Very low N's in the two last groups gives you very low power. That's a problem.

Concerning analyses: You seem to have variables on a continous measurement level, then a parametric (ANOVA) or a non-parametric test (Kruskal-Wallis) should be used. You should check each variable with descriptive analyses first (e.g., check for normality). Some variables in your example could/should be transformed before analyses (e.g., log transformation).

(see for example Field (2013): Discovering Statistics using IBM SPSS - chapt 5.4 - Transforming data)

Best

John-Kåre

I personally used SAS procedure PROC GLIMMIX for unequal sample size for different treatments. Great tool for the unequal sample size scenario and also accounts for non-normal distributions.

Hi Laurel,

Here are some suggestions based on considering the "Example.xlsx" as if it was the real McCoy. It would seem that your behavior data is continuous, but are you interested in differences in means or variability or some other aspect for comparison of the treatments?

If you are interested in mean differences you should try variance analysis (ANOVA). You would first need to find a suitable transformation that makes your data useful for the analysis. In your case, e.g. the square root transformation seems to work quite well. If you 1) square root transform the data, 2) perform Welch's robust ANOVAs (R has function "oneway.test" in the car-package; use the var.equal=FALSE option) and 3) check normality of the residuals (R has functions "skew" and "kurtosi" in the psych-package), you will find that the assumptions the tests are approximately fulfilled (check that the skew and kurtosis are at least below 2 in absolute value, preferably even smaller), but also that none of p-values of the comparisons are statistically significant (at the 0.05 level of significance).

If you wish to compare ranked distributions (means of ranks), you can try the Kruskal-Wallis non-parametric test (function "kruskal.test" in R-package stats), but the Example data this seems to yield similar results to the ANOVAs.

If you wish to test equality of medians, you can use the median test (function "Median.test" in the R-package agricolae), which seems to yield one significant result for behavior 8 (p = 0.039).

Other tests can also be used, if you are interested in some other aspect of the distributions, but if this is the case let us know a little more about the research setting. I listed three test above, but it is good to keep in mind that the test should not be chosen based on e.g. the fact that the median test seemed to produce one statistically significant test result and the others did not. Instead the choice should be based on what is best for your research question and the information content of the variables (scale of measurement).

One final point to note concerns multiple testing. No matter which test you select to use, for the Example data you would be performing 12 tests, so you would generally make a correction this many tests. For example, with the Bonferroni correction you would consider a finding statistically significant at the 0.05-level of significance, if the p-value was below 0.05/12 = 0.0041667.

As a conclusion it seems that there is a lot of variability in the measures relative to the small sample size of the study, which translates to low power for the tests. If this were you real data, you could use these results for proposing a larger study and calculate the approximate sample size needed to find significant results, if the group data is representative of the target groups.

Best regards,

Timo Törmäkangas

Just to add to what Timo Törmäkangas has very beautifully summed up. If you are using SPSS it has an option of using Welch ANOVA as well.

Hello Laurel. Please clarify what "entire behavior budget" means. Does it mean that you want to include all 12 behavior counts in a single model (i.e., with type of behavior as a repeated measures factor)?

To other followers, please note that Laurel has listed JMP as a topic. I gather that is means JMP is the only software she has available. (But Laurel can clarify if she has other options.)

HTH.

@Bruce: In the original post she does mention R, too.

Thanks Timo Törmäkangas, I missed that R was mentioned.

Hi! Yes, I have both R and JMP as options. I just finished an R-intensive course so R is on my brain at the moment--but I'm happy to use either. Timo Törmäkangas Thank you for your thought out and reasoned response! This is just a subset of my data - it is an ongoing project that will have multiple years of data. However, since the results have the potential to affect management of the focal animals we wanted to begin analysis early to be sure that there wasn't anything drastic happening that needed to be addressed immediately.

In terms of ANOVA, I do have to take into account repeated measures (we are observing the same individual under different treatments). The only way I have figured out how to do this in R is to run a lmer model.

Either way, as this is only the first iteration of this project it was more of an exploratory pilot project. I can happily say that I will end up pooling my data and creating much more robust (but still ecologically and biologically valid) data-sets.

Thank goodness!

Thanks everyone for their input!

Try iteration