2FACTOR_ANOVA_07

# 2FACTOR_ANOVA_07 - Factorial design = experimental design...

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Factorial design = experimental design in which two or more independent variables are simultaneously varied. Factor = independent variable In the simplest factorial design, two independent variables are varied and each independent variable assumes two levels. Such a design is often called 2x2 (“two-by-two”) design. The first 2 of the 2x2 indicates there are two levels of the first independent variable (i.e. Factor A) The second 2 indicates the number of levels of the second independent variable (i.e., Factor B) 4 x 3 design ?

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The combination of the two independent variables (each with 2 levels) creates four treatment conditions (i.e., 2x2=4) Depending on how treatment conditions are assigned to subjects factorial design may be between-subjects (i.e., each treatment condition is assigned to separate group of subjects), within-subjects (i.e., one sample receives all treatment conditions) or mixed (i.e., treatment conditions created for one independent variable are treated as a between-subjects and for the other one as a within-subjects).
Example - 2x2 between-subjects design: An experiment was designed to test if students performance in the Statistics class depends on (a) homework assignment and (b) frequency of tests. The 2 (Homework) x 2(Frequency of tests) between-subjects design is used. The test results on the final exam are used as a dependent variable. Homework Yes Homework No Two Tests Group 1 Group 3 Four Tests Group 2 Group 4

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Partitioning variability for a two-factor ANOVA
A factorial design provides information about the main effect of each independent variable (i.e., the differences between conditions produced by each independent variable) In our example that corresponds to the question: Is there a difference in performance between students that have homework and students that do not have homework? (i.e., Is there a main effect of homework? ) Is there a difference in performance between students

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## 2FACTOR_ANOVA_07 - Factorial design = experimental design...

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