# Analysis of means (ANOM) for 2 level, 2 factor design

This macro creates an ANOM chart for a 2 factor, 2 level factorial design. The interaction between the 2 factors is displayed on the same scale as the main effects. The default decision limits are calculated with an alpha of.05.

Be sure that Minitab knows where to find your downloaded macro. Choose Tools > Options > General. Under Macro location browse to the location where you save macro files.

###### Important

If you use an older web browser, when you click the Download button, the file may open in Quicktime, which shares the .mac file extension with Minitab macros. To save the macro, right-click the Download button and choose Save target as.

## Required Inputs

• 2 factors (A, B, )
• Response (C)
###### Note

The design must be balanced and replicated, and the levels of the factors must be numeric, not text. Center points are not allowed.

## Optional Inputs

ALPHA K
Use to set a custom significance level. The default is 0.05.
TITLE "text"
Use to add a custom title to the graphical output.

## Running the Macro

Suppose the factors are in C1 and C2 and the response is in C3. You want to use a significance level of 0.01.

To run the macro, choose Edit > Command Line Editor and type:
```%ANOM2FACT C1 C2 C3;
ALPHA .01.```

Click Submit Commands.

What does the line for the interaction show?

If the factors A and B each have 2 levels, then the length of the vertical line for the interaction is the absolute value of the effect of the interaction. In a 2 level design, the effect is twice the coefficient.

How to calculate the endpoints for the interaction line?

Let A1 represent the low level of A and A2 represent the high level of A. Let B1 represent the low level of B and B2 represent the high level of B. Given that the design is replicated at least once, the interaction between A and B can be written as

AB = .5( 1 1 A B + 2 2 A B ) - .5( 1 2 A B + 2 1 A B ), where

1 1 A B is the mean of the response values where A and B are both at the low level.

A B is the mean of the response values where A and B are both at the high level. 1 2 A B denotes the mean response where A is at its low level and B is at its high level. 2 1 A B denotes the mean response where A is at its high level and B is at its low level.

In notation suggested by Ott(1975), the interaction AB can be re-expressed as

AB = ( L - U)

where L = .5( 1 1 A B + 2 2 A B ) is the mean of the response data for the factor combinations where the two factors have the same (Like) subscripts. Therefore, L is the mean of the response data at the Like subscripts.

U = .5( 1 2 A B + 2 1 A B ) is the mean of the response data for the factor combinations where the two factors have different (Unlike) subscripts. Therefore, U is the mean of the response data at the Unlike subscripts.

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