Trend Analysis (3 of 5)

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The quadratic component of trend is used to test whether the slope increases (or decreases) as the independent variable increases. Components of trend beyond the quadratic are not usually psychologically interpretable. The cubic component, for example, tests whether the slope changes twice (decreasing and then increasing or increasing and then decreasing) as the independent variable increases.

Trend analysis is computed as a set of orthogonal comparisons using a particular set of coefficients. Coefficients for the linear, quadratic, and cubic components of trend are given below:
2 means
Lin   -1  1
 
3 means
Lin   -1  0  1
Quad   1 -2  1
 
4 means
Lin   -3 -1  1  3
Quad   1 -1 -1  1
Cubic -1  3 -3  1
 
5 means
Lin   -2 -1  0  1  2
Quad   2 -1 -2 -1  2   
Cubic -1  2  0 -2  1
 
6 means
Lin   -5 -3 -1  1  3  5    
Quad   5 -1 -4 -4 -1  5
Cubic -5  7  4 -4 -7  5
 
7 means
Lin   -3 -2 -1  0  1  2  3
Quad   5  0 -3 -4 -3  0  5 
Cubic -1  1  1  0 -1 -1  1
 
8 means
Lin   -7 -5 -3 -1  1  3  5  7
Quad   7  1 -3 -5 -5 -3  1  7
Cubic -7  5  7  3 -3 -7 -5  7
 
9 means
Lin    -4 -3  -2  -1    0    1   2   3   4
Quad   28  7  -8  -17 -20  -17  -8   7  28
Cubic -14  7  13   9    0   -9  -13 -7  14
 
10 means
Lin    -9 -7 -5 -3 -1   1   3   5   7   9
Quad    6  2 -1 -3 -4  -4  -3  -1   2   6
Cubic -42 14 35 31 12 -12 -31 -35 -14  42

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