I have two series of measurements of the same variable, coming from two different methods. The variable is represented by the weekly intake of a contaminant through diet. One method is a Food Frequency Questionnaire (FFQ), while the other is the measurement of a biomarker of exposition in the same individuals that answered the questionnaire. I want to evaluate the agreement between the two methods via Bland Altman analysis.

Before to run the analysis, I have checked the normality of the differences between the two methods (as recommended in https://pubmed.ncbi.nlm.nih.gov/26110027/) with Shapiro-Wilk normality test, and I discovered that the differences are not normally distributed. So I decided to log-transform both the series of measurements. The "problem" is that the measurements coming from the FFQ include some "0" values, and this because some participants answered that they consume none of the foods that contanin the contaminant. These same participants, however, have a value that is greater than "0" in the biomarker measurements (in other words, for some participants the intake of the contaminant inferred from the FFQ was "0", while the intake inferred from biomarker measurement was grater than 0).

How can I deal with the non-normality of differences, without losing the individuals that have "0" in the measurement series from the FFQ?

I tried to add a costant value to every values of both the series of measurement and then to log-transform, but I don't know if it is a proper way to deal with the issue.

Can anyone help me?

  • $\begingroup$ This is an old question, but still of interest to many I guess. On your last point, log(y + c) does divide opinion because how do you choose c? But more generally, it's hard to advise without seeing the data yet (1) people with 0 on one measure should not be excluded (2) other transformations might help (3) bootstrapping what you want to estimate could get round any normality assumption. $\endgroup$
    – Nick Cox
    Sep 27, 2023 at 9:09

1 Answer 1


In the Bland-Altman method the log-transform is only designed to deal with some types of non-normal distribution, not all.

Read the original papers from 1986 and 1999: https://pubmed.ncbi.nlm.nih.gov/2868172/ and https://pubmed.ncbi.nlm.nih.gov/10501650/.

These give other ways to deal with non-normal differences. If the differences look very non-normal, the best way is probably the non-parametric method in the 1999 paper.

These papers also recommend judging whether the differences are normal based on eyeballing the scatter-plot and histogram, not a statistical test for normality.

  • $\begingroup$ Thank you. I also found this paper (mdpi.com/2571-905X/3/3/22). So, if I understand well, shall I use the 2.5% and 97.5% percentiles of the distribution of the differences as limits of agreement? $\endgroup$
    – Nuthatch92
    Oct 9, 2021 at 18:28
  • $\begingroup$ Have you read the two papers that I mentioned? If not, read them carefully and follow their advice. The first step is to look at the scatterplot and histogram. Depending on the patterns they show, you might decide to use the non-parametric method with the 2.5% and 97.5% percentiles, or you might decide to use a different method. $\endgroup$ Oct 9, 2021 at 20:25

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