# Fractional Factorials (Statistics). Design Identification

1. Aug 7, 2013

### Northbysouth

1. The problem statement, all variables and given/known data
Anand, Bhadkamkar, and Moghe (1995) used a fractional factorial design to determine which of the six possible factors influenced the determination of manganese in cast iron. The six factors and their levels follow:

A-Titration speed ; Medium ; Fast
B-Dissolution time ; 20 ; 30
C-AgNO3 addition ; 20 ; 10
D-Persulfate addition ; 2 ; 3
E-Volume HMnO4 ; 100 ; 150
F-Sodium arsenite ; 0.10 ; 0.15

I have attached a data table

X1 is Titration speed
X2 is Dissolution time
etc

a) Identify this design

b) Give the defining interaction or interactions

2. Relevant equations

3. The attempt at a solution

I've read over this material in my textbook and viewed the lecture video that came with it and I'm still quite confused.

a) is it just asking for:

26-3

The 2 refers to the levels (-1 and +1+

The 6 refers to the number of factors

The -3 to how there are 8 rows of data,

2-3=1/8

64/8 = 8

b) I have no idea what it is asking for with the defining interaction or interactions

My professor sent this email out:

I = BCDE = -ADE = -ABC = -BDF = -CEF = ABEF = ACDF. Since I am giving you the defining relation, please state the alias structure for main effect A. You need to go through and add A to each part of the defining interaction to determine the answer modulo 2.

But I'm still confused.

Any clarification would be appreciated

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Last edited: Aug 7, 2013