Conclusion

The general ensemble test method was described in detail. The signal extraction tool qSigEx developed at Carleton was used and documented. Using a simple toy Monte Carlo, it was shown that

1. A pull experiment with large statistics is a powerful way to study binning effects and biases on the extracted parameters $\theta_i$ and their statistical uncertainties.

2. The standard 1D method of using the product of marginal PDF for the computation of the joint PDF should not be used for correlation larger than $\rho \raisebox{-.65ex}{\rlap{$\sim$}} \raisebox{.45ex}{$>$}0.1$.

3. The PCA method is not adequate for a precise determination of the estimators $\theta_i$ for the fraction of events of type $i$ when $\theta_1 \approx \theta_2 \approx \theta_3$.

4. The multi-D method is the more general and the best approach overall. It leads nevertheless to binning effects and hence the need of large Monte Carlo samples.

In the context of SNO [1,7]:

• In the pure D$_2$O phase of the experiments the 1D method was used for the extraction of the fluxes. Knowing $\rho=0.13$ between $T_{\rm {eff}}$ and $\cos\theta_{\rm {sun}}$ for ES events; this might lead to small biases according to our study.

• In the salt phase of the experiment, $\rho=0.14$ between $T_{\rm {eff}}$ and $\beta_{14}$ for NC events and 2D PDFs were used. On the other hand, $\rho=0.11$ between $T_{\rm {eff}}$ and $\cos\theta_{\rm {sun}}$ and $\rho=0.25$ between $\beta_{14}$ and $\cos\theta_{\rm {sun}}$ for ES events. This will lead to small biases according to our study since 1D PDFs were used for ES events. We are planning to investigate the correlation effects for the signal extraction for the next salt paper (NSP).

We recommend that the signal extraction for the solar neutrino fluxes should take into account all the correlations between the inputs variables. Large Monte Carlo samples should be generated by MCPROD to allow:

1. The computation of full multi-D PDFs.

2. The study of ensemble test.