I study behavior in C. elegans, and it is nearly impossible to control and account for the many factors that might influence behavior (temperature, age, time of day, humidity, vibration, etc, etc). If one or more of these factors has a particularly strong effect, then we are blind to it (mostly for practical reasons). As a matter of protocol, we always collect data on multiple days and combine into a single sample collection. So multimodal distribution in our sample wouldn't be surprsing, but I would consider it a consequence of technical limitations and not "real" biology for the specific behavior I'm studying. Based on published studies and my own experience with the specific behavioral assay (a populaiton-based chemotaxis assay), the data are generally normally distributed (as best as I can tell - haven't been motivated to test for normality, but suspect the data would pass as normal for the majority of samples). As such, the evidence appears to show that the data are normally distributed, and this is the assumption I make when choosing statistical tests. (Note: I use "sample" here as used in statistics, i.e., collecting a sample from a population to make inferences about the population...not to be confused with its use in most biomedical research settings where a "sample" represents collection of a single specimen.) My N is approximately 8-24 per group.
So, my inclination would be to assume normal distribution (even if on occasion, the sample distribution appears multimodal) given the fairly exhaustive published evidence that the behavior appears normally distributed. My assumption of normal distribution is for the population not the sample (especially given the relatively small N for each sample). Is it reasonable not to test for normality when a sample appears multimodal, especially in light of effects by factors that are difficult to control? I don't feel comfortable testing for normality when it is likely due to technical variation. This could lead to inconsistent application of statistical tests (where two independent samples collected for the same condition lead to applying tests assuming normal distribution for one and tests assuming multimodal distribution for the second). Thank you all for your responeses!
I don't agree with your reasoning. If your data is multi modal then it is
Not normal.as Abraham Lincoln once remarked calling a tail a leg doesn't make it so. Your entire study needs to be replaced with the assistance of a good biostatistician if at all possible one that is familiar with your organism,C.elegans. Your current study has little chance of being correct. Best wishes David Booth
With all due respect I have a different opinion than David, or possibly just a different weight matrix on your statements :)
You say that you have a lot of experience with data from this assay and experience shows that the normal distribution seems to be an approprate model to decribe the distribution. For me this would be a sufficient reason to use this model.
You further write that occasionally the observed distribution is multimodal, and you also write that this is likely due to the fact that experimental data was pooled from different days. It would make sense (and I'd strongly suggest) then to include a random intercept term by "day" in your model, which will account for the fact that there might be systematic day-to-day variations (for whatever reason).
"Is it reasonable not to test for normality when a sample appears multimodal, especially in light of effects by factors that are difficult to control?"
As I said: include a random intercept term. After this I would of course have a look at the residual diagnostic plots if this "solves the problem". If there is a considerable multimodality remaining in the residuals, then there is some source of (systematic) variation in the data that is not accounted for by your model, making it more difficult to identify/estimate the effects of the factors your are interested in. Still, the conclusions from the model would be "correct" (as they refer to the assumed population distribution and not to the actual distribution of the sample), but you are likely to get unneccesarily wide confidence intervals and large p-values. Deciding to use non-parametric or parametric tests based on each sample is stupid. If you have doubts that the parametric test will work, and if there is a possibility to use non-parametric tests, troughout (but please make sure that the intended hypotheses are tested, e.g. the U-test is not a 1:1 "nonparametric alternative" for the t-test, as often wrongly parroted, as it usually tests a different hypothesis; a bootstrap test of the mean difference would be the correct nonparametric alternative).
Summing up: try harder to model the technical variation; include it in the model so that the model can account for it. If the technical variation is (more or less) properly accounted for, it should not leave mayor traces in the residuals, and so the distribution of the residuals should be closer to the normal distribution.
David Eugene Booth thanks for your response, I appreciate you. A great reminder that the elderly are a great source of wisdom! Would love to sit down over drinks just to hear you express more golden nuggets on statistics like your Abraham Lincoln quote. In your opinion, what is the probability of finding a "good biostatistician" that is also "familiar with C. elegans"?
Jochen Wilhelm thanks for your very thoughtful and thorough response!
"You say that you have a lot of experience with data from this assay and experience shows that the normal distribution seems to be an approprate model to decribe the distribution. For me this would be a sufficient reason to use this model."
This was my default approach, but for the fact that I am now being asked to test for normality, which prompted my question after a similar line of reasoing to "Deciding to use non-parametric or parametric tests based on each sample is stupid" popped into my head. Intuitively, it just doesn't make sense. You've given me a great starting point to initiate conversations with the appropriate folks (including that elusive "good" biostatitician who is also "familiar" with C. elegans.) ;)
While I was never a worm runner myself nor did I did I publish in the worm runner digest. I do have experience with statistics, genetics and chemistry. You may find that I am so old that I am senile or perhaps just experienced. However you call it I completed my PhD at the University of North Carolina in Physical Chemistry, with a second area in molecular genetics a MS in mathematical statistics from Illinois State University and I'm an American Statistical Association accredited professional statistician (PSTAT) from the start of that program. My biological organisms were N crassa, S. Vesiae and the phage phi X 174. I have attached some relevant references in my background in these areas. Further based on my experiences I don't agree with you that you can armchair a statistical study in the manner that you assert and have a reasonable chance of being correct. I would suggest that you consult with a reasonable experienced statistician and follow standard statistical methods. Best wishes to you and and your research efforts. David Booth
Article Descriptive Statistics and Normality Tests for Statistical Data
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