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Table 3 Contrast coefficients for the balanced design with four exposures groups

From: Trend tests for the evaluation of exposure-response relationships in epidemiological exposure studies

Type of contrasts No. of contrasts Alternative Contrast c j
Isotonic 2k-1 π 1 <π 2 = π 3 = π 4 {-3 1 1 1}
   π 1 = π 2 <π 3 = π 4 {-1 -1 1 1}
   π 1 = π 2 = π 3 <π 4 {-1 -1 -1 3}
   π 1 <π 2 <π 3 <π 4 {-3 -1 1 3}
   π 1 = π 2 <π 3 <π 4 {-1 -1 0 2}
   π 1 <π 2 = π 3 <π 4 {-1 0 0 1}
   π 1 <π 2 <π 3 = π 4 {-2 0 1 1}
Change point k-1 π 1 <π 2 = π 3 = π 4 {-3 1 1 1}
   π 1 = π 2 <π 3 = π 4 {-1 -1 1 1}
   π 1 = π 2 = π 3 <π 4 {-1 -1 -1 3}
Up/down 2 π 1 <π 2 = π 3 = π 4 {-3 1 1 1}
   π 1 = π 2 = π 3 <π 4 {-1 -1 -1 3}
Single (linear) 1 π 1 <π 2 <π 3 <π 4 {-3 -1 1 3}
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