Chapter 8 SPSS Analysis of RB-4 Design

Chapter 8 SPSS Analysis of RB-4 Design

Data from Table 8.2-1

Exploratory Data Analysis With SPSS

Prior to performing an analysis of variance, an exploratory data analysis should be performed. The exploratory data analysis may uncover data recording errors, ANOVA assumptions that appear untenable, and unexpected promising lines of investigation. The reading-error data for the four altimeters in Table 8.2-1 of Experimental Design: Procedures for the Behavioral Sciences (page 289) are used to illustrate the procedures for a randomized block design. Treatment A is four kinds of altimeters. The blocks represent different amounts of flying experience of eight helicopter pilots. The dependent variable is the number of reading errors. The data are as follows.

Table 8.2-1. Reading Error Data for Four Altimeters

Treatment Levels

a1 a2 a3 a4

s1

3

4

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3 s2 2 4 4 5 s3 2 3 3 6 s4 3 3 3 5 s5 1 2 4 7 s6 3 3 6 6 s7 4 4 5 10 s8 6 5 5 8

1. Double click on the SPSS icon to open SPSS. This action opens the window shown below that ask, What would you like to do?

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2. Select the Type in data button and then the OK button in the lower right corner.

Type in data OK

This action opens the SPSS Statistics Data Editor window shown next. At the bottom lower left of the window are two rectangular buttons: Data View and Variable View. The Data View button is highlighted, which means that the window for entering new data is open. Before entering new data, the names and details of the variables in the new data set should be defined.

3. Click on the Variable View button to open the following SPSS Statistics Data Editor Variable View window where the characteristics of the data are defined.

You can go directly to the Variable View window by clicking on the Cancel button in the lower right corner of the first window instead of the OK button.

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3 4. Use row one of the Variable View window to describe the characteristics of the pilot variable. Use rows

2–5 to describe the characteristics of the altimeter variable. For the data in Table 8.2-1, fill in the columns of row 1 as follows:

Columns 1. Name. Name the variable Pilots. A variable name can have no more than 64 characters. The first character must be an upper or lower case letter; the remaining characters can be any letter, digit, or the symbols @, #, _, or $. No spaces can appear in the name. Also, variable names cannot end with a period. Information in row 1 is optional. The inclusion of the Pilots variable in row 1 helps to organize the data in the Data View window.

Column 2. Type. This column enables you to define the variable type. The default type is Numeric for number. You can change the variable type by clicking on the Type cell. This action opens the Variable Type window where you can select from nine variable types including Scientific notation, Date, Custom currency, String, and Text. If you have changed the default, you need to click on the OK button at the bottom of the Variable Type window to return to the Variable View window.

Column 3. Width. This column enables you to define the number of characters that are shown for a variable in the SPSS Statistics Data Editor. The default is 8 characters. When you click on the Width cell, a blue scroll box appears on the right side of the cell where the options are 1, . . . , 40 characters.

Column 4. Decimals. This column enables you to define the number of characters to the right of the decimal point. When you click on the Decimal cell, a blue scroll box appears on the right side of the cell. The options are 0, . . . , 16 decimals: scroll to 0.

Column 5. Label. This column enables you to provide a descriptive label for the row variable: type in Pilots.

Column 6. Values. This column is used with grouping variables. Do not change None, which is the default.

Column 7. Missing. Do not change None, which is the default. The data in Table 8.2-1 have no missing values.

When you click on the Missing values cell, a blue button appears on the right side of the cell. If you click on the blue button, the Missing Values window that is shown next opens. This window enables you to identify discrete missing values or a range of missing values.

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Click on the OK button at the bottom of the window to return to the SPSS Statistics Data Editor window.

Column 8. Columns. This column enables you to specify the number of characters in a column. When you click on the Columns cell, a blue scroll box appears on the right side of the cell where you can select from 1 to 255 characters. Do not change 8, which is the default.

Column 9. Align. This column enables you to determine the alignment of the columns. When you click on the Align cell, the cell enlarges and provides three options: Left, Right, and Center. Do not change Right, which is the default.

Column 10. Measure. This column enables you to specify the level of measurement of your variable. When you click on the Measure cell, the cell enlarges and provides three options: Scale, Ordinal, and Nominal. Click on the Nominal option. Scale denotes either interval or ratio measurement.

Column 11. Role. This column enables you to specify the role that the variable plays in the data set such as input, output, or partitioning data into samples. Do not change Input, which is the default. When you click on the Role cell, the cell enlarges and provides six options: Input, Target, Both, None, Partition, and Split. Further details about Role are available in SPSS’s help menu (Help Topics roles).

