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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?

Erik
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Katie Heath
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2 Answers2

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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.

Erik
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  • Thanks Erik, that's really helpful. I has a hunch there was a problem but couldn't work out the solution. I'm now buried in "Biostatistics - the bare essentials" in the chapter on Repeated Measure ANOVA. Hopefully this will be the sophisticated solution I was after. I'm trying to see whether any of the treatments enhance wound healing in comparison to no treatment and if so which treatment is significantly better than the others so I suspect the Repeated Measure ANOVA is the way forward, I just need to get my head round it. Thanks so much for your response I really appreciate it! Katie – Katie Heath Feb 18 '13 at 14:56
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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.

Jacques Wainer
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  • Actually I have often seen that kind of normalizing done with both animal trials and cell culture experiments. I agree that it shouldn't be the standard way. – Erik Feb 18 '13 at 15:24
  • Hi Jacques, many thanks. I was trying to use normalisation to account for the fact that some mice seem to heal much faster than others (despite being the same strain) not to make the data fit normal distribution. I had been using Kruskal-Wallis for non parametric data then using a post-hoc test too (usually Dunnett's). Is that incorrect too? It's such a minefield and we really don't get taught this stuff very well in the biological sciences. Many thanks again, Katie – Katie Heath Feb 18 '13 at 15:27
  • Katie. By using Kruskal-Wallis you are loosing (I believe) a "lot of power" because you are not using the paired/within-subject nature of your data. As for post-hoc tests, if you are going to use a paired/within-subject omnibus test (such as Friedman) you should use a paired/within-subject post hoc. I myself did not know about them, and I posted [this question](http://stats.stackexchange.com/questions/33262/what-are-the-possible-multiple-comparison-methods-for-paired-data). [This question](http://stats.stackexchange.com/questions/10309/friedmans-test-and-post-hoc-analysis) also discusses it. – Jacques Wainer Feb 19 '13 at 02:14
  • OK, thanks Jacques, I'll check it out. Presumably, if I I were testing 6 treatments, 3 per animal, two groups of animals I would have to analyse the two groups separately? Sorry if that's a daft question but I am so tired I can barely think straight... – Katie Heath Feb 19 '13 at 13:11