It it legitimate to apply a one-way ANOVA to data that have been normalised to the untreated controls? I was wondering if it is OK to use one-way ANOVA after normalisation to the untreated controls? This is in an animal model of wound healing where there are 4 wounds per animal, one untreated and 3 treated with different drugs. I have noticed that the healing rate differs between animals so in order to reduce the standard deviation and account for the inherent healing rate in the animals I normalise the data to the untreated controls in each animal so that the controls = 1. This means that they don't have a SD. Is it still OK to use one-way ANOVA or would there be a better test to use?
 A: It depends on what you want to find out. 
One possible case where it would work: You want to find out whether a certain drug treatment is better than the control. In this case you could take the (normalized) values for that treatment and do a single-sample t-test vs. 0. Even in this case you pay for the reduced variability by having less degrees of freedom. But this is a trade-off that is usually worth it.
However, you probably want to compare the different treatments against each other. In this case, normalization to control can be also be an adequate way to deal with the variation on the animal level. What you absolutely avoid is to have a control group in your ANOVA model which you normalized to have standard deviation of zero. This violates basically every assumption that ANOVA does.
So, one option would be to normalize to control and then perform paired t-tests for one drug vs. another drug. However, as said above if you want to test against controls do not use constant ones as the values for the control group, instead test against the fixed value of one.
This means you can use the normalized values and get sensible answer, but don't use an ANOVA but a method that is aware of which wounds belong to which animal. The most elementary of these is the paired t-test, which is why I suggested it.  
My suggestion is to either look into Mixed Models or Repeated Measure ANOVA, however. This would lead to a single model in which you can look at all the contrasts and will even give you information on large the animal level variation actually is.
A: Let me stress some points of the answer given by Erik: 
a) you do not want one-way ANOVA, you want a repeated measure ANOVA. Each animal makes the "pairing" of the data for each treatment.
b) normalization is not the standard way to deal with your data. Just use the repeated measure ANOVA for the 4 columns. If the standard deviations are too different than you should use the non-parametric version of the repeated ANOVA, the  Friedman test 
c) normalization will not allow you to compare the control with the other treatment, and it may reduce the differences on the standard deviations, but it may not - you still have to check it.
