The Two-Way Analysis of Variance tests the equality of means of populations classified by two factors. It requires the data to be balanced (all factor combinations must have the same number of observations).
1. Choose ProcessMA > Statistics > ANOVA > Two-Way ANOVA.
2. In Variable, select the column containing the response.
3. In Factor 1, select the column containing one of the factor levels.
4. In Factor 2, select the column containing the other factor levels.
5. Click OK.
Optional
6. In Confidence level, enter the desired confidence level for the confidence interval.
7. Check Plot confidence interval, if you want to display the confidence intervals for the means.
8. Check Plot boxplot, if you want to display the Boxplot of the data.
9. Check Plot residuals, if you want to display the residual plots for analysis.
10. Check Fit additive model, if you want to fit the model without the interaction term.
Note To select a column of data into a textbox, double-click on any of the column names shown in the list on the left of the dialog box while in the textbox.
Variable: Numeric.
Factor 1: Text or Numeric; Must have the same number of data points are variable; Must and contain at least 2 distinct categories.
Factor 2: Text or Numeric; Must have the same number of data points are variable; Must and contain at least 2 distinct categories.
Confidence level: Numeric; between 0 and 100.
You conducted an experiment to study how well organisms multiple in different temperatures and in the presence of different catalysts. You prepared 18 dishes of organisms and placed them at three different temperatures and added three different types of catalyst. You recorded the number of organism in each dish after 10 days. You want to use the Two-Way ANOVA to test if there is significant evidence of main and interactions effects.
1. Open worksheet ProcessMA > Tools > Data Files > Stat.xls.
2. Choose ProcessMA > Statistics > ANOVA > Two-Way ANOVA.
3. In Variable, select P – Organism.
4. In Factor 1, select Q – Temperature.
5. In Factor 2, select R – Catalyst.
6. In Confidence level, enter 95.
7. Check Plot confidence interval.
8. Click OK.
Interpretation
For a desired a = 0.05, there is no significant evidence for the temperature and temperature*catalyst interaction effects. There is significant evidence for the catalyst main effects on the growth of the organisms since p = 0.002 < a. From the confidence interval plot, it suggests that catalyst B promotes the growth of the organism more than the other two.