5. After you have entered the information for the pilot variable in row 1, it is a good idea to give your SPSS file a name and save the file. Select File in the menu and then Save as to name the file Table 8.2-1. The SPSS Statistics Data Editor Variable View window should appear as follows. Notice that Untitled1 in the top left of the window has been replaced with Table 8.2-1.sav.

6. Use rows 2–5 of the Variable View window to describe the characteristics of the repeated measures

variable, altimeters. The information for row 2 is given next. Rows 3–5 follow the same pattern. For the data in Table 8.2-1, fill in the columns of row 2 as follows.

Column 1. Name. Name the variable Alt_1.

Column 2. Type. Do not change Numeric, which is the default.

Column 3. Width. Do not change 8, which is the default.

Column 4. Decimals. Click on the Decimal cell. In the blue scroll box on the right side of the cell, scroll to 0.

Column 5. Label. Label this independent variable, Altimeter 1.

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5 Column 6. Values. This column is used with grouping variables. It enables you to provide a label for the repeated measures variable. When you click in the Values cell, a blue button appears on the right side of the cell. Click on the blue button to open the Value Labels window that is shown next.

Type “1” in the Value rectangle and “alt_1” in the Label rectangle. Then click on the Add button to enter the label into the large rectangle.

The Value Labels window changes as shown next.

To return to the Variable View window to enter more information about altimeter 1, click on the OK button at the bottom of the Value Labels window.

Column 7. Missing. This column enables you to designate certain scores as missing. The data in Table 8.2-1 have no missing values. Do not change None, which is the default.

Column 8. Columns. Do not change 8, which is the default.

Column 9. Align. Do not change Right, which is the default.

Column 10. Click on the Measure cell and select the Scale option.

Column 11. Role. Do not change Input; which is the default.

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7. In rows 3–5 repeat the descriptive procedures for the other three altimeters. The Variable View window should appear as follows:

8. Click on Data View in the lower left of the SPSS Statistics Data Editor window to open the Data

View window. In rows 1–8, enter the number of reading errors for each of the eight pilots. After entering the data from Table 8.2-1, the Data View window should appear as follows:

9. To obtain descriptive statistics for the hand-steadiness data, click on Analyze in the menu. Select

Descriptive Statistics from the drop down menu and then Explore (Analyze Descriptive Statistics Explore). These actions open the Explore window shown next where the independent and dependent variables are identified.

Pilots is highlighted. Click on the arrow beside Label Cases by to move Pilots into the Label Cases by rectangle. Highlight Altimeters 1–4. Click on the arrow beside Dependent List to move Altimeters 1–4 into the Dependent List rectangle.

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After these actions, the Explore window should appear as shown next.

10. Click on the Plots button in the upper right corner of the Explore window to open the Explore: Plots window shown next. Click on the Dependent together button and the Histogram check box. Click off the Stem-and-leaf check box.

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Click on the Continue button at the bottom of the window to return to the Explore window. Then click on the OK button to obtain the following descriptive statistics.

Results of the Exploratory Data Analysis

This output summarizes the information that was processed for the four altimeters. It is important to examine the table to be sure that SPSS has correctly interpreted your instructions about treatment A and number of observations.

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The exploratory data analysis indicates that there are differences among the sample means. The differences would be of practical importance if they occurred in the population. The sample means, trimmed means, and medians are similar. This suggests that the distributions are reasonably symmetrical. However, the histograms and box plots shown next suggests that three of the altimeter populations may not be symmetrical.

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The histograms and box plots suggests that the populations for altimeters 1, 2, and 4 may be slightly skewed. The box plots identified one outlier: the number of reading errors for pilot 8 in treatment level a1. The data collection procedures should be examined to determine if reasons can be found to question the accuracy of this outlier. I assume, for the purposes of this example, that the outlier is simply a manifestation of the random variability among the observations. The analysis of variance for these data is shown next.

Analysis of Variance With SPSS

1. To perform an analysis of variance on the reading-error data, click on Analyze in the menu; select General Linear Model from the drop-down menu, and then Repeated Measures (AnalyzeGeneral Linear Model Repeated Measures). These actions open the Repeated Measures Define Factors window shown next where the independent variable, Altimeters, and dependent variable, Errors, are identified.

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2. Replace “factor 1” in the rectangle with Altimeters. Type 4 in the Number of Levels box. This instructs SPSS to treat the four levels of Altimeters as different levels of the same variable, not as different variables. Click on the Add button to move Altimeters into the large rectangle. Type the name of the dependent variable, Errors, in the Measure Name rectangle. Click on the Add button to move Errors into the large rectangle. The Repeated Measures Define Factor(s) window should appear as shown next.

