Hello all!
I have some problems while analyzing my data using two-way ANOVA approach. I have 2 factors (one with 2 levels and the other one with 4 levels) with 3 repetitions in each factor combination. My response variable is the percentage of alive cells. However, only one factor combination gives only zero values (these ones are real zeros because I checked, in each repetition, the whole plates and I couldn't find any alive cell). Zero values don't appear in other factor combinations. Is it correct to perform 2 way ANOVA (parametric or non parametric) in this kind of data? Is there any alternative technique for dealing with this?
Thanks in advanced
If your data are "numbers of cells" (counted in some area of the plate), then you should use a model for count data (Poisson, negative-binomial, or quasi-Poisson). ANOVA is out then because the assumptions (normal distribution and variance homogeneity) are clearly not reasonable.*
To my knowledge, there is no way how you can test interactions of the factors in a meaningful way if you fall back on oder statistics (like many non-parametric tests would do). One non-parametric approach is to bootstrap the sampling distribution of the interesting statistics, but to work reliably this actually would also require a larger sample size. So there is no free lunch... with little data at hand, assumptions become important, and you should take care that these assumptions make sense.
---
* one might argue that these assumptions are not so important, because ANOVA is robust against deviations from these assumptions, but in your case you have a very small sample size (n=3 per combi) plus values close to zero (actually really zero!) plus a zero variance in at least one combi.
Statistic works with variation, in your case, for these combination of factors, you have a certainty. I would analyze separatedely the data, without this combination.
For future works you must to evaluate intermediate levels.
You said your data are proportions (percentages), some of which are zero. You didn;t say how many cells you're counting, in total, to get that proportion, which would be useful information.
Anova does sound a poor choice in those circumstances.
For proportion data, in principle, you can use a generalised linear model*; typically one uses a quasibinomial model with a logit link to include overdispersion, which is fairly common when there is biological variation in addition to sampling variation for counts.
I said 'in principle' because zero proportions - especially all zero in a given cell - are often be problematic even in that framework, as the best fit proportion for that cell will be zero and that messes up the likelihood. I'm afraid there isn't an easy cure for that. You could talk to a local statistician about Bayesian approaches ...
*Not 'general linear model', which is a term some stats packages use for any flexible linear modelling tool based on Normal assumptions.
Thanks @Stephen! I already tried what you suggested. However the fact that only one combination of cells is giving all zeros is messing up the model. I think I will do just some descriptive statistics considering that this is not the final experiment so I will fix the experimental design.
- Badges
- Science topic
- Similar topics
- Correction