Page's Trend Test for Ordered Repeated Measures

Page's trend test checks whether k repeated measurements per subject increase in a predicted order, using L = sum of j times the rank sum of the j-th treatment.

Page 추세 검정은 대상마다 반복 측정한 k 조건이 예측한 순서대로 커지는지를 L = Σ j × (j번째 조건의 순위합) 으로 검정하는 방법입니다.

Each participant was measured under three conditions that I expect to increase in order; can I test that ordering directly?

참가자마다 세 조건에서 측정했고 순서대로 값이 커질 거라고 예상했는데, 그 순서를 직접 검정할 수 있나요?

Rank the conditions within each subject, multiply each condition's rank sum by its predicted position and sum to get L, then compare L with its exact distribution or the normal approximation. A large L supports the predicted ordering more strongly than a Friedman test would.

When to use Page's Trend Test for Ordered Repeated Measures

• The same subjects or blocks are measured under three or more conditions.
• You predicted the order of the conditions before seeing the data.
• The outcome is ordinal or not normally distributed.

When to use something else

• There is no predicted order; use the Friedman test instead.
• The groups are independent rather than repeated; use the Jonckheere-Terpstra test instead.

Assumptions and requirements

• Blocks are independent of each other.
• Within each block the observations can be ranked; ties receive average ranks.
• The predicted order is fixed in advance.

What the analysis reports

• Page L statistic
• Exact or normal-approximation one-sided p-value
• Rank sums and mean ranks per condition
• E[L], Var[L] and z

How to report it

Page's trend test supported the predicted ordering of the [value] conditions across [value] participants, L = [value], p = [value].

Related methods

• Friedman Test
• Jonckheere-Terpstra Trend Test
• Mann-Kendall Trend Test with Sen's Slope

Run Page's Trend Test for Ordered Repeated Measures on Quorant