# Contrast, Effect, Estimate, Sum of Square, and ANOVA Table

Video 3 explains the process of developing the ANOVA table, including the contrast, effect, estimate, and sum of square for the basic 22 design.

### The Contrast

The contrast is defined by the total responses as described in Equation 9.

Therefore, the contrast of

Equation 9

### The Effect

The equations for effects are described in Equation 6.

### The Estimate

The estimates for each of the effects are simply the one-half of their respective effect. Therefore, the equations for the effects are written as.

Equation 10

### The Sum of Square, SS

Sum of square is simply the average of the square of the contrast. For an example, the sum of square for A, B and the interaction effect can be calculated using the following equations.

Equation 11

The total sum of square, SST can be calculated as in Equation 12.

Equation 12

The sum of square for the experimental error can be calculated as in Equation 13.

Equation 13

### ANOVA Table for a 22 Factorial Design of Experiment

The ANOVA table for a 22 factorial design of experiment can be developed as Table 2. One exception is the levels of A and B are denoted by small a and b respectively.

Table 2. ANOVA table for a 22 factorial design of experiment