# Completely Randomized Factorial Anova

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• Published : November 18, 2010

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Chapter 16

Completely Randomized Factorial ANOVA

This tutorial describes the procedures for computing F tests for a completely randomized factorial analysis of variance design. The reading-speed data in Table 16.4-2 of the textbook are used to illustrate the procedures.

1.Enter a description of the data in the SPSS Data Editor following steps 1–4 described in the Frequency Distribution tutorial for Chapter 2. Use rows 1, 2, and 3 of the SPSS Data Editor Variable View window to describe the two independent variables and the dependent variable. There are two levels of room illumination, Illumination Level, denoted by a1 and a2. You identify the illumination levels in the Values cell of the Variable View window. When you click on the cell below Values, a grey box appears on right side of None that is highlighted here.

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2.Clicking on the grey box opens the Value Labels window. Type 1 in the Value box and a1 in the Label box. Click on the Add button to move a1 into the large box in the center of the Value Labels window.

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3.To identify a second value of the independent variable, a2; type 2 in the Value box and a2 in the Label box. Click on the Add button to move a2 into the large box in the center of the Value Labels window. Click on the OK button in the lower left area of the window to return to the SPSS Data Editor Variable View window and finish filling out the cells in the first row.

4.Use the second row of the SPSS Data Editor Variable View window to describe the second independent variable: size of type, denoted by Type Size. This variable has three levels denoted by b1, b2, and b3. You identify the levels of the variable in the Values cell of the Variable View window. When you click on the cell below Values, a grey box appears. Clicking on the grey box opens the Value Labels window. Type 1 in the Value box and b1 in the Label box. Click on the Add button to move b1 into the large box in the center of the Value Labels window. Repeat the process for the second and third levels of the size-of-type variable. The Value Labels window should appear as shown here. SPSS automatically inserts the equal sign and the quotation marks after you click on the Add button.

Click on the OK button in the lower left area of the window to return to the SPSS Data Editor Variable View window and finish filling out the cells in the second row.

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5.Use row 3 of the SPSS Data Editor Variable View window to describe the dependent variable, denoted by R_speed. The SPSS Data Editor Variable View window should be similar to the window shown here.

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6. Click on the SPSS Data Editor Data View button to enter the data. Type 1 or 2 in the I_level column; 1, 2, or 3 in the T_level column; and the reading score in the R_speed column.

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7.To compute ANOVA F statistics, click on Analyze in the Menu Bar; select General Linear Model from the pull-down menu and then Univariate. These selections open the Univariate window in which you specify which variables are the independent and dependent variables.

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8.Select Illumination Level (I_level) and click on the arrow beside the Fixed Factor(s) box. The independent variable, Illumination Level (I_level), will appear in the Fixed Factor box. Select Type Size (T_level) and click on the arrow beside the Fixed Factor(s) box. The second independent variable, Type Size (T_level), will appear in the Fixed Factor box.

Select Reading Speed (R_speed) and click on the arrow beside the Dependent Variable box. The dependent variable, Reading Speed (R_speed), appears in the Dependent List box as shown here.

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9.Click on the Post Hoc button in the Univariate window to open the Univariate: Post Hoc Comparisons for Observed Means window. [pic]

10.The independent variable, T_size, has three levels. To obtain Tukey’s multiple comparison procedure for this variable, select T_size in the Factor(s) box and click on the arrow...