# steps on performing a 3-factor factorial design

1. An experiment was designed to see what factors affect the cleaning ability of a washing solution. Three factors were used in the experiment - the concentration of detergent, concentration of sodium carbonate, and concentration of sodium carboxymethyl cellulose. A larger value of the response indicates better cleaning ability. Three replicates of the experiment were used. The results were:

Det. Sodium Carb. Sodium Carb. Cellulose Results

-1 -1 -1 106, 93, 116

1 -1 -1 198, 200, 214

-1 1 -1 197, 202, 185

1 1 -1 329, 331, 307

-1 -1 1 149, 169, 135

1 -1 1 243, 247, 220

-1 1 1 255, 230, 252

1 1 1 383, 360, 364

a. Estimate the main effects and interactions. Make sure you clearly indicate to me which values are the estimates.

b. Carry out a complete analysis, indicating exactly what is significant and why, as well as a discussion about whether the assumptions are being met.

https://brainmass.com/math/probability/steps-performing-factor-factorial-design-587621

#### Solution Preview

Please check both excel and word file.

Answer:

Let A be concentration of detergent, B be concentration of sodium carbonate and C be concentration of sodium carboxymethyl cellulose.

So the table is

A B C Rep 1 Rep 2 Rep 3

-1 -1 -1 106 93 116

1 -1 -1 198 200 214

-1 1 -1 197 202 185

1 1 -1 329 331 307

-1 -1 1 149 169 135

1 -1 1 243 247 220

-1 1 1 255 230 252

1 1 1 383 360 364

We then run the data in the excel. Please check the attached excel ...

#### Solution Summary

The solution gives detailed steps on performing a 3-factor factorial design with 3 replicates for each factor. The design is run in excel and the report is written in word.