# IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA

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1 CALIFORNIA STATE UNIVERSITY, LOS ANGELES INFORMATION TECHNOLOGY SERVICES IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA Summer 2013, Version 2.0 Table of Contents Introduction...2 Downloading the Data Files...2 Chi-Square...2 Chi-Square Test for Goodness-of-Fit...2 With Fixed Expected Values...2 With Fixed Expected Values and within a Contiguous Subset of Values...4 With Customized Expected Values...5 One-Way Analysis of Variance...7 Post Hoc Tests...9 Two-Way Analysis of Variance...11 Importing and Exporting Data...14 Using Scripting for Redundant Statistical Analyses...17 For additional handouts, visit For video tutorials, visit

3 H 0 : Patients leave the hospital at a constant rate (there is no difference between the discharge rates for each day of the week). H 1 : Patients do not leave the hospital at a constant rate. To perform the analysis: 1. Start IBM SPSS Statistics Click the Open button on the Data Editor toolbar. The Open Data dialog box opens. 3. Navigate to the Data Files folder, select the Chi-hospital.sav file, and then click the Open button. The observed values must be declared before running the Chi-Square test. To declare the observed values: 1. Click the Data menu, and then click Weight Cases. The Weight Cases dialog box opens (see Figure 1). 2. Select the Weight cases by option. 3. Select the Average Daily Discharges [discharge] variable in the box on the left, and then click the transfer arrow button to move it to the Frequency Variable box. 4. Click the OK button. Figure 1 Weight Cases Dialog Box To perform the analysis: 1. Click the Analyze menu, point to Nonparametric Tests, point to Legacy Dialogs, and then click Chi-square. The Chisquare Test dialog box opens. 2. Select the Day of the Week [dow] variable and move it to the Test Variable List box (see Figure 2). 3. Click the OK button. The Output Viewer window opens (see Figure 3). Figure 2 Chi-square Test Dialog Box IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 3

4 Figure 3 Chi-Square Frequencies Output Table Figure 4 Chi-Square Test Statistics Output Table Reporting the analysis results: H 0 : Rejected in favor of H 1. H 1 : Patients do not leave the hospital at a constant rate. Explanation: Figure 4 indicates that the calculated χ 2 statistic, for 6 degrees of freedom, is Additionally, it indicates that the significance value (0.000) is less than the usual threshold value of This suggests that the null hypothesis, H 0 (patients leave the hospital at a constant rate), can be rejected in favor of the alternate hypothesis, H 1 (patients leave the hospital at different rates during the week). With Fixed Expected Values and within a Contiguous Subset of Values By default, the Chi-Square test procedure builds frequencies and calculates an expected value based on all valid values of the test variable in the data file. However, it may be desirable to restrict the test s range to a contiguous subset of the available values, such as weekdays only (Monday through Friday). Research Question # 2 The hospital requests a follow-up analysis. Can staff be scheduled assuming that patients discharged on weekdays only (Monday through Friday) leave at a constant daily rate? H 0 : Patients discharged on weekdays only (Monday through Friday) leave at a constant daily rate. H 1 : Patients discharged on weekdays only (Monday through Friday) do not leave at a constant daily rate. IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 4

5 To run the analysis: 1. Click the Analyze menu, point to Nonparametric Tests, point to Legacy Dialogs, and then click Chi-square. The Chi-square Test dialog box opens. 2. Select the Use specified range option in the Expected Range section (see Figure 2). 3. Type 2 in the Lower box and 6 in the Upper box. 4. Click the OK button. The Output Viewer window opens (see Figure 5 and Figure 6). Notice that the test range is restricted to Monday through Friday. Figure 6 Test Statistics Output Table Figure 5 Chi-Square (Subset) Frequencies Output Table NOTE: The expected values are equal to the sum of the observed values divided by the number of rows, while the observed values are the actual number of patients discharged. Reporting the analysis results: H 0 : Do not reject. Patients discharged on weekdays only (Monday through Friday) leave at a constant daily rate. Explanation: Figure 5 indicates that, on average, 92 patients were discharged from the hospital each weekday. The rate for Mondays was below average and the rate for Fridays was above average. Figure 6 indicates that the calculated value of the Chi-Square statistic was at 4 degrees of freedom. Because the significance level (0.213) is greater than the rejection threshold of 0.05, H 0 (patients were discharged at a constant rate on weekdays) could not be rejected. Using the Chi-Square test procedure, the hospital determined that the patient discharge rate was not constant over the course of an average week. This was primarily due to more discharges on Fridays and fewer discharges on Sundays. When the test s range was restricted to weekdays, the discharge rates appeared to be more uniform. Staff shortages could be corrected by adopting separate weekday and weekend staff schedules. With Customized Expected Values Research Question # 3 Does first-class mailing provide quicker response time than bulk mail? A manufacturing company tries first-class postage for direct mailings, hoping for faster responses than with bulk mail. Order takers record how many weeks each order takes after mailing. H 0 : First-class and bulk mailings do not result in different customer response times. H 1 : First-class and bulk mailings result in different customer response times. IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 5

