When the aim is to do paired blank correction, how does one demonstrate that the pairing method was effective?

To demonstrate that this paired correction is effective, there is the need to show that the blank correction accurately accounts for background contamination without over- or under-correcting the sample data. There is the need to: 
1) define how blanks are paired with samples and that each blank reflects the same conditions as its paired sample
2) plot raw vs corrected values for each sample
3) assess statistical significance
4) assess variability and check whether the corrected values do not fall below detection limits (or become negative).

I think this can be demonstrated by the conduct of numerous repeat paired blanks. Good reproducibility of replicate blanks increases confidence in their ability to account for method contamination.  

In order to be able to demonstrate the effectiveness of a paired blank correction method, it is very important to provide a clear evidence that the approach accurately identifies, accounts for, and removes the background signal given by the blank sample. The background signal, which often occurs from contaminants, from the instrumentation noise, or  due to matrix effects, can interfere with the true signal of interest in the analytical measurements. For a correction method to be considered  effective it should help isolate and subtract the interference signal produce by the background while preserving the integrity of the actual analyte signal. This way, the data accuracy and reliability are kept. In order to demonstrate the  effectiveness of a paired blank correction method, it should  be demonstrated that the method consistently distinguishes between the background noise and the signal given by different samples and experimental conditions. This can be done using a comprehensive and systematic approach involving experimental design, statistical analysis and clear data visualization. The validation of the experimental design should include both paired and unpaired blanks to allow comparison, as well as replicated sample-blank pairs in order  to evaluate consistency. Furthermore, the method should  be able to  reduce the variability.  Afterwards, an improvement in the signal-to-noise ratio, that is generally calculated as the mean of the signal divided by the standard deviation of the blank or noise, should be evident after the correction. Additionally, statistical studies such as t-tests or ANOVA can  be of help in establishing whether  the biological or experimental differences become more apparent after the correction, and a correlation analysis can also reveal a reduced dependency between signal and background. The visual evidence generated using tools like boxplots, clustering, or Bland-Altman plots can effectively demonstrate the reduced spread and better group separation after the correction. More than that, the recovery of the known spiked-in compounds or standards can show that their expected values are more accurately captured after the correction, providing the direct evidence of an improved quantification. Additionally, an effective correction should also result in diminished or near-zero signal in negative controls, confirming that background interference has been effectively eliminated. 

One of the approaches is to use spiked samples and do extrapolation of the responses obtained. A big issue in this respect is that availability of materials suited for spiking experiments.

Unless a method is thoroughly validated for application in regulatory setting, paired blank correction is needed as the contamination levels of MNP in blanks vary from batch to batch.  Effectiveness of paired blank correction can be demonstrated through interlab studies or replicate analysis of samples at different times in the same laboratory.  

There will be two control samples needed. There should be signal or response difference between positive and negative controls after being corrected with paired blank.  

very challenging. not sure.

To demonstrate the effectiveness of the pairing method, the corrected and the uncorrected data can be compared. 
Relating the sample and the paired blank values to show a consistent relationship.
Check if the limit of detection and limit of quantification is improved after the blank correction.