Dear Hajar Chihab , I think that you have interesting results. What is your opinion regarding using additional methods for processing your statistical data? I'd like to your attention to the use of Natural Language Processing (NLP) methods.

As of 1st step, I suggest building an incidence matrix G for 42 antibodies to 5 Flu antigens. On the 2nd stage, you can use the face-splitting product of these incidence matrices:

Article A family of face products of matrices and its properties

Such an approach in the context of NLP was proposed in the preprint of Bryan Bischof

Preprint Higher order co-occurrence tensors for hypergraphs via face-splitting

On the 3rt phase you can use the product of transposed incidence matrix GT with a face-splitting product of incidences matrices or the multiplication of vector-row of ones 1T =[1 1 1 ...1] and result of face-splitting product incidence matrices.

The results of this calculation give statistics on how used every combination of 42 antibodies to 5 Flu antigens in your test. This statistics pattern can be used for action prediction.

The algorithm of face-splitting product of matrices for Mathcad you can see on page 1059 in this paper:

Conference Paper Специальное программное обеспечение систем искусственного ин...

An example of application my method of preferences analysis you can see in the

conference paper

Conference Paper Анализ предпочтений на основе торцевого произведения матриц.

Dear Hajar,

There is no way to make a shortcut or omission during your studies. If needed, Buy the antigens, despite the high price. Handle the financial issues if needed. However, in this case I guess using statistical analyses is not the only way to interpret or report your results. You can report top 10 antibodies with the most affinity and the 10 weakest antibodies. You can also simply draw your graphs without judging them by a statistical analyses. You know nowadays statistical analyses are losing their importance, especially in cases with few biological replicates. However, I don't know the details of your study. If you explain more maybe I can advise you more precisely. Good luck

Dear Hajar, the 2SD and 3SD thresholds derive from the Gaussian distribution of errors. The Gaussian distribution displays the 95% of observations within the range of 2SD on the right and the left of the mean while 99% of observations stay in between 3SD. This implies the choice of 2 or 3 SD thresholds correspond to a level of 'significance' of the obtained result vs. a reference population from which you derived the distribution. Usually in quality control (but the same happens in clinical tests) the reference population is made of 'correctly made pieces' (normal subjects in clinical testing for blood concentration of cholesterol or any other parameter) so that having an extreme (over threshold) result in a specific sample indicates a low probability of being extracted from the same population. How low must be this probability is apt to you (as usual in statistical based decisions).

In any case it is perfectly fit to adopt this criterion to rank the different antibodies.

As for high variability of positive control and in general high variability linked to experimental conditions you can normalize by this effect but only with a standard way of doing (e.g. considering for any experiment the control positive, negative and antibody). In this case you could use the method reported in the attached file that take automatically into consideration the variability typical of each experimental setting and connecting your resul to Mann-Whitney U.