6 Before the Chi-Square test is run, the cases must be weighted. Because this example compares two different methods, one method must be selected to provide the expected values for the test and the other will provide the observed values. To weight the cases: 1. Open the Chi-mail.sav file. 2. Click the Data menu, and then click Weight Cases. The Weight Cases dialog box opens. 3. Select the Weight cases by option. 4. Select the First Class Mail [fcmail] variable and move it to the Frequency Variable box. 5. Click the OK button. To run the analysis: 1. Click the Analyze menu, point to Nonparametric Tests, point to Legacy Dialogs, and then click Chi-square. The Chi-square Test dialog box opens. 2. Select the Week of Response [week] variable and move it to the Test Variable List box. 3. Select the Values option in the Expected Values section. 4. Type 6 in the Values box, and then click the Add button. 5. Repeat step 4, adding the values 15.1, 18, 12, 11.5, 9.8, 7, 6.1, 5.5, 3.9, 2.1, and 2 (in that order). 6. Click the OK button. The Output Viewer window opens. NOTE: The expected frequencies in this example are the response percentages that the firm has historically obtained with bulk mail. Figure 8 Week of Response Test Statistics Figure 7 First-Class/Bulk Mail Week of Response Reporting the analysis results: H 0 : Do not reject. There was no statistical difference between customer response times using first-class mailing and customer response times using bulk mailing. Explanation: The manufacturing company hoped that first-class mail would result in quicker customer response. As indicated in Figure 7, the first two weeks indicated different response times of four and seven percentage points, respectively. The question was whether the overall differences between the two distributions were statistically significant. IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 6

7 The Chi-Square statistic was calculated to be at 11 degrees of freedom (see Figure 8). The significance value (p) associated with the data was 0.345, which was greater than the threshold value of Hence, H 0 was not rejected because there was no significant difference between first-class and bulk mailings. The first-class mail promotion did not result in response times that were statistically different from standard bulk mail. Therefore, bulk postage was more economical for direct mailings. One-Way Analysis of Variance One-way analysis of variance (One-Way ANOVA) procedures produce an analysis for a quantitative dependent variable affected by a single factor (independent variable). Analysis of variance is used to test the hypothesis that several means are equal. This technique is an extension of the two-sample t test. Think of it as a generalization of the pooled t test. Instead of two populations (as in the case of a t test), there are more than two populations or treatments. Research Question # 4 Which of the alloys tested would be appropriate for creating an underwater sensor array? To find the best alloy for an underwater sensor array, four different types are tested for resistance to corrosion. Five plates of each alloy are submerged for 60 days after which the number of corrosive pits on each plate is measured. H 0 : The four alloys exhibit the same kind of behavior and are not different from one another. H 1 : The four alloys exhibit different kind of behaviors and are different from one another. To run One-Way ANOVA: 1. Open the Alloy.sav file. NOTE: Each case within the One-Way ANOVA data file represents one of the 20 metal plates (5 plates of 4 different alloys) and is characterized by 2 variables. One variable assigns a numeric value to the alloy. The other variable is used to quantify the number of pits on the plate after being underwater for 60 days (see Figure 9). Figure 9 Alloy Data File 2. In Data View, click the Analyze menu, point to Compare Means, and then click One- Way ANOVA. The One-Way ANOVA dialog box opens. 3. Select the pits variable in the box on the left and move it to the Dependent List box. 4. Select the Alloy [alloy] variable in the box on the left and move it to the Factor box (see Figure 10). IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 7

8 Figure 10 One-Way ANOVA Dialog Box 5. Click the Options button. The One-Way ANOVA: Options dialog box opens. 6. Select the Descriptive, Homogeneity of variance test, and Means plot check boxes (see Figure 11). 7. Click the Continue button. Figure 11 One-Way ANOVA: Options Dialog Box 8. Click the OK button. The Output Viewer window opens. Figure 12 ANOVA Descriptive Output Figure 13 Output for Test of Homogeneity of Variances IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 8

