I'm trying to use repeated rounds of ANOVA to sort a large dataset into different categories. For each element in the dataset I have twelve data points which represent three replicates each of four conditions, which arise as two combinitions of two variable1. The data is some relative expression compared to a control, which means that for the control itself all twelve values are 1:
>at
v1 v2 values
1. a X 1
2. b X 1
3. a X 1
4. b X 1
5. a X 1
6. b X 1
7. a Y 1
8. b Y 1
9. a Y 1
10. b Y 1
11. a Y 1
12. b Y 1
which I analyze this way (the Tukey wrapper gives me Information about whether it is up or down in addition to whether it is different, which is why I'm using it):
stats <- TukeyHSD(aov(values~v1+v2, data=at))
> stats
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = values ~ v1 + v2, data = at)
$v1
diff lwr upr p adj
a-b 4.440892e-16 -1.359166e-16 1.024095e-15 0.1173068
$v2
diff lwr upr p adj
X-Y -4.440892e-16 -1.024095e-15 1.359166e-16 0.1173068
I expected the p value to be very close or equal to 1 since clearly the null hypothesis that the two groups of both of these tests are the same is correct. Instead the p-value is very low with 0.117! Clearly the difference and the bounds are tiny (e-16) so I'm guessing the problem is to do with the internal storage of the numbers as slightly off 1, but I'm not sure how to solve the problem. Any suggestions? Thanks a lot!
I'm adding some sample data:
aX1 bX1 aX2 bX2 aX3 bX3 aY1 bY1 aY2 bY2 aY3 bY3
element1 0.112 0 0.172 0.072 0.058 0.055 0 0 0.046 0 0.042 0
element2 0.859 0.294 0.565 0 0.669 0 0.11 0 1.707 0 1.324 0
element3 1.255 0.721 3.645 1.636 5.36 6.701 0 0.097 0.533 0.209 0.358 2.219