3. Click on the Define button in the lower left corner of the Repeated Measures Define Factor(s) window. This action opens the Repeated Measures window. Select Altimeter 1–4 and click on the arrow beside the Within-Subjects Variables box to move Altimeter 1–4 into the large box to replace the four _?_(Errors). This action identifies the different levels of the repeated measures variable.

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4 Click on the Plots button on the right side of the Repeated Measures window to open the Repeated

Measures: Profile Plots window that is shown next.

5. Transfer Altimeters into the Horizontal Axis rectangle by clicking on the arrow beside the rectangle.

Then click on the Add button to transfer Altimeters into the large Plots rectangle in the lower part of the Repeated Measures: Profile Plots window. Click on the Continue button at the bottom of the window to return to the Repeated Measures window. In the Repeated Measures window, click on the Options button. This action opens the Repeated Measures: Options window shown next.

15 6. In the Repeated Measures: Options window, highlight Altimeters and click on the arrow beside the

Display Means for rectangle to transfer Altimeters to the rectangle. Check the box beside Compare main effects. Scroll in the Confidence interval adjustment rectangle to select Bonferroni. Then in the Display area check the boxes beside Descriptive statistics and Estimates of effect size. The window should appear as shown next.

7. In the Repeated Measures: Option window, click on the Continue button to return to the Repeated

Measures window. Click OK at the bottom of the Repeated Measures window to obtain the results of the randomized block ANOVA.

Results of the Analysis of Variance

The SPSS output contains some results that are not relevant to a randomized block analysis of variance. SPSS lists of all of the results sub tables on the left side of the results window. A partial list of these sub tables is shown below.

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Sub tables for Multivariate Tests, Tests of Between-Subjects Effects, and so on are not relevant for a randomized block design. These tables can be deleted by highlighting each one and selecting Edit from the menu and then Delete. Alternatively, the irrelevant sub tables can be ignored. The following output contains only the relevant sub tables.

It is important to examine the Within-Subjects Factors and the Descriptive Statistics tables to be sure that SPSS has correctly interpreted your instructions about the variables and number of observations.

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According to Mauchly’s test, the sphericity condition is tenable. When, as in this example, n ≤ 8, it is customary to adopt the α = .25 level of significance for preliminary tests on a model. As I discuss on page 310 of Experimental Design: Procedures for the Behavioral Sciences, Mauchly’s test is less powerful than an alternative test called the locally best invariant test. The computation of the locally best invariant test statistic, V*, is illustrated on page 311 of my text. The test is significant: V* = 6.45 >

Hence, I conclude that the sphericity condition is not tenable.

The Mauchly table provides three ε values : ̂! = .620, = .834, and the lower bound for ε that is equal to .333. I recommend the use of ̂! = .620 for adjusting the degrees of freedom of the F tests. In SPSS the use of ̂! = .620 corresponds to performing the Greenhouse-Geisser test. Note, the designations of the Greenhouse-Geisser and Huynh-Feldt tests in SPSS do not correspond to my designations on pages 312–314.

According to SPSS, the null hypothesis for treatment A can be rejected: F = MSA/MSRES = 16.333/1.405 = 11.627, p = < .001.

V

.25; 3, 8*

= 5.88.

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The Within-Subjects Contrasts table provides tests of the linear, quadratic, and cubic trends for a quantitative independent variable. Because the four altimeters represent a qualitative variable, the tests are not relevant.

When sphericity is tenable, it is customary to use MSRES in the denominator of the F tests for trends. When sphericity is not tenable, as in the altimeter data, an error term appropriate for the specific trend, for example, MSRESlin, should be used (see pages 319–320 of Experimental Design: Procedures for the Behavioral Sciences). SPSS used MSRESlin, for example, in the test of the linear trend contrast, although Mauchly’s test led to the conclusion that the sphericity condition is tenable.

The Pairwise Comparisons table provides 95% two-sided confidence intervals for mean contrasts using the Bonferroni correction to control the per family error rate at α = .05. The Fisher-Hayter and REGW F, FQ, and Q statistics provide more powerful tests of a posteriori mean contrasts. I illustrate the computation of the Fisher-Hayter test on pages 315–319 of Experimental Design: Procedures for the Behavioral Sciences.

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The Profile Plots figure provides a picture of the sample data.

Reference

Kirk, R. E. (2013) Experimental Design: Procedures for the Behavioral Sciences. (4th ed.). Thousand Oaks, CA: Sage.

Suggested Readings

Brace, N, Kemp, R., & Snelgar, R. (2013). SPSS for Psychologists (5th ed.) New York, NY: Routledge.

Kinnear, P. R., & Gray, C. D. (2011). IBM SPSS Statistics Made Simple 18. New York, NY: Psychology Press.