CONTRAST Subcommand (MANOVA: Univariate command)

CONTRAST specifies the type of contrast that is desired among the levels of a factor. For a factor with k levels or values, the contrast type determines the meaning of its k−1 degrees of freedom. If the subcommand is omitted or is specified with no keyword, the default is DEVIATION for between-subjects factors.

  • Specify the factor name in parentheses following the subcommand CONTRAST.
  • You can specify only one factor per CONTRAST subcommand, but you can enter multiple CONTRAST subcommands.
  • After closing the parentheses, enter an equals sign followed by one of the contrast keywords.
  • To obtain F tests for individual degrees of freedom for the specified contrast, enter the factor name followed by a number in parentheses on the DESIGN subcommand. The number refers to a partition of the factor’s degrees of freedom. If you do not use the PARTITION subcommand, each degree of freedom is a distinct partition.

The following contrast types are available:

DEVIATION. Deviations from the grand mean. This setting is the default for between-subjects factors. Each level of the factor (except one level) is compared to the grand mean. One category (by default, the last category) must be omitted so that the effects will be independent of one another. To omit a category other than the last category, specify the number of the omitted category (which is not necessarily the same as its value) in parentheses after the keyword DEVIATION. For example:

MANOVA A BY B(2,4)
  /CONTRAST(B)=DEVIATION(1).

The specified contrast omits the first category, in which B has the value 2. Deviation contrasts are not orthogonal.

POLYNOMIAL. Polynomial contrasts. This setting is the default for within-subjects factors. The first degree of freedom contains the linear effect across the levels of the factor, the second degree of freedom contains the quadratic effect, and so on. In a balanced design, polynomial contrasts are orthogonal. By default, the levels are assumed to be equally spaced; you can specify unequal spacing by entering a metric—consisting of one integer for each level of the factor—in parentheses after the keyword POLYNOMIAL. For example:

MANOVA RESPONSE BY STIMULUS (4,6)   
  /CONTRAST(STIMULUS) = POLYNOMIAL(1,2,4)

The specified contrast indicates that the three levels of STIMULUS are actually in the proportion 1:2:4. The default metric is always (1,2,...,k), where k levels are involved. Only the relative differences between the terms of the metric matter. (1,2,4) is the same metric as (2,3,5) or (20,30,50) because, in each instance, the difference between the second and third numbers is twice the difference between the first and second numbers.

DIFFERENCE. Difference or reverse Helmert contrasts. Each level of the factor (except the first level) is compared to the mean of the previous levels. In a balanced design, difference contrasts are orthogonal.

HELMERT. Helmert contrasts. Each level of the factor (except the last level) is compared to the mean of subsequent levels. In a balanced design, Helmert contrasts are orthogonal.

SIMPLE. Contrast where each level of the factor (except the last level) is compared to the last level. To use a category (other than the last category) as the omitted reference category, specify its number (which is not necessarily the same as its value) in parentheses following the keyword SIMPLE. For example:

MANOVA A BY B(2,4)    
  /CONTRAST(B)=SIMPLE(1).

The specified contrast compares the other levels to the first level of B, in which B has the value 2. Simple contrasts are not orthogonal.

REPEATED. Comparison of adjacent levels. Each level of the factor (except the last level) is compared to the next level. Repeated contrasts are not orthogonal.

SPECIAL. A user-defined contrast. After this keyword, enter a square matrix in parentheses with as many rows and columns as there are levels in the factor. The first row represents the mean effect of the factor and is generally a vector of 1’s. The row represents a set of weights indicating how to collapse over the categories of this factor in estimating parameters for other factors. The other rows of the contrast matrix contain the special contrasts indicating the desired comparisons between levels of the factor. If the special contrasts are linear combinations of each other, MANOVA reports the linear dependency and stops processing.

Orthogonal contrasts are particularly useful. In a balanced design, contrasts are orthogonal if the sum of the coefficients in each contrast row is 0 and if, for any pair of contrast rows, the products of corresponding coefficients sum to 0. DIFFERENCE, HELMERT, and POLYNOMIAL contrasts always meet these criteria in balanced designs.

Example

MANOVA DEP BY FAC(1,5)
  /CONTRAST(FAC)=DIFFERENCE
  /DESIGN=FAC(1) FAC(2) FAC(3) FAC(4).
  • The factor FAC has five categories and therefore four degrees of freedom.
  • CONTRAST requests DIFFERENCE contrasts, which compare each level (except the first level) with the mean of the previous levels.
  • Each of the four degrees of freedom is tested individually on the DESIGN subcommand.