Question

If there is an overall significant F in a one-way ANOVA, can we conclude that the group membership or treatment variable cause the observed difference in the group means? Why or why not?

Answer 1

See the alternative for one way ANOVA is "At least one pair of treatments means are significantly different".

If we reject null hypothesis and so we accept the alternative hypothesis then we say that there is at least one pair of treatment means are significantly different.

This does not means the difference among all the treatment means. There may be some pairs of treatment which are not significantly different.

So the answer of this question is "We cannt conclude that the group membership or treatment variable cause the observed difference in the group means".