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steps on performing a 3-factor factorial design

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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.

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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.

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