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Description
There are currently two widely opposing interpretations of how Barrovian metamorphism affected elemental mass in the Littleton Formation, New Hampshire. Shaw (1954, 1956) and Moss and others (1995, 1996) argued that no elemental mass, other than volatile phases, changed during prograde metamorphism of mudstones in the Littleton Formation. In contrast, Ague ( 1994, 1996) concluded that an apparent loss of silica mass may have accompanied prograde metamorphism. Shaw (1954, 1956), Ague (1996) and Moss and others (1995, 1996) in their statistical treatment of the chemistry of the Littleton Formation controlled for Type I errors setting a. :::().05 as the probability of rejecting the null hypothesis, H0, that no elemental mass change occurred during metamorphism, when it is true. In setting a. to 0.05 these authors were willing to take the chance that they might be wrong 5 times out of a 100 if they rejected H0• However, none of the above authors considered Type II errors, which would have involved controlling for 8, the probability of accepting H0 when it is false. Thusconclusions based on accepting H0 may have been in error. An analysis of Type II errors showed that acceptance of H0 carries with it an unacceptably high risk of being in error. Specifically for the chemical data derived from the Littleton Formation analysis of Type II errors shows that the Student's t test provides little guidance as to the question of whether or not elemental mass for Si, Ti, Fe, Mg, K, Na, P, Ba, Ga, Zn, Th, Nb, Y, Hf, Ta, U, Rb, La, Ce, Nd, Sm, Eu, Gd, Tb, Yb, Lu, Sc, As, B, Br, Co, Se, or Sn changed during medium-grade metamorphism or whether or not elemental mass for Si, Ti, Fe, Mg, K, Na, P, Ni, Cr, V, Ba, Zr, Ga, Zn, Th, Nb, Y, Hf, Ta, U, Rb, Cs, La, Ce, Nd, Sm, Eu, Gd, Tb, Yb, Lu, Sc, As, B, Br, Co, Se, or Sn changed during high-grade metamorphism. Thus, much of the controversy over whether or not silica mass changed during metamorphism of the Littleton Formation may have stemmed from an incomplete understanding of how Type II errors affected acceptance or rejection of H0• In short, the controversy over the Littleton Formation is an exceJlent example of why geologists should not indiscriminately apply the Student's t test without first controlling for B.
