Planned Contrasts and Polynomial Trend Analysis

Planned contrasts test pre-specified weighted combinations of group means, and polynomial trend analysis uses orthogonal polynomial weights to test linear, quadratic and higher trends across ordered groups.

계획 대비는 미리 정한 가중치로 집단 평균의 조합을 검정하고, 다항 추세 분석은 직교다항 가중치로 순서 있는 집단의 선형·이차 추세를 검정하는 방법입니다.

I predicted that scores rise steadily across four dose levels; how do I test that specific pattern instead of a general ANOVA?

용량 네 단계에서 점수가 꾸준히 오를 거라고 예상했는데, 일반 분산분석 말고 그 패턴만 직접 검정하려면 어떻게 하나요?

Specify a contrast whose weights encode the predicted pattern, or request a linear trend, and test psi = sum c_j * mean_j against its standard error from the pooled error term. If the group variances differ, use separate variances per contrast with Welch-Satterthwaite degrees of freedom.

When to use Planned Contrasts and Polynomial Trend Analysis

• You have specific comparisons or a predicted ordering stated before seeing the data.
• Groups form an ordered factor such as dose, grade or time point and you want linear or quadratic components.
• You want more power than an omnibus ANOVA followed by all pairwise tests.

When to use something else

• You want to explore all pairwise differences after the fact; use Tukey HSD or Games-Howell instead.
• The groups have no meaningful order and no prior hypothesis; use one-way ANOVA instead.

Assumptions and requirements

• Independent observations within and between groups.
• Approximately normal residuals within groups.
• Equal group variances for the pooled version; otherwise use the Welch option.
• Contrast weights sum to zero and are chosen in advance.

What the analysis reports

• Contrast estimate psi with standard error, t, df, p and 95% CI
• Orthogonal polynomial coefficients for each trend order (using numeric group values as spacing when available)
• Sum of squares and share of SS between for each contrast
• Deviation-from-trend F test computed by n-weighted regression of the group means
• Holm-adjusted p for reference

How to report it

A planned linear trend contrast was significant, psi = [value], 95% CI [[value], [value]], t([value]) = [value], p = [value], while deviation from linearity was not, F([value], [value]) = [value], p = [value].

Related methods

• One-Way ANOVA
• Jonckheere-Terpstra Trend Test
• Dunnett's Test

Run Planned Contrasts and Polynomial Trend Analysis on Quorant