Let's say we have a number of profile data arranged into main groups and each profile can also be separated into sub-profile groups. Then my question is which sub-profile group better describe the main grouping. I have tried the Permanova test (mainly because the data is highly non-normal) for each sub-profile group over the main grouping and recorded the value of the F statistic for each of them. Then I would say that the sub-profile group with the highest value for F is the answer to my question. However, what to do when, for example, two of those F are very close, say, 12.45 vs 12.47? Is there a way to statistically determine if the difference between these values is significant? I tried 10000 permutations in this test and all p-values were 10-4. Thanks for your time.
Well, F tests are about comparing variances. The basic problem here revolves around the question which sub-profile group better describes the main group. the various groups are undefined. E.g.Different clustering algorithms will give different groupings. Further what it means to best describe the main grouping is unclear. Perhaps when these issues are resolved the answer may become more clear about what if any test to use.. Best, David
Hello David, thanks for answering. Here is my attempt to clarify what I've done. The Permanova tests (or Anova) for each sub-profile group will compute a F value (F-test) using the information from the variances within and between the main groups. So, the F value somehow encodes a measure of the general main grouping (in simple words, the higher the F value the better for rejecting the null hypothesis), in this case for each sub-profile group of the data. In this way, I thought that I can compare these F values for each sub-profile group to determine which of them "better describe" the general grouping of the data. For this I need to compare different F-values, and I would like to know if there is a rigurous way to that because some of those F-values are very similar in many cases. Thanks.
Hello, I think you missunderstood the PERMANOVA method. The F-statistic and p-value computed for each grouping factor says only, if we can reject the hypothesis (assumption) about equal means in all groups created by that grouping factor. You cannot compare F-statistics for two different factors.
I still don´t understand your question: which sub-profile group better describes the main group. Provide some structure of your data, to clear what you want to do. PERMANOVA is not the right method, I think.
Hello Veronika. PERMANOVA is aimed to determine differences between groups when multiple response variables are measured. An F-statistic (like in ANOVA) is used to ultimately test the statistical significance of these differences. I just want to see if I can partition those multiple response variables into subgroups of variables (or dimensions), and find out which of those subgroups has the maximum difference between groups and the minimum difference within groups (which would reflect the subgroup of variables that "better" addapt to the grouping). If still a structure of the data is needed then you can imagine this: samples are counts for 1000 genes. Every sample was taken in multiple environments belonging to different biomes. Then imagine that those 1000 genes can be partitioned into 10 categories of 100 genes each. Then my question is what category would better predict the biome? For that I performed PERMANOVA tests using the 10 categories, and I thought that comparing the F-statistic value would answer my question (intuitively, the category in which the F-statistic was higher). Please correct me if I am wrong using this technique this way. Thanks again and best regards.
Hello, Salvador. If I have already captured your data right, then you had done 10 PERMANOVA tests, each with genes from only 1 gene-category to examine the differences between bioma-environments.
You can use PERMANOVA, but it won´t give you an answer to your question: what category would better predict the (type of) biome?
The only result would be, that there are significant differences in groups of "observed values" for different bioma for that particular gene-category (as a result from one PERMANOVA). But you cannot compare the 10 F-statistics you have, to get an answer, which category of genes predict the biome.
If the question is about the prediction of some value (which indicates the type of biome, or whatewer), then you can try Regression Trees, Logistic regression, etc. depending on the type of data you have.
If the question is about the dimension reduction (from 1000 genes = variables you want to create reasonable subgroups = 10 variables, which cover the most of the variability of the original variables), then you may use the Principal Components Analysis or Factor Analysis. And if you know, what the groups of genes should be, you can use Confirmatory Factor Analysis.
As David said, also cluster analysis can be used (creates clusters of genes, which have the small variability inside the clusters and big variability between clusters - puts similar genes together in some sense).
Best regards.
Hello Veronika. Thanks again for your answer. I understand what you say, however in general, regresion analyses, PCA (principal components analysis) and CCA (canonical or factor analysis) can only be used when euclidean distances can be defined. Unfortunately, euclidean distances are not meaningful in many biological situations for different reasons (I won't expand on this here unless necessary, but normally more appropriate ones are correlation-associated or cosine-related distances). Also, when you (and David) mention cluster analysis I wonder what statistical technique do you suggest? silhouette measure for example? well, I've tried those and also a more raw measure of cohesion and separation of clusters. However, none of these techniques provide hypothesis testing statistics for assessing how well the clustering has been done. That is why I've being trying to look for a way to compare those F-values coming from my different testings. Nonetheless, maybe you are right, I can't compare those values and so I wonder if there is another technique (hypothesis testing related) that I can use in this situation. Thanks again and best regards.
Salvador, I understand that you have some specific data, and therefore most of the classical approaches cannot be used. I just googled this:
Article Supervised Clustering of Genes
wouldn´t it be helpful to you? There is no Euclidean distance used.And to assess how well the clustering has been done - CVI (cluster validity indices) can be used for any type of clustering method. If you don´t know the true clustering (as I assume), the internal CVIs are used. I have no other ideas, maybe some other experts closer to biostatistics yould help.
Best regards.
Thanks Veronika, but I don't really need to cluster my data -- in fact I was very clear (despite my english I hope) that I have data already clustered so to speak. My question is the other way around, which is, given a grouping of the data, what subset of the variables can better describe the already predefined clustering or grouping. I wonder if can evaluate whether a predefined clustering or grouping of the observations (according to the biome of origin) is better described with one subset of the variables or with another. So I can use CVIs over this predefined clustering, and in fact I've done it, but I don't know any CVI associated to a statistic to assess the statistical support or significance of the result, which would be the subset of variables with the highest CVI. Best regards.
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Modeling
- Analyses of Variance
- ANOVA