Orthogonal design

The orthogonal design contains each of the level combinations (factor pairs) an equal number of times.

Orthogonal design

A

B

C

-1

-1

1

1

-1

-1

-1

1

-1

1

1

1

For example, for the AB pairing, you have (-1, -1); (1, -1); (-1, 1); and (1,1). Looking at the other two pairings, AC and BC, you find that they also have only one occurrence at each level combination.

 

The non-orthogonal design does not contain each of the level combinations (factor pairs) the same number of times.

Non-orthogonal design

A

B

C

-1

-1

1

1

-1

-1

-1

1

-1

1

1

-1

For example, for the AB pairing, you have (-1, -1); (1, -1); (-1, 1); and (1,1). But for the other two pairings, AC and BC, you find that they have a duplicate combination and are missing combination. For AC, you have (-1, 1); (1, -1); (-1, -1); (1,-1); and the (1,1) combination is missing. For BC, you have (-1, 1); (-1, -1); (1, -1); (1,-1); and the (1,1) combination is missing.

 

Experimental analysis of an orthogonal design is generally straightforward because you can estimate each main effect and interaction independently. If your design is not orthogonal, either by plan or by accidental loss of data, your interpretation may not be as straightforward.

 

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