Specifying the model terms
main topic
 

You must specify the model terms in the Model box. This is an abbreviated form of the statistical model that you may see in textbooks. Because you enter the response variables in Responses, in Model you enter only the variables or products of variables that correspond to terms in the statistical model. Minitab uses a simplified version of a statistical model as it appears in many textbooks. Here are some examples of statistical models and the terms to enter in Model. A, B, and C represent factors.

Case

Statistical model

Terms in model

Factors A, B crossed

yijk = m + ai + bj + abij + ek(ij)

A B A* B
 

Factors A, B, C crossed

yijkl = m + ai + bj + ck + abij + acik + bcjk + abcijk + el(ijk)

A B C A*B A* C B*C A* B*C

3 factors nested
(B within A,
C within A and B)

yijkl = m + ai + bj(i) + ck(ij) + el(ijk)

A B(A) C(AB)

Crossed and nested
(B nested within A,
both crossed with C)

yijkl = m + ai + bj(i) + ck + acik + bcjk(i) + el(ijk)

A B (A) C A*C B*C

In Minitab's models you omit the subscripts, m, e, and +'s that appear in textbook models. An * is used for an interaction term and parentheses are used for nesting. For example, when B is nested within A, you enter B (A), and when C is nested within both A and B, you enter C (A B). Enter B(A) C(B) for the case of 3 sequentially nested factors. Terms in parentheses are always factors in the model and are listed with blanks between them. Thus, D * F (A B E) is correct but D * F (A * B E) and D (A * B * C) are not. Also, one set of parentheses cannot be used inside another set. Thus, C (A B) is correct but C (A B (A)) is not. An interaction term between a nested factor and the factor it is nested within is invalid.

See Specifying terms involving covariates for details on specifying models with covariates.

Several special rules apply to naming columns. You may omit the quotes around variable names. Because of this, variable names must start with a letter and contain only letters and numbers. Alternatively, you can use C notation (C1, C2, etc.) to denote data columns. You can use special symbols in a variable name, but then you must enclose the name in single quotes.

You can specify multiple responses. In this case, a separate analysis of variance will be performed for each response.