In an experiment with t 4 populations means consider
In an experiment with t = 4 populations means, consider the four linear combinations of those means.
l1 = μ1 – μ2 + μ3 + μ4
l2 = μ1 + μ2 – μ4
l3 = μ1 + μ2 + μ3 + μ4
l4 = μ1 + μ2 –μ3 + μ4
a. Which of the four linear combinations are contrasts?
b. Which pairs of contrasts are orthogonal?
c. Suppose we have two contrasts:
Is testing H0: l1 = 0 equivalent to testing H0: l2 = 0? Justify your answer.
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