There were 3 trees, all three tree crowns were sampled at four heights, four directions, and three position(ouside,center,inside) respectively.There were totally 48 samples each tree.
Finally, those 148 samples were measured indoor for measuring value.
What kind of experiment design should I use to analyze the data?
Thank you so much！
Dear Dr. Di, Is it possible to learn your research question and research hypothesis (and perhaps the context of your research)? I think it is rather difficult to address your interesting question without these. Kind regards, I.H. (P.s. Is 148 not 144?)
More detail would be useful but this looks like a 4x4x3 (three-way) repeated measures ANOVA. This assumes that you have a continuous DV (though it may OK to use discrete DVs with our without transformation depending on the data).
See page 139 and page 147
http://staff.cs.psu.ac.th/ladda/subjects/344-592/chapter/Wiley.Interscience.Introduction.to.Statistics.Through.Resampling.Methods.and.Microsoft.Office.Excel.Jul.2005.pdf
see p129 of
http://www.resample.com/content/software/excel/userguide/RSXLHelp.pdf
You have partly paired data ie within the same tree, and unpaired data across trees. You could use a resampling method also known as a permutation method as explained in the above reference. This method as described in the references above originates from Fisher (1936) (Fisher RA. (1936). Coefficient of racial likeness and the future of craniometry. J R. Anthropol Inst, 66, 57–63). The method never took on till computers came along.
Essentially, you compare the configuration of the data you do have with other random configurations you could have had and thus derive the significance of your actual data.
The statistical package R could be used, or RSXL as described in various examples in the second reference. Resampling methods allow you to design tests for complicated data structures for which statistical tests may not exist and you do not need to worry about whether the data is normally distributed or not. However the method needs to be llearned and you do need software.
For Statistical package R see:
https://www.r-project.org/about.html
For RSXL see:
http://www.resample.com/download-excel/
The real question here seems to be are you comparing something across trees or within 1 tree three times? In other words, I agree with Dr. Horvath that you have not provided enough information. Helpful suggestion: If you ask this question prior to actually taking the samples, the probability of success goes up quite a bit. That is what statisticians are for. Rescue attempts are much more difficult.
The data set seems like mixed between-within subjects ANOVA (4 heights X 4 directions X 3 positions) replicated three times (3 trees). The key question here is which factor you would like to analyze with higher precision. Normally, the within factor is analyzed with higher precision than the between-factor. Therefore, it would be good to provide more information about your research questions and hypotheses, as stated by colleagues above, to suggestion the possible design for your data analysis.
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