ANOVA

1. ANOVA Richard Rivera (aka Rico)

2. ANOVA • In this lesson I will kill two birds with one stone. You’ll be introduced on how to • import excel data files into SPSS • conduct analyses of variance in SPSS

3. Need some Data Files • But first, you need to download an Excel data file. • Open up your internet Explorer • Copy and paste the following two links into the web browser. http://www.west.asu.edu/statlab/downloads/WorkshopExample.xls http://www.west.asu.edu/statlab/downloads/WorkshopExample.sav • Please save them to your Desktop.

4. Two Topics • Prepping an Excel spreadsheet to be imported into SPSS • Types of Analyses of variance (ANOVA).

5. Excel spreadsheet • Each column is indicative of a variable • First row contains the variable names • You want to keep the same rules that apply to variable names in SPSS • The subsequent rows contain the data for each case (subject) • Gender has two levels • Male = 1 • Female = 2 • Age has three levels • < 25 = 1 • 25 - 40 = 2 • > 40 = 3 • Time has three levels • Baseline = time0 • Time 1 = time1 • Time 2 = time2 • Composite scores for “attitude towards research”

6. Excel spreadsheet I sorted the data based on gender and age variables for instructional purposes.

7. Between subjects (aka independent samples) • What are two between-subject factors that have independent samples? • Gender: 2 samples • Age: 3 samples Within subjects (aka related samples) • What is the one within-subject factor that is indicative of three related samples? • Time: 3 samples

8. Importing Excel Data into SPSSStat Lab Staff: you may want to print this slide and follow the SPSS directions below • After formatting the data in Excel • First row contains the variable names • Other rows contain the data values • Save and close Excel file • Open up SPSS • Click on File > Open > Data • Navigate to the location you save the Excel file • In “Files of type:” choose either • Excel (*.xls) • or All files (*.*) • Open the Excel file you saved • You’ll get a dialogue box called: Opening Excel Data Source • There is a green check mark in box: Read variable names from the list from the first row of data • Worksheet: choose the worksheet in which the data is located • Click the OK button. • You just imported an excel file into SPSS

9. Analysis of Variance • One-way ANOVA • One between subjects factor • Example: Age (discrete variable) • Two-way ANOVA • Usually consist of two between subjects factors • Example: Age and Gender • Repeated Measures • One-way within subjects ANOVA • One within subjects factor • Example: Time • Two-way between and within subjects ANOVA • One between subjects factor (e.g., Age) • And one within subject factor (e.g., Time)

10. One-way ANOVA You may want to open the SPSS data file that you downloaded. • Differences among 2 or more independent sample means with SPSS • Analysis of Variance: between subjects factor • Analyze > Compare Means > One-Way ANOVA … • One dependent variable (e.g., baseline, time0) goes into the “Dependent List:” • One between subjects factor (e.g., Age) goes into “Factor:” • If the factor has more than three level, click on Post Hoc… • Click on Tukey and Dunett’s C (unless your instructor wants you to use a different one). • Click on continue • Click on Options • Chose • descriptive Statistics • Homogeneity of variance test • Perhaps on Means plot • Click on continue • Click on OK

11. Descriptive Statistics • The first column contains the three levels of the Age factor. • The mean column contains the mean “attitude toward statistics” • Does it appear that there may be an age effect? • Do you notice a trend? • Which age group has the greatest mean?

12. F-test • The F-test looks tells us if there is an age effect. • Is the F-test significant? • Look at the p value (in column called Sig.) • Is it less than an alpha of .05? • However, the F-test does not tell us which pair of means are significantly different. • We look at the multiple comparisons for that.

13. Multiple Comparisons • Mean difference column was calculated by subtracting the means for age categories in column (j) from means for age categories in column (I). • If there is an asterisk, the mean difference is significant.

14. Two-way ANOVA • Example: two between subjects factors • Analyze > General Linear Model > Univariate… • Dialogue box titled Univariate • Dependent variable: move one dependent variable (e.g., baseline: time0) • Fixed Factor(s): move in the between subjects factors (e.g., Gender and Age).

15. Dialogue box titled Univariate(continued) • Click on Plots • Move one of factors into horizontal axis and the other into separate lines • Click Add • If you wish, you can do the inverse of that, then click add again • Click Continue

16. Dialogue box titled Univariate(continued) • Click on Post Hoc… • Choose only factors that have three or more levels. (e.g., Age). • Click on Tukey and Dunett’s C (unless your instructor wants you to use different ones). • Click on continue

17. Dialogue box titled Univariate(continued) • Click on Option… • Choose Descriptive statistics • Homogeneity tests • Click on continue • Click on OK

18. Repeated Measures • Within Subjects ANOVA example • Analyze > General Linear Model > Repeated Measures… • Dialogue box: Repeated Measures Define Factor(s) • Within-Subject Factor Name: • Change name to: time • Number of levels: 3 levels (i.e., baseline, time0, and time1) • Click on Add • Click on Define

19. Dialogue Box: Repeated Measures • Within-Subjects Variables (time): • Choose the three variables (time0, time1, time2) the insert them in the correct order. • Between-Subjects Factor(s): • Insert the factors that you are interested in. • In this case, enter in Age.

20. Dialogue Box: Repeated Measures(continued) • Click on Plots • I recommend that you move the Time factor into horizontal axis and the other (Age) into separate lines • Click Add • Click Continue

21. Dialogue Box: Repeated Measures(continued) • Click on Post Hoc… • Choose only factor(s) that have three or more levels. (e.g., Age). • Click on Tukey and Dunett’s C (unless your instructor wants you to use different ones). • Click on continue

22. Dialogue Box: Repeated Measures(continued) • Click on Option… • Choose Descriptive statistics • Homogeneity tests • Click on continue • Click on OK

23. Results Coach • In many instances there is a results coach in SPSS for certain types of output. • In the SPSS output, you can right click on a table and choose “results coach” • Results coach, which uses an example from a different data set, will introduce you to some of the concepts in the tables. • Good luck!