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I have two different sets of internal standards in a sample (1), and a sample (2) with these internal standards as well as about 30 peptides. Each peptide has one of each of these kind of standards. From sample 1, I can get the true ratio between standard 1 (S1) and standard 2 (S2), and from sample 2 I can get the ratio between the analyte (L) to each of the standards:

Sample 1: S1/S2

Sample 2: L/S1, L/S2

I can thus calculate the ratio S1/S2 from the measured ratios in sample 2. Each sample is run in 5 technical replicates (that is; 5 injections into the LC-mass spectrometer), so S1/S2 ratios for one particular analyte could look like this (mock data):

measured    calculated
0.967       0.987
1.007       0.967
1.044       1.012
1.041       1.025
1.048       1.046

I want to compare the measured ratios to the calculated, to see if there are any bias in my acquisition of data. As the calculated and the measured ratio are from different samples, the replicates aren't "linked" so I could not use for example Bland Altman analysis. Should I use some kind of ANOVA? Or do you have any other recommendation?

I would also like to make an overall assessment of the ratios of all 30 peptides to see if the bias is different for different peptides. How could I do that?

Any input would be greatly appreciated.

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    $\begingroup$ Hi Max Jonatan Karlsson, thanks for your question and welcome to Bioinformatics Stack Exchange. My first glance at this question suggests it might be a pure statistics question, and therefore would be more appropriate on the stats Stack Exchange, Cross Validated. If you can give more context/story as to why this question would be be helped by computer science and/or biological knowledge (e.g. you're calculating thousands of these statistics), feel free to update your question. $\endgroup$
    – gringer
    Jun 9 '17 at 15:28
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    $\begingroup$ The reason why I posted it here is because it is proteomics data, but I stripped down the context as I deemed it not to be important for the question. I see that you are right that this belongs in statistics however, so I will post my question there, as well as update the question here with some context. Thanks! $\endgroup$ Jun 9 '17 at 15:39
  • $\begingroup$ Context is always helpful for bioinformatics questions. It's frequently the case that there are multiple tools that serve a similar purpose, and the best tool (or tools) can change depending on the nature of the problem. Context also helps to identify when the core problem doesn't match the question (i.e. the XY problem); that doesn't seem to be the case here, but it's worth bearing in mind when asking questions in the future. $\endgroup$
    – gringer
    Jun 9 '17 at 15:42
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From a statistical perspective ratios are icky because the variance of the sampling distribution of a ratio decreases with the size of the numerator and denominator being sampled to create the ratio. If you can get at the numerator and denominator separately, then you should absolutely do that and look at count based tests like the Chi-square test, Fisher's exact test, or Poisson regression.

That said, a t-test would be appropriate in the two-sample case if its assumptions are met. You need to check that both samples are normally distributed, ideally via a qq-plot. You also need to check the variance of both samples and choose a variant of the t-test that does or does not assume equal variances.

If the samples are not normally distributed, then the next approach would be a Mann-Whitney U test.

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