How are you measuring "contribution" ?

Well dear friend, those are the weird questions of the ResearchGate. Do not complicate the subject.

In the ANOVA analysis, the p-value, depending on whether the subject of the analysis are two or more factors with multiple modalities, confirms us whether we will accept or reject the hypothesis that is pre-set. So, the p-value does not serve us to determine which of the factors or modalities of these factors are more influential or more significant.

Abolfazl Ghoodjani , it's not complicating. It's simple clarification.

"Contribution" could be measured by partial eta-squared or by some other way to assess a change in r-square. Or, "contribution" could be measured by the size of the beta coefficients from the regression. Or "contribution" could be measured by sum of squares or by F value.

Each of these could have a different answer.

My dear friend, I did not say this is a complicated matter. I said, do not complicate the matter. Incidentally, the issue is simple.

The issue is not simple, because the question is not clear. Depending on what measurement the OP is looking at for contribution, the answer is likely to be different.

In this particular case, the question is specific to the Minitab output for multiple regression.

"Contribution" in this output is calculated as the percent of sequential sum of squares attributed to that factor. On the other hand, the F value and p value are calculated by what Minitab calls "adjusted sum of squares" , which I believe to be the Type III sum of squares.

These two types of sums of squares are different. I find it strange that these two are listed in the same output table.

So there is not necessarily a correspondence in this output between "contribution" and the F and p values.

You could calculate a "contribution" for the "adjusted sum of squares" if you wanted. But the values won't add up to 100%.

But I would recommend looking up eta-squared and partial eta-squared.

See: https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/regression/how-to/fit-regression-model/interpret-the-results/all-statistics-and-graphs/analysis-of-variance-table/#contribution