in which we are grouping responses the factor variable. Be sure to click the options icon and check descriptive so that the output will produce the mean responses by student classification for the sample data. As with the t test, the ANOVA test produces a table of descriptives based on sample data. If our ANOVA test is significant, the descriptives can be used to determine, for example, which student classification places the most importance on comfortable seats. From our sample data, can we generalize our results to the population by saying that there are significant differences across the classification of students by the importance they place on the following movie theater items? Answer: 1. Video arcade at the movie theater (Q5a)? No. .548 2. Soft drinks and food items (Q5b)? 3. Plentiful restrooms (Q5c)? 4. Comfortable chairs (Q5d)? 5. Auditorium-type seating (Q5e)? 6. Size of the movie theater screen (Q5f)? 7. Quality of the sound system (Q5g)? 8. Number of screens at the movie theater (Q5h)? 9. Clean restrooms (Q5i)? 10. Using only descriptive statistics, which classification group (Q13) places the least amount of importance on clean restrooms (Q5i)? Answer: 11. Using only the descriptive statistics, which classification group (Q13) places the greatest amount of importance on quality of sound system (Q5i)? Answer: Summarize the results of your ANOVA analysis using a table similar to the one below: How important is the DF F Sig Interpretation 4, 442 0.766 .548 There are no significant differences between the following when choosing a movie theatre... a) Video Arcade at the Movie Theatre classifications Chapter 18. P. 496498. SPSS exercise 1. (40 points). EXERCISE 1: Multivariate Regression This exercise uses Multivariate Regression to explain and predict how many movies a respondent attends in a month. 1. Go to the Web site for the text and download the Movie database. 2. Open the database in SPSS and view the variables under Variable View. We will be using the independent variables Q2, Q4, Q6, Q8a, Q8b, Q9, Q10, Q12, and Q13 to predict the dependent variable Q3. We are including the variables Q4 and Q6 as is. Strictly speaking, is this proper? What might you want to do instead and why? Why might you decide to leave the variable in bins instead? Would it ever be proper to use a variable like Q11 as is? Answer (provided already, you don't need to answer this question): Q4 and Q6 are ordinal scaled, whereas regression requires metric scaled predictors. The appropriate method would be to create three dummy variables for Q4 (it has four categories) and four dummy variables for Q6 (it has 5 categories). Q11 is nominally scaled. It would not be useful to try to apply numerical analysis to nominal data beyond a simple frequency analysis. Q4 has four categories, so you can create three dummy variables. Category / value Never buy food items at movies Up to $7.49 X1 0 X2 0 X3 0 1 0 0 $7.50 to $14.99 $15.00 or more 0 0 1 0 0 1 Q6 has five categories, so you can create four dummy variables. Category / value Zero X1 0 X2 0 X3 0 X4 0 1 to 9 miles 1 0 0 0 11 to 24 miles 0 1 0 0 25 to 49 Miles 50+ miles 0 0 0 0 1 0 0 1 The data from question 11 is nominal. The categories are assigned arbitrary values, so the data is not useful for regression or many other types of quantitative analysis. 3. Go to analyze/descriptive statistics/descriptives and move Q3, Q2, Q4, Q6, Q8a, Q8b, Q8c, Q8d, Q9, Q10, Q12, and Q13 to the Variable(s) box and click OK. Multivariate techniques require that every variable have a legitimate value. If a respondent did not answer every question, then the analyst must either ignore the observation entirely or impute estimates for the missing values. The default for statistical software is to ignore those observations automatically. We will not do imputation for this exercise. a. What will be the sample size for later multivariate techniques? Descriptive Statistics N (Q3)On average, about how many Minimum Maximum Mean Std. Deviation 448 .0 12.0 1.576 1.2519 448 1 4 2.25 .803 449 0 3 .94 .748 448 0 4 2.47 .821 446 0 95 7.11 16.177 446 0 100 82.08 23.727 446 0 100 10.06 17.167 movies do you attend at a movie theatre each month? (Q2)Indicate how important you consider going to the movies at a movie theatre, relative to other leisure activities. (Q4)Not including the cost of the movie ticket, about how much do you spend on popcorn, candy, softdrinks, etc. at a movie? (Q6)If your community did not have a "big screen" theatre, how much further would you drive beyond the cinema nearest to you to see a movie at