Why is normal distribution important in ANOVA?
In ANOVA, the entire response column is typically nonnormal because the different groups in the data have different means. If the data for each individual group follow a normal distribution, then the data meet the assumption that the errors follow a normal distribution.
How robust is ANOVA to violations of normality?
The one-way ANOVA is considered a robust test against the normality assumption. As regards the normality of group data, the one-way ANOVA can tolerate data that is non-normal (skewed or kurtotic distributions) with only a small effect on the Type I error rate.
When do we use the effects model in factorial design?
The model we have written gives us a way to represent in a mathematical form a two-factor design, whether we use the means model or the effects model, i.e., There is really no benefit to the effects model when there is interaction, except that it gives us a mechanism for partitioning the variation due to the two treatments and their interactions.
How to create an unreplicated 2 k factorial design?
CTRL + SHIFT + F (Windows) ⌘ + ⇧ + F (Mac) These are 2 k factorial designs with one observation at each corner of the “cube”. An unreplicated 2 k factorial design is also sometimes called a “single replicate” of the 2 k experiment.
How many possible conditions are in a factorial experiment?
Notice that the number of possible conditions is the product of the numbers of levels. A 2 × 2 factorial design has four conditions, a 3 × 2 factorial design has six conditions, a 4 × 5 factorial design would have 20 conditions, and so on. Also notice that each number in the notation represents one factor, one independent variable.
How to calculate factorial designs with two treatment factors?
Next, let’s calculate the α and the β effects; since the overall mean is 10, our α effects are -2 and 2 (which sum to 0), and our β effects are -3 and 3 (which also sum to 0). If you plot the cell means you get two lines that are parallel.