Stats.Blue
Go Back

Balanced Two-Way ANOVA

Balanced Two-way ANOVA analyzes the effect of two categorical variables on the mean of a response variable. Suppose there are $r$ values of the row categorical variable, and $c$ values of the column categorical variable for a total of $rc$ treatments. The assumptions and guidelines are:
• The design is balanced. That is, every combination of treatments has exactly the same number of observations.

• Moreover, as implied by the above, the design is crossed. That is, every possible combination of treatments from both categorical variables must be applied.

• We have $rc$ independent SRSs, one from each of $rc$ populations. We measure the same response variable for each sample.

• The $ij$th population (row $i$, column $j$) has a Normal distribution with unknown mean $\mu_{ij}$.

• All the populations have the same standard deviation $\sigma$, whose value is unknown.

• Balanced Two-way ANOVA tests three null hypotheses:
• The row variable has no effect on the mean response.
• The column variable has no effect on the mean response
• The is no interaction between the row and column variables.

• The results of the ANOVA are approximately correct when the largest sample standard deviation is no more than twice as large as the smallest sample standard deviation in each treatment group.

 Category Name Columns (Optional):
 Category Name Rows (Optional):

Interaction Plots

 Mean

 Mean