# Quick one please: Difference between 1-way and 2-way ANOVA - Example provided

#### Sagan_24

##### New Member
Hello, I apologize in advance if this is too simple for these forums, but I am just wanted to be very sure.

Example:

A study that looks at 2 sleep treatments and their effect on 1) how long they think they slept, 2) how rested they feel, 3) how alert they are, 4) how good their sleep was

There will be 2 groups (Group A getting treatment 1 and Group B getting treatment 2).

My questions:

1) What makes this NOT an ANOVA?

2) What would make it a 1-way ANOVA?

3) Most important: For the above example, would you say that "Sleep Treatment" was the Independent Variable, and the two sleep treatments used are the "Levels" of the IV? Or, would Treatment 1 be its own independent variable, and Treatment 2 be its own independent variable??

4) What would make this a 2-way ANOVA?

Me taking a crack at my own questions:

1) Its not an ANOVA because there is only two groups, so therefore, we can just run a T-test?

2) To make it a 1-way ANOVA, we would JUST add another group?

3)?????

#### Karabiner

##### TS Contributor
1) What makes this NOT an ANOVA?
2) What would make it a 1-way ANOVA?
I might be missing something, but this looks like a silly question.
One can perfoam a oneway-ANOVA with 2 groups. It is absolutely
equivalent to a t-test.

4) What would make this a 2-way ANOVA?
If you had 2 factors, e.g. treatment A yes/no and treatment B yes/no
and combined them, resulting in 2x2 groups (A+B, A-only, B-only, none of them).

Just my 2pence

K.

#### noetsi

##### No cake for spunky
One way Anova = ttest for two levels

If this is one way ANOVA than for 3 it has to be two levels of one IV. If you have two IV than you don't have one way ANOVA anymore....

The way to make it two way ANOVA, would be to test both treatments [you would have to do this at different times or on different people in a matched population so it would be a complex design]. More generally you need to have more than one IV.

#### janessa642

##### New Member
One way Anova = ttest for two levels

If this is one way ANOVA than for 3 it has to be two levels of one IV. If you have two IV than you don't have one way ANOVA anymore....

The way to make it two way ANOVA, would be to test both treatments [you would have to do this at different times or on different people in a matched population so it would be a complex design]. More generally you need to have more than one IV.
yeah.. you are right

#### CB

##### Super Moderator
yeah.. you are right
This post was flagged as spam in our moderation queue. I've released it now, but in future please try to ensure your posts actually add something of value, otherwise it's unclear to us whether you're actually a real person.

#### GretaGarbo

##### Human
If you had 2 factors, e.g. treatment A yes/no and treatment B yes/no
and combined them, resulting in 2x2 groups (A+B, A-only, B-only, none of them).

Just my 2pence

K.
But you can put the two factors together in just one factor with four levels (A+B, A-only, B-only, none of them). Then you will have a one-way-anova (analysis of variance) with four levels.

An if you also have several measured dependent variabels you will ha a multivariate one-way-anova.

Another 2-pence.

#### rogojel

##### TS Contributor
But you can put the two factors together in just one factor with four levels (A+B, A-only, B-only, none of them). Then you will have a one-way-anova (analysis of variance) with four levels.
This gave me a start why would I ever use a two-way ANOVA then? But i think adding the levels together into a single factor would be a bad idea - I can not figure out the effects of the individual factors and have definitely no way of checking for interactions -right?

#### GretaGarbo

##### Human
This gave me a start why would I ever use a two-way ANOVA then? But i think adding the levels together into a single factor would be a bad idea - I can not figure out the effects of the individual factors and have definitely no way of checking for interactions -right?
The advantage with a two-factor layout is that you can estimate (the intercept and) the main effect for A, the main effect of B and the interaction effect. Maybe the experiment can be described by just the intercept and the two min effects. That is an advantage especially if the layout is 5 levels of A and 6 levels on B. Then you only need to estimate the intercept and (5-1) parameters for the main effect for A and (6-1) parameters för the main effects for B. That is 10 parameter to estimate instead of the full model with 5*6 = 30 parameters.

In the 2x2 layout you can estimate the intercept, the two main effects and the interaction effect. Four parameters. That will give exactly the same values as if the four cell means had ben estimated in a one-way-anova.

But if there is an imbalance in the design (i.e. not the same number of observations in each group) then I think that less confusion is caused by using a one-way-anova.

Maybe this could be of some help for the original poster. But I guess that we have lost her a long ago.