1 factor ANOVA

Discuss statistics related things
Post Reply
jamovi_user
Posts: 15
Joined: Mon Sep 26, 2022 8:41 am

1 factor ANOVA

Post by jamovi_user »

Can we (naively) think of the one factor ANOVA as a statistical method of analysis of levels of a single factor rather than as a statistical method for the analysis of "the differences among means" ?
Basically, what I mean is: Y ~ A, where A is a single factor with 3+ levels.
jamovi_user
Posts: 15
Joined: Mon Sep 26, 2022 8:41 am

Re: 1 factor ANOVA

Post by jamovi_user »

In my case the problem was in understanding what is the difference between "One-way ANOVA" and "ANOVA" menu entries.
the first one deals with testing let say: "What is the difference between conventional treatment, new treatment 1, and new treatment 2?"
The second helps to answer: "What is the difference between conventional treatment, new treatment 1, and new treatment 2 in females and males?"
That is: "One-way ANOVA" --- factor 1 with levels 1..3
That is: "ANOVA" --- factor 1 with levels 1..3, factor 2 with levels 1,2.
User avatar
jonathon
Posts: 2613
Joined: Fri Jan 27, 2017 10:04 am

Re: 1 factor ANOVA

Post by jonathon »

"one way ANOVA" and the "ANOVA" are the same procedure ... just we can provide more options in the "one way ANOVA" that don't apply where you have more than one factor.

jonathon
simonmoon
Posts: 17
Joined: Thu Oct 27, 2022 3:45 pm

Re: 1 factor ANOVA

Post by simonmoon »

It might be helpful if you understand the relationship between ANOVA and regression. ANOVA is a special case in regression. In regression terms, ANOVA with 2 group means is the same as saying that the DV is regressed on a dichotomous categorical predictor. The dichotomous predictor can be coded as 0 and 1 using dummy coding representing the two groups. If this predictor has a statistically significant effect on the DV, the DV value for 0 group is statistcally significantly increased to the DV value for 1 group. In ANOVA, this is the same as saying that the two group means are statistically significantly different.

(When you have more than 3 groups, there should be more than 1 code. But the basic principles in interpretations remain the same.)

The expressions we use in means comparisons such as ANOVA make more sense when we are focused on comparing group means. These expressions are a translated version of regression (or general linear model).
Post Reply