9 Figure 14 ANOVA Output Reporting the analysis results: H 0 : Reject in favor of H 1. H 1 : The four alloys do not exhibit the same kind of behavior. They are statistically different from one another. Explanation: Figure 12 lists the means, standard deviations, and individual sample sizes of each alloy. Figure 13 provides the degrees of freedom and the significance level of the population; df1 is one less than the number of sample alloys (4-1=3), and df2 is the difference between the total sample size and the number of sample alloys (20-4=16). Figure 14 lists the sum of the squares of the differences between means of different alloy populations and their mean square errors. In Figure 14, the Between Groups variation is due to interaction in samples between groups. If sample means are close to each other, this value is small. The Within Groups variation is due to differences within individual samples. The Mean Square values are calculated by dividing each Sum of Squares value by its respective degree of freedom (df). The table also lists the F statistic , which is calculated by dividing the Between Groups Mean Square by the Within Groups Mean Square. The significance level of is less than the threshold value of 0.05 indicating that the null hypothesis can be rejected. In conclusion, the alloys are not all the same. Post Hoc Tests In ANOVA, if the null hypothesis is rejected, then it is concluded that there are differences between the means (μ 1, μ 2,, μ a ). It is useful to know specifically where these differences exist. Post hoc testing identifies these differences. Multiple comparison procedures look at all possible pairs of means and determine if each individual pairing is the same or statistically different. In an ANOVA with α treatments, there will be α*(α-1)/2 possible unique pairings, which could mean a large number of comparisons. Research Question # 5 Is the mean difference between alloy sets statistically significant? The rejection of the previous null hypothesis leads to the conclusion that all the alloys do not exhibit the same behavior. The next part of the analysis determines if the mean difference between individual alloy sets is statistically significant. H 0 : μ 0 = μ 1 = μ a H 1 : μ 0 μ 1 μ a To run post hoc tests: 1. In Data View, click the Analyze menu, point to Compare Means, and then click One- Way ANOVA. The One-Way ANOVA dialog box opens (see Figure 15). IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 9

10 Figure 15 One-Way ANOVA Dialog Box 2. Click the Post Hoc button. The One-Way ANOVA: Post Hoc Multiple Comparisons dialog box opens. 3. Select the LSD check box (see Figure 16). 4. Click the Continue button, and then click the OK button. The Output Viewer window opens. NOTE: LSD stands for List Significant Difference, which compares the means one by one. Figure 16 One-Way ANOVA: Post Hoc Multiple Comparisons Dialog Box Figure 17 Multiple Comparisons Output IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 10

11 Reporting the analysis results: H 0 : Reject in favor of H 1. H 1 : At least one of the means is different. Figure 18 Means Plot Explanation: Figure 17 shows the results of comparing pairs of means between different alloy sets. Each row indicates the difference between the two corresponding treatments. Alloys 1 and 4 have a mean difference of 2.4 (a relatively small value). Also, the significance level of indicates that the null hypothesis cannot be rejected for the comparison of alloys 1 and 4. There is no statistically significant difference between them. Alloy pairs 1 and 2, 1 and 3, 2 and 3, 2 and 4, and 3 and 4 have large mean differences with significance values of In these cases, the null hypothesis can be rejected, leading to the conclusion that they are statistically different. Also, the means plot (see Figure 18) shows that alloys 1 and 4 have average mean values of pits very close to each other. Because alloys 1 and 4 have the lowest mean number of corrosive pits, they are the best choices for the array. Depending on the relative costs of the two alloys, the one that is more cost effective can be chosen. Two-Way Analysis of Variance Two-way analysis of variance (Two-Way ANOVA) is an extension of the one-way analysis of variance. With Two-Way ANOVA, two or more independent variables can be tested instead of just one. Using multiple variables has two advantages: increased efficiency and an increase in the result s statistical power. Research Question # 6 Will test anxiety and different teachers affect student test scores? To answer the question, two classes were given a cumulative standardized test. Before the test, students were asked about the level of anxiety they were feeling: none, some and lots. The experiment compared two different classes taught by teachers A and B using the same test. After evaluating the standardized test, each group s mean score was examined. H 0 : Test anxiety and teacher do not affect student test scores. H 1 : Test anxiety and teacher do affect student test scores. IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 11

