I have four different groups of independent samples with nonparametric data (low number of samples). To compare the frequency of data between groups, I used Kruskal-Wallis with Dunn post-test. In addition, I want to determinate the trend between groups. Which nonparametric test for trend should I use?
PS. Statistical software: Graphpad Prism
Jose, the sample size is neither indication nor contra-indication of any statistical analysis.(*) If you can reasonably assume a particular error model (**), then you can (and should) perform a parametric analysis. If you don't have such a model but you can reasonably assume that the (unknown) model is the same for all groups, then you can do a non-parametric analysis. If you cannot reasonably assume the same model for all groups, then there is nothing (sensible) you can do.
Further note that non-parametric tests have a considerably low power for small sample sizes. This also applies to any permutation- or bootstrap-based procedure.
(*) I suspect you mean that in small samples you can't expect the central limit-theorem to do a good job so that the frequency distributions of sample means is still considerably deviating from a normal distribution (so you can't use the normal distribution as error model). If your errors have a symmetric distribution, n=5 is already fine. Skewed distributions may cause problems and considerably larger sample sizes (n>30-50) are required to assure a reasonably good normal approximation.
(**) For frequencies, a Poisson model may be reasonable. If you doubt a strict correlation of mean and variance you can use a negative binomial model. There are also zero-inflated Poisson models available, when the expected frequencies of zero counts are higher than predicted from pure Poisson processes.
any type of permutation test might be useful - there were recently a few questions on permutation, so check them out. Otherwise, I don't know Graphpad Prism at all - in R and PRIMER you could also do ANOSIM instead of the Kruskal Wallis and Dunn post hoc test. What exactly do you mean by trend? Development over time or space? If you are ok with a visualization, MDS based on a reasonable distance measure might work for biotic data, and PCA (Euclidean distance) for most abiotic data. It is possible that GraphPadPrism does not easily allow for these multivariate analyses ..
Is it necessary to insist on nonparametric testing? Isn’t it possible to transform data and use parametric analysis? How large your sample is? I’d recommend using parametric tests, something like a general regression model which allows you more sophisticated analysis of residuals.
I work with a low number of data between groups, then I can't make a parametric analysis. When I say trend, I mean a trend to increase (or reduce) of the data median between different groups, for example, I observed an increase data median in the last group compared with the first group. I work with frequencies of cells from patients with different degrees of disease severity in one moment in the time, I want to assess the trend between this groups of patients.
Thank for your help.
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Statistics
- Statistical Software