Tuba Sena Ogurlu I am not sure but you may use Z scores.

Tuba Sena Ogurlu, I believe you have two basic approaches to normalize the two data values.

1. Parametric statistical - you can calculate the mean and standard deviation (SD), then from this, the coefficient of variation (CV) which is: CV = SD/Mean. This will show spread or deviation and is an index of the variability of the data. Then this can be used to adjust each data point based on a formula like: absolute( Mean - Data Point) * CV + Data Point. This is just one example to weight the data point based on how far it is from the mean but it will reduce the extreme variation. Some software can calculate geometric mean weights or other weights.

2. Normalize all data using eigen vector math, to transform each value to a ratio point between 0 and 1, according to how each value differs from the minimum or maximum (or alternatively the median). Some statistical software can perform this analysis. I have a couple of papers published about using the Analytical Hierarchy Process to normalize complex data, as referenced below. I hope this helps or at least suggests a research path to investigate?

Strang, K. D. (2010). Radiology manufacturing projects and politics: Scientist and politician normalized risk decision processes. International Journal of Management and Decision Making, 11(3/4), 231-248. Doi:210.1504/IJMDM.2011.040701

Strang, K. D. (2021). Symmetrical normalization of food insecurity causes and remedies in developing countries. International Journal of Agriculture Innovation, Technology and Globalisation, 2(1), 62-81. DOI:10.1504/IJAITG.2021.115774 https://www.inderscience.com/info/inarticle.php?artid=115774

Transformation of data may be option.

I'm pretty sure that the previous answers have misunderstood the use of the word "normalization" in the original question. Here, "normalize" means to adjust the value of a variable based on the value of another variable.

Tuba Sena Ogurlu , I think what you want to do is build a single general linear model that includes the Factors and a Group variable for Chip-Seq1 and Chip-Seq2. Such a model can take into account the effect of the Factors. You don't need to adjust the Chip-Seq values separately for the Factors. You can then look at least square means or estimated marginal means for the two Groups (lsmeans, emmeans, depending on your software).

I would start by looking at ancova (analysis of covariance), with the idea that you can add as many Factors or Groups as you need to construct your model.

The best approach for this forum is to provide a small set of toy data, and explain what it is exactly you want to do with these data.

THIS IS THE EDITED VERSION OF THE QUESTION

Yes you are right Salvatore S. Mangiafico , since I am not good at english, I probably misoriented them by using wrong notions. Let me elaborate my question with an image:

Here in the image, you see two different chip-seq data: one of them is my actual data I want use later to compare the green rpkm values with blue rpkm values with t-test. However I know that my data has some bias. Let us say the second chip-seq data gives us the chromatin accessibility. When the chromatin accessibility is high it is normal to have a high number of protein on it. Likewise when the chromatin accessibility is low, it is normal to see low protein level. In the image I gave 3 examples in black boxes.

What I want is to eliminate this factor (chromatin accessiblity in this case). In order to achieve that I should somehow "adjust" the values in the chip-seq 1 according to chip-seq 2. In the chip-seq2 , colors of red and purple correspond to green and blue respectively. Each value should be adjusted according to corresponding value in chip-seq 2.

So the question is how to do that ? Should I simply divide the first values to second values ? Should I divide the first values to the ratio of "2nd value/mean of chipseq2". Or another reasonable method ?

That's a very helpful figure.

It's possible that what you want is ancova (analysis of covariance). With My_rpkm as the dependent variable, Group(Green/Blue) and Chromatin_accessibility as the independent variables. You might also want to include the Group x Chromatin_accessibility interaction on the right

I would probably start with this.

Actually, maybe even before that, I might see if Green My_rpkm is correlated with Chromatin_accessibility, and if Green My_rpkm is correlated with Chromatin_accessibility.

Thank u so much. Now, I have so rough idea about ancova. I am gonna search for it. Salvatore S. Mangiafico

If you think that the rpkm values of Chip-seq #1 are (should be) roughly proportional to those in Chip-seq #2, then it should be ok just to use the ratios (#1/#2).

Using ANCOVA on rpkm would not be correct, but on log(rpkm) it it would have the same effect as just dividing the rpkm values. Even when you use the division, the t-test should eventually be done using the log-ratios anyway.

The problem is that I use two different methods and I got completely different results:

1. in simply division method (#1/#2), I see that the blue DNA fragments have much more protein in question than the green ones.

2.when I adjust the values according to the mean of #2 (#1/(#2/mean)), my results showed the reverse pattern (green>blue). This method makes the mean of #2 as 1. So when I divide the #1 value corresponding to value 1, it doesn't change, I say the value in that fragment is in the way it should be. The reason why I tried the 2nd method is not to get too divergent results.

I don't know how but I checked my codes many times in case I made a mistake. By the way, I am trying to adjust my values according to 3 different data. So there are 3 division steps.

For the log form of the data, unfortunately, I have highly skewed data. Would you still recommend to use log ?

Thank you so much for your help. Jochen Wilhelm

This seems to be a slightly complicated approach, considering several sources of data to normalize against. I suggest a collaboration with a local statistician (or a statistically experienced bioinformatician) on this project to get that clear. It would also help to identify possible mistakes in your code.

I don't get the problem with the log-transform. Do you mean that the log-transformed values are still right-skewed?

My advisor is a bioinformatician, obviously, I should discuss this topic with him in a detailed way. Even if I can't adjust my original data according to 3 factors at the same time, I want to see the effect of them (how they change the result when they are eliminated) separately. The reason why I was looking for another method rather than simply division (#1/#2) was to get visually comparable graphics (not too divergent).

For the one with no adjustment, yes, I have still right-skewed data. So I can not apply t-test since it doesn't show gaussian. For the adjusted one, I can. So I can't see if the factor elimination affects the result or not. With the light you and others shed on, I will search for options.

You already helped me a lot thank u so much Jochen Wilhelm

But I have just one more question, would all of you mind?

During the transformation log(1+ (#1/#2)). What should I do if I have zero values in #2 ?

Why not using log((#1+1)/(#2+1)) ? You assume having one observation more in each group, what seems to make more sense to me.

Your suggestion could be written as log(1 + (#1/#2)) = log((#2/#2) + (#1/#2)) = log((#2+#1)/#2), so you actually assume the number of observations in #2 being "overseen" in #1 and assuming to have the full information about #2. This seems hard to defend to me.

You may read something about Laplace's "Rule of Succession".