sample values: bac- Bacteria, prop- Properties
Image shows sample values: bac- Bacteria, prop- Properties
I am studying 300 bacteria sequenced from same sample.
They are grouped in 7 groups having varying number of members. e.g. some group has only 2 while some group has 200. I am comparing the gene properties of those groups. e.g. number of genes doing some required function.
How to normalize these properties (observations are values ranging from 1 to 100) for such uneven group sizes for proper comparison (similarity or difference) with statistical significance.

I just want to compare which properties are significantly high or low in a particular group. But due to uneven group sizes I can see the values are gonna be high in larger groups while values are low for small groups.
The values from a group of 2 members may have values like 2, 4, or any small number and for groups of 100 or more the values will cross 50 to 100. So may I simply divide the values with number of members of the group? or there is any better method.

  • 2
    $\begingroup$ I am voting to close this question as unclear because it's unclear if the question is asking about how to test for normality or how to adjust for disparate group sizes. $\endgroup$
    – Sycorax
    Dec 21 '15 at 19:19
  • 3
    $\begingroup$ I see nothing in it that hints at testing for normality. The author just wants to know how to compare the counts when the group sizes are so different. $\endgroup$
    – John
    Dec 21 '15 at 20:33
  • 1
    $\begingroup$ I can't see that "normalize" is a reference to the Gaussian distribution. But on the other hand, it's not clear what alternative meaning of "normalize" might be intended. I think the answer to this question is "you can analyze the frequencies as they are - the fact they are so disparate does not mean you are unable to perform a hypothesis test." But since the OP has not made clear which hypothesis they are intending to test ("are the results statistically significant" is not a testable statement without clarification!) I think this question will only be answerable after an edit. $\endgroup$
    – Silverfish
    Dec 21 '15 at 21:18

You should establish a hypothesis test about normality than test wheter they've come normal distribution or not. You can use ks.test() in R;

  x <- rnorm(50)
  y <- runif(30)
  ks.test(x, y)

    Two-sample Kolmogorov-Smirnov test

data:  x and y
D = 0.46, p-value = 0.0004387
alternative hypothesis: two-sided

If you reject null hypothesis which means two population comes from different distribution. There is a few things you can do;

  1. Mathematical transformation(commonly used logaritmic transformation).
  2. Increase sample size. This refers central limit theorem.
  3. Nonparametric tests. Applying in R can be found this link.
  • 3
    $\begingroup$ How does this address the OP's question about how to rescale the data to be comparable between groups with dramatically different counts? $\endgroup$
    – Sycorax
    Dec 21 '15 at 18:45
  • $\begingroup$ He can compare means after transforming(if the group doesn't come normal distribution) with t-test which has no assumptions but normality. $\endgroup$ Dec 21 '15 at 19:09
  • 1
    $\begingroup$ The data and problem are not well explained but the data look like counts in a cross-classification. If so, this does not answer the question at all. $\endgroup$
    – Nick Cox
    Dec 21 '15 at 19:33
  • 2
    $\begingroup$ Although this appears to be both wrong & irrelevant, it was clearly intended as an answer to the question. I think it should stay. $\endgroup$ Dec 22 '15 at 16:18
  • $\begingroup$ I agree with @gung for which reason I have downvoted. I think the underlying confusion here is the OP's use of the word "normalize". $\endgroup$
    – Silverfish
    Dec 22 '15 at 16:27

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