Two-way repeated-measures ANOVA?

[SylvainL]

Dear all,

A researcher came with this design of data and asked me which statistical test will be the most appropriate to see if the difference after treat ment between cells1 and cells2 is significant...

>mydata
    Cell Experiment Treatment Value
1  Cell1          1 untreated  4.41
2  Cell1          1   treated 17.60
3  Cell1          2 untreated  4.10
4  Cell1          2   treated 11.50
5  Cell1          3 untreated  5.21
6  Cell1          3   treated  7.84
7  Cell2          1 untreated  4.67
8  Cell2          1   treated  5.55
9  Cell2          2 untreated  4.23
10 Cell2          2   treated  5.41
11 Cell2          3 untreated  5.61
12 Cell2          3   treated  7.69

I have now to mention that I am not a statistician. After having a look, it seems that Two-way repeated-measures ANOVA would be the most appropriate test. Is it correct?

I set the model like this: Value ~ Cell * Treatment + Error(Experiment/Treatment)

and called

aov.out <- aov(Value ~ Cell * Treatment + Error(Experiment/Treatment), data=mydata)

> summary(aov.out)

Error: Experiment
          Df Sum Sq Mean Sq F value Pr(>F)
Residuals  2  7.056   3.528               

Error: Experiment:Treatment
          Df Sum Sq Mean Sq F value Pr(>F)  
Treatment  1  62.38   62.38   11.28 0.0784 .
Residuals  2  11.06    5.53                 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Error: Within
               Df Sum Sq Mean Sq F value Pr(>F)
Cell            1  25.52  25.521   2.882  0.165
Cell:Treatment  1  30.34  30.337   3.426  0.138
Residuals       4  35.42   8.855

But I am absolutely not sure about my model and I do not understand the output...

Thanks in adavance,

s.

[dpryan]

I personally wouldn't use a random effect for something like this, there aren't enough samples taken in each group for it to be of much use (IMHO, though I'm sure there's a paper with suggestions regarding this). I'd just:

summary(aov(Value~Experiment+Treatment*Cell, df))

Note that there's nothing that you can reasonably do to make the interaction p-value < 0.05, there's too much variance in cell1.

[SylvainL]

Hi,

So, to be sure, since what I want to see it whether the treatment as a different effect on the cell type, the pvalue I am insterested by is the Treatment:Cell. Is it correct?

> summary(aov(Value~Experiment+Treatment*Cell, mydata))
               Df Sum Sq Mean Sq F value Pr(>F)  
Experiment      2   8.13    4.07   0.515 0.6261  
Treatment       1  62.84   62.84   7.958 0.0371 *
Cell            1  23.58   23.58   2.986 0.1446  
Treatment:Cell  1  37.20   37.20   4.711 0.0821 .
Residuals       5  39.48    7.90                 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Which in this case is not

s.

[dpryan]

Correct. It's trending toward significance and might well get there, but more samples would be needed.