# Two-Way Analysis of Variance

An experimenter has investigated the effects of cigarette smoking on learning. Two levels of the smoking variable were used (smoked, did not smoke). There are also two levels of the learning variable (intentional learning and incidental learning).

1) Practice the two-way between-subjects ANOVA on these data.

2) Interpret the main effects and interaction of this experiment.

Please see the attached file for table.

© BrainMass Inc. brainmass.com June 3, 2020, 9:56 pm ad1c9bdddfhttps://brainmass.com/statistics/analysis-of-variance/two-way-analysis-variance-206454

#### Solution Preview

** Please see the attached document for the complete solution **

This is an example of a balanced two-way analysis of variance (ANOVA). By balanced, we mean that each of the cells in the data table have the same number of observations, in this case 5 observations. When the experiment is balanced the hand calculations for the analysis become quite simple.

Rather than working with means, things are simpler if you work with sums. I summed the data for each cell and put it in the table below. On the margins of the table I have shown the row and column totals of the data. In the lower right hand corner of the table, I have shown the sum of all observations in the data set. In this balanced experiment, each cell sum is the sum of 5 observations. Each row and column total is the sum of 10 observations and the grand total is the sum of 20 observations.

(please see the attached file)

The first step in the analysis is to calculate what some call the "correction for the mean". There are 20 observations in the data set. To calculate the ...

#### Solution Summary

This solution is an example of a two-way analysis of variance. The 700 word solution shows calculation details and an interpretation of the analysis.