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Comparing gaussian distributions with Gumbel-like distribution

  1. Sep 29, 2015 #1
    Hi all,

    I study binding of analytes in a platform where I have 10.000 sensors. Theres is one binding event per sensor and I identify it as a sudden positive change in the signal. I do first a control experiment without analytes. I measure the maximum change in the signal for each sensor and I obtain a narrow gaussian distribution around cero due to electric noise (green curve). When I measure the analytes I obtain a kind of Gumbel distribution because some sensors detect a positive binding event (larger than the electronic noise, red curve). When I compare the histograms is clear that there is a difference before and after but I would like to do a quantitative analysis of how different the distributions are. Do you have any clue on how to do this? Which test I could apply? One of the distributions is normal but the other is not so I'm not sure.

    Thank you! Untitled-1.png
  2. jcsd
  3. Oct 2, 2015 #2

    First of all, I'm curious as to what led you to think that the measurements of the analytes experiment follow a kind of Gumbel distribution. Were you given prior information stating that a Gumbel distribution was to be expected or did you just assume it followed that distribution by looking at its shape? Also, how confident are you that the data of the control experiment follow a normal distribution? I would definitely start by testing that. You can use the Shapiro-Wilk test for normality or you can compare the data of the control experiment with a normal distribution using the one-sample Kolmogorov-Smirnov test. You can also use the two-sample K-S test to compare both samples and see if they're significantly different. Finally, if you want to compare the means of both experiments and see if there's a significative difference, you can use a nonparametric test like Wilcoxon's rank-sum test, since I believe normality can't be assumed for at least one of both samples.

    I hope this helps!
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