a "big screen" theatre? (Q8a)Of all the movie tickets that you have ever purchased, what percentage were purchased: Via the Internet (Q8b)Of all the movie tickets that you have ever purchased, what percentage were purchased: At the theatre right before the movie started (Q8c)Of all the movie tickets that you have ever purchased, what percentage were purchased: At the theatre, but the movie played at a later time (Q8d)Of all the movie tickets that you 446 0 30 .75 3.709 498 1 4 3.21 .723 500 1 4 3.26 .749 (Q12)Gender: 500 0 1 .54 .499 (Q13)Classification: 500 1 5 3.10 1.239 Valid N (listwise) 442 have ever purchased, what percentage were purchased: Using some other purchase option (Q9)How physically active do you consider yourself? (Q10)How Socially active do you consider yourself? Answer: 442 (answer provided) b. Is this sample size large enough for multivariate regression? Answer: c. What would some possible problems be if the sample size were not large enough? Answer: d. Are the minimum and maximum values for each variable within the proper range? Answer (provided): Yes. A value that is out of range would indicate either a data input error or a user-defined missing value like \"Refused\" or \"Don't Know.\" Data input errors should be corrected or deleted. User-defined missing values should be declared in SPSS. e. Are all the variables within the proper range? Answer: 4. Go to analyze/regression/linear. Move Q3 to Dependent Move Q2, Q4, Q6, Q8a, Q8b, Q8c, Q8d, Q9, Q10, Q12, and Q13 to Independent(s). Change Method to Stepwise Click OK a. Which independent variables did the stepwise regression select? Why not the rest? Answer: b. Is each variable chosen significant? Answer: c. Are the variables that have not been chosen necessarily insignificant? Answer: d. Is the model significant? Answer: you need to provide the necessary output and highlight the key number. e. Does this method guarantee that you will get the \"best\" model? Answer: 5. Go to analyze/descriptive statistics/descriptives and remove Q6, Q8a, Q8b, Q8c, Q8d, Q9, Q10, and Q12 from the Variable(s) box, so that only Q3, Q2, Q4, and Q13 remain in the box and then click OK. What is the sample size now? Answer: 6. Go to analyze/regression/linear Move Q3 to Dependent Remove Q6, Q8a, Q8b, Q8c, Q8d, Q9, Q10, and Q12 from Independent(s) so that only Q2, Q4, and Q13 remain. Change Method to Enter Click OK Answer: You need to present the ANOVA table and coefficients table. a. How and why does this model differ from the model based on stepwise regression? Answer: b. Which model is better? Answer: INTERPRETATION 1. How does stated importance affect the number of times one attends movies? Answer: 2. How does spending money on snacks affect the number of times one attends movies? Answer: 3. How does student classification affect the number of times one attends movies? Answer: 4. If a sophomore thought that going to movies was somewhat important and typically spent $12 on snacks, how many times per month would he or she attend movies based on this model? Answer: using the following formula to calculate Y (i.e., Q3). The final answer should be 4.79. Y = a + b1X1 + b2X2 + b3X3 + . . . bnXn 5. Do any of the variables, according to the results, appear to have an effect on the number of times one attends movies, or does it seem that other factors not covered in this survey are driving movie attendance? Answer: SPSS exercise 2. (40 points). EXERCISE #2: Factor Analysis This exercise used Factor Analysis to explore how survey respondents consider various aspects of a theater visit. 1. Go to the Website for the text and download the Movie database. 2. Open the database in SPSS and view the variables under Variable View. Notice that question 5 has 9 importance rating items. (Q5a)Movie Items: How important in your selection of a movie theatre is: video arcade at the Movie Theatre (Q5b)Movie Items: How important in your selection of a movie theatre is: Soft drinks and food (Q5c)Movie Items: How important in your selection of a movie theatre is: Plentiful restrooms (Q5d)Movie Items: How important in your selection of a movie theatre is: Comfortable chairs (Q5e)Movie Items: How important in your selection of a movie theatre is: Auditorium type seating (Q5f)Movie Items: How important in your selection of a movie theatre is: Size of screen(s) (Q5g)Movie Items: How important in your selection of a movie theatre is: Quality of sound system (Q5h)Movie Items: How important in your selection of a movie theatre is: Number of screens available (Q5i)Movie Items: How important in your