POLYNOMIAL Subcommand (ONEWAY command)

POLYNOMIAL partitions the between-groups sums of squares into linear, quadratic, cubic, or higher-order trend components. The display is an expanded analysis-of-variance table that provides the degrees of freedom, sums of squares, mean square, F, and probability of F for each partition.

• The value specified on POLYNOMIAL indicates the highest-degree polynomial to be used.
• The polynomial value must be a positive integer less than or equal to 5 and less than the number of groups. If the polynomial specified is greater than the number of groups, the highest-degree polynomial possible is assumed.
• Only one POLYNOMIAL subcommand can be specified per ONEWAY command. If more than one is used, only the last one specified is in effect.
• ONEWAY computes the sums of squares for each order polynomial from weighted polynomial contrasts, using the category of the independent variable as the metric. These contrasts are orthogonal.
• With unbalanced designs and equal spacing between groups, ONEWAY also computes sums of squares using the unweighted polynomial contrasts. These contrasts are not orthogonal.
• The deviation sums of squares are always calculated from the weighted sums of squares¹.

Example

ONEWAY WELL BY EDUC6 
  /POLYNOMIAL=2.

• ONEWAY requests an analysis of variance of WELL by EDUC6 with second-order (quadratic) polynomial contrasts.
• The ANOVA table is expanded to include both linear and quadratic terms.