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What would be an appropriate statistical test to test whether one sample is more significantly spread out around zero than other?

I believe that what I am looking for is a kind of f-test but instead of comparing variances (variations around the mean of each sample) I would want to compare "variances" around a fixed predefined value (in my case zero) between the two samples.

Here's a pic in an attempt to depict qualitatively how the test I seek should work:

enter image description here

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  • $\begingroup$ Why are you interested in zero? $\endgroup$ Dec 13 '16 at 15:12
  • $\begingroup$ I am interest in allelic expression. And I would like to be able to test if two samples (homozygous and heterozygous) have expression values sufficiently different from zero (in log-scale, that is). So I would like to be able to detect if the spread from zero of heterozygous samples is greater than that of the homozygous samples. $\endgroup$
    – plant
    Dec 13 '16 at 16:03
  • $\begingroup$ Can you post an example dataset to clarify your situation? $\endgroup$ Dec 13 '16 at 17:41
  • $\begingroup$ @gung: Just added a pic which I hope clarifies what I am looking for. $\endgroup$
    – plant
    Dec 13 '16 at 18:55
  • $\begingroup$ What would you guys say about using Mann–Whitney U test (en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test) on samples A' and B', where A' and B' are absolute-value-transformed samples of A and B, respectively? $\endgroup$
    – plant
    Dec 13 '16 at 19:41
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Perform the Mann–Whitney U test on the absolute values.

Here's some code in R that does the job:

stat.test <- function(sample_A, sample_B, difference = 0) {
  sample_A_abs <- abs(sample_A)
  sample_B_abs <- abs(sample_B)

  wilcox.test(x = sample_B_abs, y = sample_A_abs,
              alternative = "greater", mu = difference)

}
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