Specifying Univariate and Multivariate Between-Groups Designs - One-Way Between-Groups ANOVA and Contrast Analysis

Between-groups designs are ANOVA designs with several distinct groups of subjects (or observations). For example, you can use three different algebra textbooks, one in each of three classes, and subsequently measure students' performance on a standardized algebra test. The three classes would then represent three distinct groups, and if you wanted to compare their performance, a one-way between-groups analysis of variance would be specified. Each group in this design was "exposed" to a different algebra textbook; thus, the type of algebra book used represents the between-groups factor. Because three different textbooks were used, this between-groups factor contains three levels.

When entering the data for this study, you must create a datafile with at least two variables. One variable should contain students' scores on the standardized algebra test. This variable is referred to as the dependent variable. Another variable that needs to be included in the datafile should contain code numbers or text codes that uniquely identify the group membership of each case in the data file; this variable is referred to as the independent or grouping variable.

For example, you can assign the text label Book 1 to a student if he or she was in the class in which the first algebra textbook was used; you can assign the text label Book 2 if the respective student was in the class in which the second algebra textbook was used, and you can assign the text label Book 3 if the student participated in the class in which the third algebra textbook was used. The resulting data file looks like this:

Independent Variable	Dependent Variable
Book 1	23
Book 3	48
Book 3	26
Book 2	27
Book 1	43
Book 1	39
Book 2	30
-	-
-	-
-	-

In this example, the grouping variable only contains the three different text codes that you entered in order to code the between-groups factor. If a datafile contains cases with numeric or text labels for the grouping variable that were not specified in the list of valid codes, those cases are excluded from the analysis. Note that when entering data into the file, it is not necessary to enter the subjects (cases) in any particular order.

In order to analyze the data, select One-way ANOVA from the General ANOVA/MANOVA Startup Panel - Quick tab or the GLM Startup Panel Quick tab. Then click the Variables button on the ANOVA/MANOVA Quick Specs - Quick tab or GLM Quick Specs Dialog - Quick tab, and specify as the categorical predictors factor (between-groups factor) the variable number 1. Then variable 2 would be specified as the dependent variable. Next, specify (via the Factor codes button on the ANOVA/MANOVA Quick Specs - Quick tab or GLM Quick Specs Dialog - Quick tab) the independent variable codes as entered in the data file. Note that it is not necessary to explicitly enter into the codes window all integer codes representing the text labels; you can also click OK at this point and let Statistica select all codes by default. After clicking OK, Statistica processes the data and displays the ANOVA Results or GLM Results dialog.

Planned comparisons are useful if you want to compare specific groups in the design. Statistica expects you to enter a set of contrasts that identifies the desired comparisons. If, in the present example, you want to compare the group taught with the first algebra textbook (i.e., group 1) with the group that was taught with the third algebra textbook (i.e., group 3) and ignore group 2 in this particular comparison, one set of contrasts would be entered, namely 1, 0, and -1 (on the Specify Contrasts for this Factor dialog).

The rules for generating these contrasts are as follows.

1. The contrast must have as many coefficients as there are levels for the respective factor.
2. Groups to be omitted in the contrast are given a 0 (zero).
3. Groups that are to be compared against each other are assigned positive or negative integer values, respectively; however, it is important that the sum of such contrast coefficients is equal to zero.
4. Groups that are to be collapsed in the contrast are assigned identical integer values.

For example, if you wanted to compare group 1 with groups 2 and 3 combined, the proper set of contrast coefficients would be 2, -1, -1. If you wanted to compare group 2 against groups 1 and 3 combined, the proper contrast would be 1, -2, and 1. If you wanted to compare group 2 with group 3 (ignoring group 1), the proper contrast would be 0, 1, and -1.

The discussion so far has been restricted to univariate analysis of variance. However, if you select multiple dependent variables, then a multivariate analysis of variance will automatically be performed (unless the multiple dependent variables are specified to be levels of repeated measures factors). For example, if in the previous example students' algebra ability had been measured with three tests rather than just one, the data file could look like this:

Independent Variable	Dependent Variables
Book 1	23	24	28
Book 3	48	43	40
Book 3	26	38	21
Book 2	27	29	35
Book 1	43	42	42
Book 1	39	40	31
Book 2	30	29	27
-	-	-	-
-	-	-	-
-	-	-	-

In order to perform a multivariate analysis of variance (MANOVA) of the three test scores, enter all three variables into the dependent variable list. When subsequently testing the main effect or planned comparisons, both multivariate test results (for all dependent variables simultaneously) and the results of the univariate tests (testing one variable at a time) will be calculated.

The manner in which planned comparisons are specified is basically identical to the univariate case. However, when entering contrast coefficients for a planned comparison, you also have the option to enter contrasts for the dependent variables. To do this, you will first need to select the Yes option button in the Contrasts for dependent variables group box on the GLM and ANOVA Results - Comps tab.