Hello everyone,
I measured the cellular (re)orientation in response to mechanical stretch.
Cells (re)-orient in various angles in response to 48 hours stretch.
After I put the data in Excel, I end up with graphs like the one attached, that depicts the percentage of cells that orient in a specific angle (0-90) in relation the the axis of stretch. The columns show averages and the error bars standard deviation from a cell population.
The question is, what statistical test do I run to see if these differences are significant? (I am at a loss, considering the fact that not all differences are equal here, e.g. I may find that the difference is significant between control and stretched in certain angles but not in others).
Thank you so much!
It is quite obvious from the data and it makes pretty much sense theoretically, that percentage (of cells being oriented in a particular angle) is a sinus-function of the angle.
It is clearly not appropriate to compare the percentages between the values at specific orientations. Instead you should fit an appropriate (sinusoidal) model over the entire data, allowing a different amplitude, phase, and offset for the two groups (stretch/control). Within this model you can then specifically test differences in these three parameters between the groups (it looks as if the amplitude of "stretch" is higher, wereas I don't expect considerable differences in phase or offset).
Dear Eleanna, I totally agree with Jochen if you want a detailed analysis of orientation profile. On the other hand if you are only interested in the degree of order of the system ('how much they point toward a unique direction) it is sufficient you compute the Shannon Entropy (or Gini Index, is the same, H(x) : https://en.wikipedia.org/wiki/Entropy_(information_theory)
for both situations and see if (and how much) they differ.
You have circular data. Though it's years since I pointed live ammunition at such data, you might look at Nick Cox's circstat package for Stata, which you can read about here: https://www.stata.com/meeting/2italian/Cox.pdf
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