Two-Way ANOVA (Factorial)

In a simple Two-Way ANOVA, data from groups related to two "factors" are compared. For example, what if we wanted to compare test scores of students in Rural and Urban high schools (factor one) being taught geometry by two different methods ( A & B ). This design is called a 2X2 Factorial.

Factor One : Method of teaching

A

B

Factor Two : School Setting

Rural

8 or more
Test Scores*
8 or more
Test Scores*

Urban

8 or more
Test Scores*
8 or more
Test Scores*

The ANOVA analysis will indicate if there is a significant difference between the teaching methods by comparing the mean of the Group A Scores with the mean of the Group B Scores (comparing scores in the A & B columns). It will also indicate if there is a significant difference between the mean scores of students in the rural school and those in the urban school (comparing scores in the Rural & Urban rows). Finally, the ANOVA will tell if there is a significant interaction between the groups. What does that mean? Graphing the mean test scores of the four groups in the 2x2 Factorial might yield one of the figures shown below. The figures indicate whether the rural and urban students react in the same way to the teaching methods;


or whether they react differently to the teaching methods.


In Figures A and B, the Urban and Rural groups reacted in the same way to the different teaching methods; in Figure A both group's performance improved under method B and in Figure B both group's performance decreased under method B. In this case, we would not expect a significant interaction term in the ANOVA.

In Figures C & D, the Urban and Rural groups responded differently to the teaching methods. In Figure C, the urban students declined sharply under method B while the rural students performance increased. In Figure D, The Urban group's performance increased sharply under method B, but the rural group's performance decreased slightly. In this case we would expect a significant interaction term in the ANOVA.

Statistical Hypothesis

Factor One
Null: the mean of the A Scores = the mean of the B Scores
Alternate:the mean
A Scores does NOT equal the mean of the B Scores

Factor Two
Null:the mean of the Urban Scores =
the mean of the Rural Scores
Alternate: the mean of the Urban Scores
does NOT equal the mean of the Rural Scores

Interaction
Null: There is no significant interaction between teaching method and school setting
Alternate: There is a significant interaction between teaching method and school setting.

In the previous menu, the Materials and Clouds activities use a Two-Way ANOVA to analyze the data sets. The activities assume that you have access to Excel.


Copyright © 1997 Central Virginia Governor's School for Science and Technology Lynchburg, VA