#StackBounty: #distributions #p-value #inference #data-transformation #controlling-for-a-variable Generate null distribution from pvalues

Bounty: 50

I have a set of experiments on which I apply the Fisher’s exact method to statistically infer changes in cellular populations.
Some of the data are dummy experiments that model our control experiments which describe the null model.

However, due to some experimental variation most of the controlled experiments reject the null hypothesis at a $ p_{val} <0.05$. Some of the null hypotheses of the actual experimental conditions are also rejected at a $ p_{val} <0.05 $. However, these pvalues, are magnitudes low than those of my control conditions. This indicates a stronger effect of these experimental conditions. However, I am not aware of a proper method to quantify these changes and statistically infer them.

An example of what the data looks like:

ID      Pval            Condition
B0_W1   2.890032e-16    CTRL 
B0_W10  7.969311e-38    CTRL
B0_W11  8.078795e-25    CTRL    
B0_W12  2.430554e-80    TEST1 
B0_W2   3.149525e-30    TEST2
B1_W1   3.767914e-287   TEST3
B1_W10  3.489684e-56    TEST4
B1_W10  3.489684e-56    TEST5

One idea I had:

  1. selecting the ctrl conditions and let $ X = -ln(p_{val}) $ which will distribute the transformed data as an expontential distribution.
  2. Use MLE to find the $lambda$ parameter of the expontential distribution. This will be my null distribution.
  3. Apply the same transformation to the rest of the $p_{val}$ that correspond to the test conditions
  4. Use the cdf of the null distribution to get the new "adjusted pvalues".

This essentially will give a new $alpha$ threshold for the original pvalues and transform the results accordingly using the null’s distribution cdf. Are these steps correct? Is using MLE to find the rate correct or it violates some of the assumptions to achieve my end goal? Any other approaches I could try?

Get this bounty!!!

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