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I performed with SAS an ANOVA and I got insignificant differences for each coefficient. So I planed to looked at the linear and quadratic effects of the Ca concentration (6 levels), and the linear was not significant, but the quadratic was. I remember for multiple comparison, it is always require an significant model to do the next step.

Is it the same situation for orthogonal contrast? Does it makes sense to have significant contrast effects but no main effects?

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Yes, you can have orthogonal tests that come out significant even in the face of nonsignificant omnibus. Technically, if you perform the omnibus you didn't have that trend as a hypothesis in mind a priori, so you should have stopped and not conducted the test. Alternatively, if you predicted that trend, you should have jumped right to that contrast without performing the omnibus.

But those are the 'stats playbook' rules that nobody follows because it's too easy to perform every allowable test. You might at least interpret the p value with bonferroni correction.

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