One-Way ANOVA Contrasts

You can partition the between-groups sums of squares into trend components or specify a priori contrasts.

Polynomial
Partitions the between-groups sums of squares into trend components. You can test for a trend of the dependent variable across the ordered levels of the factor variable. For example, you could test for a linear trend (increasing or decreasing) in salary across the ordered levels of highest degree earned.
  • Degree. You can choose a 1st, 2nd, 3rd, 4th, or 5th degree polynomial.
Coefficients
User-specified a priori contrasts to be tested by the t statistic. Enter a coefficient for each group (category) of the factor variable and click Add after each entry. Each new value is added to the bottom of the coefficient list. To specify additional sets of contrasts, click Next. Use Next and Previous to move between sets of contrasts.
Estimate effect size for contrasts
Controls the calculation of the effect size for the overall test. When this setting is enabled, at least one of the following options must be selected to calculate the effect sizes. This setting is enabled when at least one contrast is specified and results in an ANOVA Effect Sizes table in the output.
Use pooled standard deviation for all the groups as the standardizer
Uses the pooled standard deviation for all the groups as the standardizer in estimating the effect size. This is the default setting and is available when Estimate effect size for contrasts is selected.
Use pooled standard deviation for those groups involved in the contrast as the standardizer
Uses the pooled standard deviation for the groups involved in the contrast as the standardizer. The setting is available when Estimate effect size for contrasts is selected.

The order of the coefficients is important because it corresponds to the ascending order of the category values of the factor variable. The first coefficient on the list corresponds to the lowest group value of the factor variable, and the last coefficient corresponds to the highest value. For example, if there are six categories of the factor variable, the coefficients –1, 0, 0, 0, 0.5, and 0.5 contrast the first group with the fifth and sixth groups. For most applications, the coefficients should sum to 0. Sets that do not sum to 0 can also be used, but a warning message is displayed.