We can obtain the sum of squares of a contrast for a regression of degree $j$ by: $$ SSR_j=\frac{\left(\displaystyle\sum_{i=1}^{I} C_{ji}T_i\right)^2}{rK_j}, $$

where $I$ is the number of levels of the factor, $r$ is the number of repetitions, $C_{ji}$ is the $i$-th coefficient for the $j$-th regression degree, $T_i$ is the total (sum of repetitions) of the factor level and: $$ K_j=\displaystyle\sum_{i=1}^{I} C^2_{ji}. $$

This works good for the case where the factor levels have the same number of repetitions (balanced). How should I proceed to estimate the $SSR_j$ for the case I have:

  • Means: 56.5000, 39.6667, 42.5000, 57.5833
  • N: 5, 6, 5, 5

for the linear, quadratic and cubic trends?



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