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I have data that looks like this:

  selected_genes <- c("A","X","Y")
  pooled_genes <- c("A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", 
"M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", 
"Z")

The question I want to answer is that if we pick 3 genes from pooled_genes how likely that selected_genes is obtained.

What's the appropriate statistical test to obtain p-value for that?

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    $\begingroup$ Does the order of selected_genes play a role? Can genes be picked twice? Can selected_genes contain the same gene twice? Please extend your question, so that answers are either right or wrong and not depending on interpretation. $\endgroup$
    – Bernhard
    Mar 14, 2018 at 7:29
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    $\begingroup$ @Bernhard Thanks a lot. Order of selected genes doesn't matter. Yes the genes can be picked twice. No selected genes cannot contain the same gene twice. $\endgroup$
    – neversaint
    Mar 14, 2018 at 7:31
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    $\begingroup$ Oh sorry for the second comment. As "A" is in the selected_genes but not in the pooled_genes, the answer is easy: It is not likely at all. $\endgroup$
    – Bernhard
    Mar 14, 2018 at 7:31
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    $\begingroup$ @Bernhard Can you elaborate. We (my boss) need a p-value to justify. $\endgroup$
    – neversaint
    Mar 14, 2018 at 7:32
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    $\begingroup$ @neversaint, what Bernhard meant is that gene "A" in "selected_genes" does not occur in "pooled_genes", thus "A" cannot be picked, and the corresponding probability is zero. $\endgroup$
    – crlb
    Mar 14, 2018 at 7:51

1 Answer 1

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Assuming the order of picking does not matter, and genes are sampled with replacement from pooled genes (you dont delete a sample from pooled genes after it has been picked), the corresponding distribution is the Multinomial distribution.

From the distribution and assigning probabilities of picking genes, $p_i$, $i \in \{A,B,...\}$, the p-value can be calculated given an observation.

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  • $\begingroup$ c("A","X","Y") is the observation. How can I get the p-value with R code? $\endgroup$
    – neversaint
    Mar 14, 2018 at 8:06

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