12 To run Two-Way ANOVA: 1. Open the Two-Way-ANOVA.sav file (see Figure 19). Figure 19 Two-Way ANOVA Data File 2. In Data View, click the Analyze menu, point to General Linear Model, and then click Univariate (see Figure 20). The Univariate dialog box opens. 3. Select the SCORE variable in the box on the left and move it to the Dependent Variable box. 4. Select the ANXIETY and TEACHER variables in the box on the left and move them to the Fixed Factor(s) box (see Figure 21). Figure 20 Analyze Menu When Selecting Univariate Figure 21 Univariate Dialog Box 5. Click the Options button. The Univariate: Options dialog box opens. 6. Select the Descriptive statistics check box, and then click the Continue button (see Figure 22). 7. Click the OK button. The Output Viewer window opens (see Figure 23 and Figure 24). IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 12

13 Figure 22 Univariate: Options Dialog Box Figure 23 ANOVA Descriptive Output Table Figure 24 Output Table for Tests of Between-Subjects Effects IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 13

14 Reporting the analysis results: H 0 : Reject in favor of H 1 for Anxiety and the interaction between Anxiety and Teacher (Anxiety*Teacher). H 1 : Testing anxiety and teacher affect student test scores. Explanation: Figure 23 lists the means and standard deviations from three anxieties in two classes. Students who have some testing anxiety and are in Teacher B s class have the highest mean score (mean=36.67). Because the significance value of the Teacher variable (0.901) is more than the threshold value (0.05) as indicated in Figure 24, it can be concluded that the Teacher factor alone does not affect test scores. The significance values of the Testing Anxiety variable (0.033) and the interaction between the two factors Anxiety*Teacher (0.047) are less than the threshold value (0.05), leading to the conclusion that both Testing Anxiety alone and the combination of Testing Anxiety and Teacher (Anxiety*Teacher) do affect student test scores. Importing and Exporting Data SPSS Statistics can be used to analyze data in a Microsoft Excel spreadsheet. SPSS Statistics provides the ability to import an Excel spreadsheet directly into the Data Editor window and automatically create variables based on the spreadsheet s column headings. Data can also be exported from SPSS Statistics into Microsoft Excel and PowerPoint. To import an Excel spreadsheet into SPSS Statistics: 1. Click the Open button on the Data Editor toolbar. The Open Data dialog box opens. 2. Click the Files of type arrow and select Excel (*.xls, *.xlsx, *.xlsm) from the list. 3. Select the demo.xls file, and then click the Open button (see Figure 25). The Opening Excel Data Source dialog box opens (see Figure 26). NOTE: If the Excel file contains multiple worksheets, select the desired worksheet by clicking the Worksheet arrow (see Figure 26). To import a specific range of cells, specify the range in the Range box. Figure 26 Opening Excel Data Source Dialog Box Figure 25 Open Data Dialog Box 4. Click the OK button. SPSS Statistics processes and reads the Excel file and converts all first row column headings into variables using the best approximation for the variable attributes (see Figure 27 and Figure 28). IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 14

15 Figure 27 Excel File Figure 28 Excel File Imported into SPSS Statistics The reverse situation may also arise, where data in an SPSS Statistics file must be analyzed using Excel. This can be accomplished by exporting the contents of the Data Editor window into an Excel spreadsheet. To export SPSS Statistics data into an Excel spreadsheet: 1. In the Data Editor window, click the File menu, and then click Save As. The Save Data As dialog box opens. 2. Click the Save as type arrow and select Excel 97 through 2003 (*.xls) or Excel 2007 through 2010 (*.xlsx) from the list (see Figure 29). NOTE: Selecting the Write variable names to spreadsheet check box will cause SPSS Statistics to write the variable names as column headings in the spreadsheet. IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 15

16 NOTE: If only certain variables from the Data Editor window are desired in the spreadsheet, users can click the Variables button and select or deselect variables in the Save Data As: Variables dialog box (see Figure 30). Figure 29 Save Data As Dialog Box Figure 30 Save Data As: Variables Dialog Box 3. Click the Look in arrow and select a location to save the file. 4. Type a name for the Excel file in the File name box. 5. Click the Save button. The Output Viewer window opens with a report summarizing the details and results of the export operation (see Figure 31). Figure 31 SPSS Statistics Export Output Report To export an SPSS Statistics Output chart into a PowerPoint slide: 1. In the Output Viewer window, click to select the table. A box appears around the table and a red arrow to the left of it. 2. Click the File menu, and then click Export. The Export Output dialog box opens. 3. Click the Type arrow and select PowerPoint (*.ppt) from the list (see Figure 32). 4. Click the Browse button. The Save File dialog box opens. 5. Click the Look in arrow and select a location to save the file. 6. Type a name for the PowerPoint file in the File name box (see Figure 33). 7. Click the Save button. 8. Click the OK button. IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 16

