[R] stats and generating a figure for a simple sign test with high inter-experiment variance

From: Robin Colgrove <robin_at_hms.harvard.edu>
Date: Mon 06 Jun 2005 - 12:26:17 EST

Hello all,

Sorry if this is an FAQ. I have been trying to search the archives without success.
I have a dataset (ChiPs microarray) where the experiment to experiment variability is very high
but where within an experiment, the data nearly always goes in the "right" (hypothesis confirming) direction. I am trying to figure out the right way to use R to do the statistics and generate an appropriate figure.

To be specific, we have a virus and a mutant derivative, and the hypothesis is that the wild type virus is specifically suppressing active transcription in a manner that is abrogated in the mutant.

The experiment is to measure the amount of viral chromatin associated with overall histone (should be the same between wild type and mutant), vs. transcriptionally active chromatin (mutant should be greater than wild type) vs. inactive chromatin (wild type should be greater than mutant).

For each experiment there is a histone type (general, active, inactive), a specific gene assayed (four different genes), and a virus used for infection (wild type or mutant). These are hard experiments to do (involving dissecting out small numbers of cells from a mouse) so the numbers are small, but in each case, there are 3-5 pairs of wild type vs mutant virus for each condition.

If I look at simply whether the hypothesis is confirmed for each condition (whether the wild type/mutant difference goes the way you would expect), then the sign is right 34/35 times, which is way beyond reasonable significance. However, since the inter-experiment variance is so high, if I try to do a simple rank-sum test for a particular chromatin-gene-virus combination (3-5 pairs), the result is usually non-significant, or never significant if Bonferroni corrections for multiple tests are applied.

My questions are:

  1. what would be the right way to use R to do and report a simple sign test on this sort of data (paired samples, non-normal, high-inter experiment variability).
  2. What is the best way to plot this and how to do it? I was thinking of having each (wildtype-mutant) experiment pair as the ends of line segments with different colors or line-types for each gene-chromatintype combination. I know this is a standard kind of plot but I can't figure out how to do it in R.
  3. What is the best way to input this data? A 4d array with virus type (wild type or mutant) on one axis, chromatin type (non-specific, active, inactive) on the second, gene (one of four different genes) on the third, and experiment number (1-5) on the last? Is there a good way to do this with data frames?

Thanks for any help. I am not trying to be a sponge and am really trying to figure this out myself, but as a virologist/bioinformaticist I still have a lot to learn statistics-wise.

robin colgrove
dept. of microbiology
harvard medical school

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