Estimating if a distribution is significantly less conserved than others when one group is involved. I am looking at levels of genes in a dataset and want to identify genes that do not vary much in terms of their expression level. While I can do this using the coefficient of correlation, calculating the covariance or by looking for  number of genes within the botton x percent of genes using median absolute deviation those methods appear to be arbitrary. 
What I am interested in is defining a cutoff based on P.values - is there any way of finding out which genes show significantly less variability than would be expected by chance without having external controls to compare it to? 
Cheers,
Ankur.
 A: If you're only interested in checking the variability, it sounds like an analysis of variance would be a good start. 
Idea 1: Perform an F-test against the different variances for each control. The null hypothesis is that the two controls come from the same normal distribution, but potentially with different means. 
Idea 2: an analysis of variance (ANOVA) on the continuous variable separated into the controls. The idea is to look at the variance of the continuous variable within each class $s_i$ and compare it to the total variance $s_t$. The correlation coefficient for one class compared to the total is then $\eta_i = \sqrt{s_i / s_t}$. The test is then an F-test. There is an assumption of a normal distribution here also.
As for the p-values, they represent the level where you can accept or reject the null hypothesis (the variances are all equal). If the p-value is low (below a 5% level, for example) you reject the null hypothesis and assume that the variables have different variances based on the control groups.
