I am looking at the association of two molecules within a cell (expressed as a %association of one with the other). I have looked at this association at three different time points (i.e 6h, 12h, and 24 h) and would like to know if the % association is statistically significant. I'm not entirely sure that ANOVA can be used with percentage data, but I am not sure of what other test I could use to compare the % association amongst these three groups.
The problem in applied ANOVA with results in % (0-100) is that the results are not approximately normal mainly in the results near to limits (0% or 100%). A way to solve the problem is with a logit transformation of results. If you transform your responses (p) as y=ln(p/(100-p), you can perform ANOVA with y.
Hello Erika,
I'd suggest plotting both the original scores (at each time point) and the model residuals to see whether there are any obvious issues. While percents are bounded (0,100), and therefore can't extend to infinity, your data set may behave sufficiently well so as not to cause any concerns.
As Miguel's answer suggests, there are transforms (arcsine is one, for stretching bounded data, and still treat as ordinary continuous variable) that may work better, if the data (e.g., proportions/percents) are problematic.
Good luck with your work.
In addition to David Morse suggestion, there are other regression methods that might be more suitable. I would investigate those. See for example: https://www.bing.com/search?q=How+to+regress+percentages+as+Dependent+variables&pc=U528&form=QBLH&sp=-1&pq=how+to+regress+percentages+as+dependent+variable&sc=1-48&qs=n&sk=&cvid=767C8A02952D49BDAF62036118FAAC31
See also: https://www.bing.com/search?FORM=U528DF&PC=U528&q=Limdep+regression
Why am I mentioning regression? see this link:
https://www.bing.com/search?q=anova+as+regression&qs=NM&pq=anova+as+a+regress&sc=1-18&cvid=AF99F60CDDAD44458DB4A9AE51B92F98&FORM=QBRE&sp=1
Your problem may be dealt with easier in the regression form. Check it out.
Best, David Booth
For Modeling both ways, see:
https://www.bing.com/search?FORM=U528DF&PC=U528&q=Montgomery+D+C+design+and+Analysis+of+experiments
and/or: https://www.amazon.com/Applied-Linear-Statistical-Models-2013/dp/1259064743/ref=sr_1_1?sy=books&ie=UTF8&qid=1550125901&sr=1-1&keywords=applied+linear+statistical+models+kutner
Good luck, David Booth
When you say percent association, what do you mean? How is this calculated? I imagine whatever components that you use to create this association will be used in whatever type of analyses that you may use.
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