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# One-way ANOVA vs two-way ANOVA

Dear team,

I would like to ask for your clarification about the different results of one-way ANOVA and two-way ANOVA for the same factor.

At first I applied one way ANOVA with variable x, and I got significant results.

After that, I applied two-way ANOVA with variable x and variable z, now there are three values in the output:

1. variable x: it changed to be NOT significant.
2. variable z: not significant
3. variable x * variable z: not significant,

Is this expected? should not the results for variable x be the same in both one-way and two-way ANOVA?

Best Regards,

Sameha

• edited November 2021

No. The results may not be the same, especially if you have unequal group sizes. For example, the mean response value for Condition X1 could be different when all response values in X1 count equally, versus when X1 consists of a large subgroup (X1Z1) and a small subgroup (X1Z2) making each value in X1Z2 count more than each value in X1Z1. Put differently, when there are two factors X and Z, the estimated marginal mean for the values in X1 is not the mean of those values. Instead it is the mean of two means: X1Z1 and X1Z2.

R

• Thank you andersony3k for the clarification. From my reading to get further details on your clarification, i found that the variable mean can be calculated using either "weighted mean" or "unweighted mean" method. would you know when to use either of them? and which method does JASP use?

Thank you,

Sameha

• Hi. Perhaps you should take a look at this . . .

R

• Thank you andersony3k ..It was a helpful resource!