If you have a principled reason a priori to favor one algorithm over another, then great use that algorithm. Selecting an algorithm because it gives the answers you expect seems suspect - not good scientific method.
I completely agree with Nicholas on these points.
It's also important to keep in mind that most of these matrix correction methods were tuned to one particular data set of another. PAP and XPP were tuned to the Pouchou k-ratio dataset, Bastin's matrix method was tuned to his k-ratio dataset, while John Armstrong tuned his Phi-Rho-z to the Shaw dataset. Others were tuned to others.
And that is why his CITZAF (and now CalcZAF/Probe for EPMA) offer all these matrix correction methods for comparison. Paul Carpenter spent many years of work plotting these datsets against the 10 matrix methods in CalcZAF and also the 6 different MAC tables! It's an exercise worth pursuing:
https://probesoftware.com/smf/index.php?topic=924.0As an example (using just one MAC table) here is a GaSb synthetic (which should be 50:50 atomic concentrations) analyzed using GaAs and Sb metal as primary standards for all 10 matrix corrections in Probe for EPMA:
Summary of All Calculated (averaged) Matrix Corrections:
Un 2 GaSb as unk
LINEMU Henke (LBL, 1985) < 10KeV / CITZMU > 10KeV
Elemental Weight Percents:
ELEM: Sb Ga In As TOTAL
1 62.757 38.023 -.014 .043 100.809 Armstrong/Love Scott (default)
2 63.973 32.855 -.014 .038 96.852 Conventional Philibert/Duncumb-Reed
3 63.144 33.355 -.014 .040 96.525 Heinrich/Duncumb-Reed
4 62.761 35.664 -.014 .058 98.468 Love-Scott I
5 62.904 36.426 -.014 .069 99.384 Love-Scott II
6 64.539 37.036 -.014 .035 101.596 Packwood Phi(pz) (EPQ-91)
7 63.281 37.885 -.014 .055 101.207 Bastin (original) Phi(pz)
8 63.826 36.720 -.014 .063 100.594 Bastin PROZA Phi(pz) (EPQ-91)
9 63.718 36.467 -.014 .039 100.211 Pouchou and Pichoir-Full (PAP)
10 63.725 36.151 -.014 .043 99.905 Pouchou and Pichoir-Simplified (XPP)
AVER: 63.463 36.058 -.014 .048 99.555
SDEV: .589 1.720 .000 .012 1.757
SERR: .186 .544 .000 .004
MIN: 62.757 32.855 -.014 .035 96.525
MAX: 64.539 38.023 -.014 .069 101.596
Atomic Percents:
ELEM: Sb Ga In As TOTAL
1 48.570 51.387 -.012 .054 100.000 Armstrong/Love Scott (default)
2 52.699 47.262 -.012 .051 100.000 Conventional Philibert/Duncumb-Reed
3 51.996 47.963 -.012 .054 100.000 Heinrich/Duncumb-Reed
4 50.161 49.776 -.012 .075 100.000 Love-Scott I
5 49.683 50.241 -.012 .088 100.000 Love-Scott II
6 49.931 50.037 -.012 .044 100.000 Packwood Phi(pz) (EPQ-91)
7 48.861 51.082 -.012 .069 100.000 Bastin (original) Phi(pz)
8 49.850 50.082 -.012 .080 100.000 Bastin PROZA Phi(pz) (EPQ-91)
9 49.995 49.966 -.012 .050 100.000 Pouchou and Pichoir-Full (PAP)
10 50.213 49.743 -.012 .055 100.000 Pouchou and Pichoir-Simplified (XPP)
AVER: 50.196 49.754 -.012 .062 100.000
SDEV: 1.266 1.261 .000 .015 .000
SERR: .400 .399 .000 .005
MIN: 48.570 47.262 -.012 .044 100.000
MAX: 52.699 51.387 -.012 .088 100.000
It's interesting to see which methods do a better job...
The point being (as Nicholas mentions further on) that depending on the material, different matrix methods may or may not work very well. That's because none of them are really "universal" methods, as they've all been tuned to one dataset over another. If one is analyzed a stoichiometric standard material, one can see that, but if the sample is an unknown, one must be careful not to "pick and choose" what one is hoping for.
The Si-Ir alloy is a classic example of this accuracy issue:
https://probesoftware.com/smf/index.php?topic=158.0My personal hope is that a more physics based fundamental parameters methods will finally get us a universal matrix correction method.