17 Figure 32 Export Output Dialog Box Figure 33 Save File Dialog Box Using Scripting for Redundant Statistical Analyses Every statistical analysis used by SPSS Statistics is executed through a special programming language. The code used for each analysis can be captured, stored as a script file, and edited if necessary. A series of scripts in a script file can be run either individually or all at once. Scripting automates a series of statistical analyses that are performed on a file that always has the same variables, but contains data that changes. Scripts are captured and edited in the IBM SPSS Statistics Syntax Editor window. IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 17

18 The following example illustrates the benefits of capturing, storing and running scripts. The sample data is taken from a classroom setting for a weeklong course. At the end of each week, each student s data is compiled. The variables in the set include the subject name, gender, pretest scores, posttest scores, grade point average, computer ownership, and method of administering examinations. Each week, a report is generated that answers a series of questions about the class from the previous week. The questions answered and the statistical analyses used are the same every week, as described in Table 1. Table 1 Scripted Questions and Statistical Techniques Question Does the data set include equal numbers of each gender and each test method? Is there a difference between the male and female pretest scores? Is there a difference between the male and female posttest scores? Is there a difference between the overall pretest and posttest scores? Do gender, computer ownership, and test method affect test scores? Do gender, computer ownership, and test method affect test scores differently depending on gender? Is there a linear relationship between the pretest and posttest scores for each gender? Can pretest scores predict posttest scores for each gender? Is there an overall linear relationship between pretest and posttest scores? Can pretest scores predict posttest scores? Statistical Technique(s) to Answer Question Split the file Crosstabs Select all cases Independent-Samples T Test Independent-Samples T Test Paired-Samples T Test Three-Way ANOVA Split the file Two-Way ANOVA Scatter plot graph with file split Simple regression with file split Select all cases Scatter plot graph Simple regression To construct a script file that will automatically run the analyses: 1. Open the ClassData.sav file. 2. Click the Edit menu, and then click Options. The Options dialog box opens. 3. Click the Viewer tab, select the Display commands in the log check box, click the Apply button, and then click the OK button (see Figure 34). NOTE: The script file is built by performing each statistical analysis in the desired order. All analyses must be performed manually one time while the file is being built. In this example, the file will first be split before creating a crosstabs table. 4. Click the Data menu, and then click Split File. The Split File dialog box opens. 5. Select the Compare groups option, and then move the gender variable to the Groups Based on box. 6. Click the Paste button to add the command to the script file. The Split File dialog box closes and the IBM SPSS Statistics Syntax Editor window opens with the pasted command displayed (see Figure 35). 7. In the IBM SPSS Statistics Data Editor window, click the Analyze menu, point to Descriptive Statistics, and then click Crosstabs. The Crosstabs dialog box opens. IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 18

19 Figure 35 IBM SPSS Statistics Syntax Editor Window Figure 34 Options Dialog Box 8. Move the gender variable to the Row(s) box and the method variable to the Column(s) box. 9. Click the Paste button. The Crosstabs dialog box closes and the command is pasted in the IBM SPSS Statistics Syntax Editor window (see Figure 36). The first question in Table 1 has been entered into the script file. NOTE: Scripts for each of the remaining analytical techniques can be entered into the script file by choosing the desired parameters in each dialog box, and then clicking the Paste button. Figure 36 IBM SPSS Statistics Syntax Editor Window Figure 37 Save Syntax As Dialog Box 10. To save the script file, click the File menu in the IBM SPSS Statistic Syntax Editor window, and then click Save As. The Save Syntax As dialog box opens (see Figure 37). 11. Select a location to save the file, enter a file name, and then click the Save button. SPSS Statistics script files have the.sps file extension. The program provides several options for running script files. The Run menu of the IBM SPSS Statistic Syntax Editor window contains commands for All, Selection, and To End (see Figure 39). IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 19

20 To run an existing script file: 1. In the Data Editor window, click the File menu, point to Open, and then click Syntax (see Figure 38). The Open Syntax dialog box opens. 2. Locate and select the WeeklyAnalysis.sps syntax file, and then click the Open button. The IBM SPSS Statistics Syntax Editor window opens with the script displayed. 3. In the IBM SPSS Statistics Syntax Editor window, click the Run menu, and then click All (see Figure 39). Every command in the script file is executed and the results are displayed in the Output Viewer window. NOTE: If the Display commands in the log check box on the Viewer tab of the Options dialog box remains selected, individual script commands will appear with the output in the Output Viewer window. Figure 38 File Menu When Selecting Syntax Figure 39 Run (Syntax) Menu IBM SPSS Statistics 20 Part 4: Chi-Square and ANOVA 20

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