Clarification of question 4.3: What are best practices for ensuring appropriate statistical significance of reporting trace numbers of particles in various samples?

While I agree with the MDA calculation algorithms cited, which show that the minimum reportable number must be 3 to account for sample contamination. In practice, this will be far more and I would say that a figure of around 50 MNPs per sample is the minimum reportable quantity.

Shortly:  replicate sampling, blanks and controls (as discussed), adequate statistical tests (e.g., non-parametric tests for data that are not normally distributed), reporting of LoD and LoQ, and data normalization (for easy comparison). 

When reporting trace numbers of particles in samples, in order to ensure an appropriate statistical significance a careful attention to both methodology and interpretation should be given. Due to the fact that low particle counts often follow a Poisson distribution rather than a normal one, the statistical models suited for rare events should be applied, and confidence intervals, rather than just means or p-values, should be reported to reflect the inherent uncertainty. Also, a particular important attention should be given to the replication, since single measurements at trace levels are not reliable. Having a  sufficient number of replicates helps capture variability and strengthens conclusions. Background controls and blanks must always be included to establish detection thresholds and distinguish true signal from contamination or noise, with results interpreted relative to these controls. When multiple samples or particle types are analyzed, corrections for multiple testing should be used to prevent false positives. Transparency in documenting assumptions, statistical methods, detection limits, and raw data improves both credibility and reproducibility. Taken together, these practices, replication, appropriate statistical models, careful use of controls, reporting of uncertainty, and methodological transparency could help ensure that trace particle reporting is statistically sound and scientifically defensible.

Here are some best practices when reporting trace numbers of particles:

1. Use the Minimum Detectable Amount (MDA) framework. 
2. Use multiple blanks and controls. 
3. Report standard deviations.
4. If particle counts are below MDA, report them as below detection limit.

In general terms such best practices are similar to the best QA/QC practices for any analytical detection method. This includes the whole cascade of using reference and standard materials, blancs, spiking with (for instance labelled ) reference materials, assessment of recovery efficiency, assessment of detection and quantification limits.

Study design should include adequate sample size in order for data to be statistically analyzed.  Again, mass spec methods measure MNPs as a mass and with appropriate sample size it is possible to perform parametric or nonparametric statistical analysis.  For methods involving MNP particle analysis, statistical analyses can be tricky due to different types, shapes, sizes and colors.  

The very essence of analytical data is the reproducibility.  While detection limit can vary depending on the analytical methodology and sample type, sample preparation can be optimized to achieve analysis within little uncertainty.  Although manuscript states the need to achieve 100 particles, this recommendation not scientifically based.  Many human tissue  analysis detected <10 particles (e.g., placenta study) and achieving 100 particles (e.g., in placenta, brain) can be impossible.   Instead, focus on the reproducibility of the data is needed, instead of statistical significance.  

My apologies, no expertise in 'appropriate statistical significance' for trace number of particles.

It is not expertise area. I would like to comment that biological study should adopt hypothesis driving approach to be more meaningful, have a null hypothesis and target to approve or disapprove the hypothesis. Rather than, go into a black box test and make hypothesis based on what have been observed in the study. 

I'm sorry, I'm not sure what this question means by statistical significance of reporting numbers. Is it about statistical power, or significant difference from zero, or something else? I would not change my answer from before, the measured value of a sample is the measured value unless it's below the limit of detection or quantification.  If it is below LOD or LOQ, then report the value as <LOD or <LOQ.