Final answer:
Non-orthogonal contrasts in SPSS include Scheffé, Tukey, and Helmert contrasts, each serving different purposes for mean comparisons, with polynomial contrasts focused on trends. Proper selection of contrasts is vital for accurate statistical interpretation.
Step-by-step explanation:
Non-orthogonal contrasts refer to statistical tests used to compare means across different groups in which the comparisons are not independent of each other. In SPSS, the non-orthogonal contrasts include Scheffé contrasts, Tukey contrasts, and Helmert contrasts. Polynomial contrasts, on the other hand, might be considered a separate category as they deal with trends along an ordinal or continuous predictor, for example, linear, quadratic, or cubic trends in time series data.
Each of these contrasts serves a different purpose: Scheffé contrasts are typically used when conducting post hoc analysis following ANOVA to control for family-wise error rate; Tukey contrasts are generally used for pairwise comparisons; and Helmert contrasts compare each mean to the mean of subsequent levels, which is a technique useful for time series data or when examining sequential differences.
It's essential to choose the appropriate contrast based on your research question and data structure, recognizing that the chosen contrasts can affect your interpretation of the statistical results.