Anomalies in experimental data for the EPR-Bohm experiment: Are both classical and quantum mechanics wrong?

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We analyze anomalies in data to test the violation of Bell's inequality for the EPR-Bohm experiment. We found that the experimental correlations for photon polarization have an intriguing property. In the experimental data there are visible non-negligible deviations of probabilities P₊₊exp(α, β), P₊₋exp(α, β), P₋₊exp(α, β), P₋₋exp(α, β) from the predictions of quantum mechanics, namely, P₊₊(α, β)=P₋₋(α, β)= 1/2²(α-β) and P₊₋=P₋₊(α, β)=1/2²(α-β). However, in some mysterious way those deviations compensate each other and finally the correlation Eexp(α, β)= P₊₊exp(α, β)- P₊₋exp(α, β)- P₋₊exp(α, β)+ P₋₋exp(α, β) is in the complete agreement with the QM-prediction, namely, E(α, β)= P₊₊(α, β)- P₊₋(α, β)- P₋₊(α, β)+ P₋₋(α, β)= 2(α-β). Therefore such anomalies play no role in the Bell's inequality framework. Nevertheless, other linear combinations of experimental probabilities do not have such a compensation property. There can be found non-negligible deviations from predictions of quantum mechanics. Thus neither classical nor quantum model can pass the whole family of statistical tests given by all possible linear combinations of the EPR-Bohm probabilities. Does it mean that both models are wrong?