selection of a movie theatre is: Clean restrooms 3. Go to analyze/descriptive statistics/descriptives and move Q5a to Q5i to the Variable(s) box and click OK. a. Which item is the most important? Answer: b. Which item is the least important? Answer: Multivariate techniques require that every variable have a legitimate value. If a respondent did not answer every question, then the analyst must either ignore the observation entirely or impute estimates for the missing values. The default for statistical software is to ignore those observations automatically. We will not get involved with imputation for this exercise. a. What will the sample size be for later multivariate techniques? Answer: b. Is this sample size large enough for factor analysis? Answer: c. What would some possible problems be if the sample size were not large enough? Answer: d. It is a good idea to check that the minimum and maximum values for each variable are within the proper range. A value that is out of range indicates either a data input error or a user-defined missing value such as \"Refused\" or \"Don't Know.\" Data input errors should be corrected or deleted. User-defined missing values should be declared in SPSS. e. Are all the variables within the proper range? Answer: 4. Go to analyze/descriptive statistics/descriptives and move Q5a and Q5i to the Variable(s) box and click OK. Examine the resulting correlations matrix a. Other than the 1's down the main diagonal of the matrix, what is the highest correlation in absolute value? Answer: b. Does any variable \"just not fit\" with the others? Answer: c. Does multicollinearity appear to exist among some of the items? Answer: 5. Go to analyze/dimension reduction/factor. Move Q5a through Q5i to the Variables box. Click the Rotation button, place a check in front of \"Varimax,\" and click Continue. Click the Options button. Place a check in front of \"Sorted by size.\" Place a check in front of \"Suppress absolute values less than\" and set the value after it to .25. Click Continue. Click OK. SPSS produces a lot of output Factor Analysis. It is possible to create much more output than we have generated here by setting various subcommands and options. a. How many factors did SPSS create? Answer: b. Why did it stop at that number? Answer: c. How could you change the defaults to create a different number of factors? Answer d. Go to the output entitled Total Variance Explained. How much variance was explained in this Factor Analysis? Answer (provided): Total Variance Explained Component Initial Eigenvalues Total % of Variance Extraction Sums of Squared Loadings Cumulative % Total % of Variance Cumulative % Rotation Sums of Squared Loadings Total % of Variance Cumulative % 1 4.103 45.590 45.590 4.103 45.590 45.590 3.409 37.878 37.878 2 1.222 13.581 59.171 1.222 13.581 59.171 1.891 21.015 58.893 3 1.002 11.132 70.304 1.002 11.132 70.304 1.027 11.411 70.304 4 .666 7.400 77.704 5 .629 6.987 84.691 6 .471 5.238 89.929 7 .400 4.449 94.377 8 .320 3.560 97.937 9 .186 2.063 100.000 Extraction Method: Principal Component Analysis. Factor 1 explains 45.6% of the variance, Factor 2 explains an additional 13.6%, and Factor 3 explains an additional 11.1%, for a total of 70.3%. e. Go to the output entitled Rotated Component Matrix. Why are some of the elements in this matrix blank? Answer (provided): We instructed SPSS to suppress values (loadings) smaller than .25. Rotated Component Matrixa Component 1 (Q5f)Movie Items: How important in 2 3 .864 your selection of a movie theatre is: Size of screen(s) (Q5g)Movie Items: How important in .861 your selection of a movie theatre is: Quality of sound system (Q5e)Movie Items: How important in .829 your selection of a movie theatre is: Auditorium type seating (Q5d)Movie Items: How important in .741 .350 your selection of a movie theatre is: Comfortable chairs (Q5h)Movie Items: How important in .651 your selection of a movie theatre is: Number of screens available (Q5c)Movie Items: How important in .829 your selection of a movie theatre is: Plentiful restrooms (Q5b)Movie Items: How important in .787 your selection of a movie theatre is: Soft drinks and food (Q5i)Movie Items: How important in your selection of a movie theatre is: Clean restrooms .442 .610 (Q5a)Movie Items: How important in your selection of a movie theatre is: video arcade at the Movie Theatre Extraction Method: Principal Component Analysis. Rotation Method: Varimax with Kaiser Normalization. a. Rotation converged in 4 iterations. f. Do the components or factors make sense? Answer (provided): Yes. .954