Having zero-values is not a problem for an ANOVA. But I think you actually have a different problem: what is the response variable? How are its values measured/determined? It is limited to positive values (like a concentration for instance)?  Is it discrete (like counts)? If so, ANOVA won't be a good choice.

Depending on the nature of your response variable you might better use a beta-, a gamma- or a Poisson-model, or maybe something completely different. Hard to say with the little information provided.

If all you are interested in is a p-value you might probably use a Kruskal-Wallis-Test. However, the result will be uninterpretable when the variances in the groups are different (what I strongly suppose).

Having zero-values is not a problem for an ANOVA. But I think you actually have a different problem: what is the response variable? How are its values measured/determined? It is limited to positive values (like a concentration for instance)?  Is it discrete (like counts)? If so, ANOVA won't be a good choice.

Depending on the nature of your response variable you might better use a beta-, a gamma- or a Poisson-model, or maybe something completely different. Hard to say with the little information provided.

If all you are interested in is a p-value you might probably use a Kruskal-Wallis-Test. However, the result will be uninterpretable when the variances in the groups are different (what I strongly suppose).

I agree with Jochen. I would add one thing though. Is the zero value a true zero? If it is really below detection limits, meaning it's in there, you just can't quantify it, you might want to use survival analysis. 

Hi guys,

Thanks for your thoughts. The response variable are numbers, so as Jochen pointed out an ANOVA it is not ideal. However, at least they are real zero, as it was an absolute absence of what we were counting. Would tranforming the data (to meet parametric assummtions) make it more correct to using an ANOVA, or it just better to explore other models? Thanks!

As Jochen pointed out zeros have no problem, but I do think ANOVA can be performed on counts but not on categorical data. Please see attached example

Transforming data unknowing the distribution of the real data is a "tricky" way to go. As it was said Zero values are not a problem for ANOVA analysis. In my opinion, the best way to be sure about if there are differences or not is checking all the posibilities, the amount of your values equal to zero is a important thing.

My advice:

1º Transform your dependent variable data in a dichotomic variable 0 or 1 and assess Chi-Square or Mc-Nemar analyses.

2º Perform non-parametric analyses like Jochen suggested.

3º perform ANOVA analyses (already done).

With all these results togheter, it should be clear is there is a significant difference.

Another important thing is your sample size: 5 treatmens x 4 replicates x 2 groups(at least) needs a important size of subjects to work.

Final advice, before you perform ANY statistical analyses after check the data, you should check the model assumptions of the model you will work on, otherwise you will be not making science but "fishing" a

A few possibly useful references here:

Elhai JD, Calhoun PS, Ford JD. Statistical procedures for analyzing mental health services data.Psychiatry Res. 2008 Aug 15;160(2):129-36. 

In mental health services research, analyzing service utilization data often poses serious problems, given the presence of substantially skewed data distributions. This article presents a non-technical introduction to statistical methods specifically designed to handle the complexly distributed datasets that represent mental health service use, including Poisson, negative binomial, zero-inflated, and zero-truncated regression models. A flowchart is provided to assist the investigator in selecting the most appropriate method. Finally, a dataset of mental health service use reported by medical patients is described, and a comparison of results across several different statistical methods is presented. Implications of matching data analytic techniques appropriately with the often complexly distributed datasets of mental health services utilization variables are discussed.

Comparison of methods for modelling a count outcome with excess zeros: application to Activities of Daily Living (ADL-s)

J Epidemiol Community Health 2011;65:3 205-210.

Khan A, Ullah S, Nitz J. Statistical modelling of falls count data with excess zeros. Inj Prev. 2011 Aug;17(4):266-70. doi: 10.1136/ip.2011.031740. Epub 2011 Jun 8.

Rose CE, Martin SW, Wannemuehler KA, Plikaytis BD. On the use of zero-inflated and hurdle models for modeling vaccine adverse event count data. J Biopharm Stat. 2006;16(4):463-81.

Lewsey JD, Thomson WM. The utility of the zero-inflated Poisson and zero-inflated negative binomial models: a case study of cross-sectional and longitudinal DMF data examining the effect of socio-economic status. Community Dent Oral Epidemiol. 2004 Jun;32(3):183-9.

I have a similar problem regarding zero value in experimental treatments.  We test 16 treatments of plant hormones in plant tissue culture assay. Five of 16 treatments have no results (not responses). If I eliminate unresponsive treatment  from population, can I conduct ANOVA  of the remaining treatments? help.

For what you have described, you cannot just drop these five treatment results - these are results - not 'non-response' in the research methods sense. You should have identified an analysis plan before the experiment started - as such, I would suggest you need to speak with your mentors locally to plot a way forward.