## 2x2 factorial design anova

Occasional Contributor
Posts: 5

# 2x2 factorial design anova

Hello, I am a beginner with SAS, and I am a graduate student who is stuck on a data analysis problem. I have 2 sets of data. Both sets are in a 2x2 design. I have four treatments that I am comparing, with 3 repititions. I previously ran the repeated measure ANOVA, but I am supposed to find the replication interaction.

My data looks like this-What is the input to compare the 4 treatment Salmonella count while also assessing if the 3 replications had an impact? I have another set of data with the same set up, but instead of salmonella count, the result is a positive or negative. My question is if I ran multiple Fisher tests, is there a way to assess the impact of the replication?

Treatment   Rep     Egg Number    Salmonella Count

1                  1                        1                         3.2 Log CFU/mL

1                    2                      1                         2

1                   3                        1                         3

2                  1                       1                            3

2                     2                       1                        2.2

2                     3                      1                         1

3                    1

3                    2

3                    3

4                   1

4                  2

4                  3

Posts: 2,055

## Re: 2x2 factorial design anova

"replication interaction"?

Normally, replication is treated as a RANDOM effect, and so it doesn't interact with other things. You would get an estimate of the variability due to replication, combined across all four of your treatments.

So, if that's what you want, then try the following (untested code)

``````proc glm;
class treatment;
model salmonella = treatment;
run;
quit;``````

The error sum of squares is the variability sum of squares due to the replication. If it is small, then the replication has caused little variability in your data.

If you want something else, please explain in more detail.

--
Paige Miller
Occasional Contributor
Posts: 5

## Re: 2x2 factorial design anova

Thank you, I think that answers my question. Would your answer change at all if I told you the initial inoculum concentration to inoculate the eggs was slightly different between repititions?

Posts: 2,055

## Re: 2x2 factorial design anova

If you have recorded this initial concentration, then yes, you could make use of it in the analysis. Since I don't really have a background in this subject matter, I can't really be specific, but maybe you can. How does a change of initial concentration affect the output measurement of salmonella count?

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Paige Miller
Occasional Contributor
Posts: 5

## Re: 2x2 factorial design anova

I am not entirely certain, but I believe an increase in inoculum concentration should increase the number of surviving Salmonella cells on the egg, to a certain point. However, in my experiment, the 3 inoculum concentrations were intended to be as similar as possible. I found this paper on the topic- http://www.sciencedirect.com/science/article/pii/S0956713512002563

Posts: 2,055

## Re: 2x2 factorial design anova

I haven't read the article, but if the effect of changing this concentration is linear on the final salmonella measurements, then this is relatively easy to incorporate into the analysis. If the effect is non-linear and known, we could also incorporate this into the analysis. If the effect of changing concentration is unknown, then it could be difficult to use.

Also, some people would just lump this changing of concentration into the variability due to replicates.

--
Paige Miller
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