# Two-Way ANOVA without raw scores

#### Alsvartr

##### New Member
Hey,

I need to be able to perform a two-way ANOVA without raw data - i.e. with only means, standard deviations and sample sizes available.

Following the information given here I can do everything I need apart from the within variance calculation (sum of squares within), as the formula given there requires raw scores. I've looked around everywhere for a solution but to no avail.

Can anybody help?!

#### Dragan

##### Super Moderator
Hey,

I need to be able to perform a two-way ANOVA without raw data - i.e. with only means, standard deviations and sample sizes available.

Following the information given here I can do everything I need apart from the within variance calculation (sum of squares within), as the formula given there requires raw scores. I've looked around everywhere for a solution but to no avail.

Can anybody help?!

I don't understand what your problem is. That is you say that " I can do everything I need apart from the within variance calculation (sum of squares within)"...

Well, if you've determined the SSa, SSb, SSaxb, and SStot, then it follows that:

SSw = SStot - (SSa + SSb + SSaxb).

#### Alsvartr

##### New Member
OK, so I don't have everything I need. Do you know a way to calculate either the SStot or SSw?

#### Dragan

##### Super Moderator
OK, so I don't have everything I need. Do you know a way to calculate either the SStot or SSw?

Yes - sure. Just take each cell variance (I believe you say you have the standard deviations - square these values) and multiply each by the associated df = sample size -1. This gives the sums of squares (SSij) for each cell. Thus, SSw = SS11 + SS12 + SS21 + SS22.

#### Alsvartr

##### New Member
Great, thanks very much! That seems to work...I tried it on the example given in the link I gave in my first post, and bizarrely it was 1 out (I got 37, they got 38) but I tried it on another data set and it was spot-on. Must be a typo on the other one.