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## Two-Way (Factorial) ANOVA

Good afternoon,

I performed a factorial experiment and obtainded a not significant ANOVA.

But on the Effect test one factor is significant.

How can I interpret the results? Wich results I have to consider correct? ANOVA (Prob > f) or EFFECT TEST?

Thank you 4 REPLIES 4

## Re: Two-Way (Factorial) ANOVA

Both of these tests are correct. They are two different tests.

The F-test in the Analysis of Variance tests the whole model. It compares the full model (all terms present) to the reduced model (intercept only). The F ratio is the mean model sum of squares divided by the mean error sum of squares. It is concluded in this case that the full model is not statistically significantly different from the reduced model using alpha = 0/05.

The F-test in the Effect Tests tests individual terms. It compares the full model to a reduced model without the given term but conditional on the other terms being present. The F ratio is the (term sum of squares divided by the numerator degrees of freedom) divided by the mean error. It is concluded in this case that the TAGLIO term is statistically significantly different from zero using alpha = 0.05.

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## Re: Two-Way (Factorial) ANOVA

You could first remove the crossed term for the interaction effect and re-examine the regression results. You could likely also remove the CONC term for the main effect and re-examine the regression results. At this point the whole model is simply TAGLIO, so that F-tests In the Analysis of Variance and the Effect Tests must be the same.

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## Re: Two-Way (Factorial) ANOVA

Thank you so much for your answer,

but I still didn't get it.

Can i still conclude (with ANOVA not significant) that I have significant effects of TAGLIO?

Thank you.

## Re: Two-Way (Factorial) ANOVA

Yes.

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