# (3x4) 2way anova

#### ivn

##### New Member
Hi there. I have a problem with conducting the 3x4 anova test. I have two independent variables - data through 3 years divided into 4 seasons (spring, winter...). The dependent variable is the frequency of patients.

No matter in what statistical software I try to do the test, I always get the same - a nice plot with interactions, but no F test and p value. Can someone try to give an advice on what I am doing wrong?

In the attachment you can find the dataset and a plot which shows the problems I am facing.

#### Miner

##### TS Contributor
If you included an interaction term, you have a fully saturated model with zero degrees of freedom for the error term, which is used to calculate the F-statistic, which is used to determine the p-value. Since you probably cannot replicate this data, your only option is to remove the interaction term from the model. This will free a degree of freedom for the error term.

#### ivn

##### New Member
thanks, but... how can i do that?

#### ivn

##### New Member
although i am new to R, i tried to do this, and i managed to get some results, but i am not sure if this is correct.

Response: kalk$count Df Sum Sq Mean Sq F value Pr(>F) kalk$year 1 32.00 32.00 0.3039 0.5965
kalk$season 1 299.27 299.27 2.8424 0.1303 kalk$year:kalk$season 1 152.10 152.10 1.4446 0.2638 Residuals 8 842.30 105.29 #### Dason ##### Ambassador to the humans although i am new to R, i tried to do this, and i managed to get some results, but i am not sure if this is correct. Response: kalk$count
Df Sum Sq Mean Sq F value Pr(>F)
kalk$year 1 32.00 32.00 0.3039 0.5965 kalk$season 1 299.27 299.27 2.8424 0.1303
kalk$year:kalk$season 1 152.10 152.10 1.4446 0.2638
Residuals 8 842.30 105.29
Looks like you were treating year and season as continuous in this output. That is probably not what you want to do. You want year and season to be in R as 'factors'.

#### ivn

##### New Member
Thank you Dason, you're right.

I did it another time, but i'd like someone to comment on this. I wrote the test using the coding example from the website below:

https://personality-project.org/r/r.anova.html

> aov.ex2 = aov(klak$N.cases.~klak$season*klak$year) > summary(aov.ex2) Df Sum Sq Mean Sq F value Pr(>F) klak$season 3 877.7 292.56 7.179 0.0435 *
klak$year 1 32.0 32.00 0.785 0.4256 klak$season:klak$year 3 253.0 84.33 2.070 0.2470 Residuals 4 163.0 40.75 I am a bit confused with it. Can someone write the correct R code? Those results seem to be intuitively correct, because if I run a one way ANOVA for the klak$season, i get an p=0.0274 * and for klak\$year an p=0.63.

Is it appropriate to substitute the 2way anova for the 2 separate one way ANOVA if I cannont calculate the p value, because of the degrees of freedom?

#### rogojel

##### TS Contributor
Hi,
if you use + instead of the * in the function call, you get a model without the interaction term. Other then that your output seems completely ok to me, what is the problem with it?

regards
rogojel

#### ivn

##### New Member
The problem appears when using the same dataset in statistica and spss, because i don't get the p values and f test, mainly because of the reasons Miner said. That's why I'm not sure if the R results are correct