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I'm a biologist with a very little statistical background and I've been encountering many questions during a recent dataset analysis.

I have two sets of values from measurement in different conditions plus one set of control measurement ('background').

I would like to remove the background from my 2 datasets, and then calculate the signal reduction between the two datasets.

I started by simply subtracting the background from the datasets but this created a relatively large number of negative value which are completely meaningless in my case.

Question 1: Is signal-to-noise ratio a better approach than a simple subtraction of the background?

Even so, I have datapoints equal to zero that create a bias when calculating the ratio between the two datasets. The only solutions I found were to either set the upper limit of the ratio or to set the lower limit of the values in the datasets. But this can have a considerable impact on the statistical significance of the analysis.

Question 2: Is there a correct 'statistical' way to deal with null values?

Edit Some precisions about the data and the analysis I want carry out:

One part of the data I'm working with, represents the DNA sites that are bound by a specific factor in three different genetic conditions (conditions A, B and control). It is expressed as reads from sequencing, on delimited positions of the genome. The second part of the data comes from a publicly available dataset that represents the accessibility of DNA, also expressed as reads from sequencing on specific positions of the genome.

What I am trying to do is to see if a correlation can be drawn between the reduction of the factor binding observed between conditions A and B (calculated as A/B), and DNA accessibility.

What I did so far to remove the background was to substract the reads from the control condition to both A and B datasets. However this happens to create some negative values. Also, for some positions reads are equal to zero in both A or B conditions and the control.

The clearest representation of the data I have found so far is to express the log reduction in function of the log DNA accessbility. But to do so, the dataset has to be clear of negative and 0 values.

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    $\begingroup$ I do not understand why negative values are "completely meaningless," because you are looking at differences between measurements. That means they include measurement variability (and perhaps other sources of variability as well) in addition to the true difference in values. Even when one measures a quantity known to be non-negative, it is not surprising to obtain negative values and when one computes a difference of two such measurements, negative values should be expected. (Radiation readings are a good example of this, because they need to subtract background, too.) $\endgroup$
    – whuber ♦
    Feb 18, 2014 at 8:51
  • $\begingroup$ By meaningless I meant that negative value don't have a biological relevance, but you're right about including measurment variability. But even when taking into account negative values I have troubles dealing with the null values. $\endgroup$
    – GeorgeDean
    Feb 18, 2014 at 9:46
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    $\begingroup$ Yes, I get that you have trouble: but what kind of trouble? How are you trying to "calculate the signal reduction"? Some information showing us what your data look like and what the biological meaning of the signals is would be most helpful. Also, please note that such negative differences definitely are not "null" values (which would represent altogether missing information): by using this term you risk getting some answers that are irrelevant or even misleading. $\endgroup$
    – whuber ♦
    Feb 18, 2014 at 16:57
  • $\begingroup$ Signal-to-noise ratio does not make sense to me because in order to get that you'll need to first parse out the signal, but you only have two (signal + noise) variables in two conditions and a noise variable from the background. Which means somewhere somehow a subtraction needs to happen and it's all back to the same trouble. I would, actually, suggest a more critical look at what "signal" you're trying to capture. If the background can drawn out the signal and created many negative numbers, then what does it mean to be a "signal?" Was it even measured correctly? $\endgroup$
    – Penguin_Knight
    Feb 18, 2014 at 17:21
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    $\begingroup$ I'm voting to close this question as off-topic because cannot be answered without further clarification from OP, which hasn't been seen for years $\endgroup$
    – kjetil b halvorsen ♦
    Oct 11, 2018 at 19:06

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