New critical values for F and their use in the ANOVA and Fisher's F tests for evaluating geochemical reference material granite G-2 (USA) and igneous rocks from the Eastern Alkaline Province (Mexico)
Por:
Cruz-Huicochea, R, Verma, SP
Publicada:
1 ene 2013
Resumen:
Monte Carlo method was used to simulate precise and accurate critical
values (with 2 to 7 decimal places) of Fisher's F test for degrees of
freedom (nu(1) and nu(2)) of up to 2000 and confidence levels of 20% to
99.9% for two-sided or two-tailed test (or equivalently to 60% to
99.95% for one-sided or one-tailed test). Unlike the existing
literature, we present 15 new critical value tables along with 15
additional tables of the error estimates of individual values. For the
two degrees of freedom horizontal (nu(1)) as well as vertical (nu(2))
the critical values orrespond to
1(1)30(5)100(10)160(20)200(50)400(100)1000 and
6(1)30(5)100(10)160(20)200(50)400 (100)1000(200)2000, respectively,
where the numbers before and after the parenthesis are the initial and
final values for which critical values were simulated and the numbers in
parenthesis indicate the step size how the initial value of degrees of
freedom approached to the final one. Thus these critical values consist
of 62x62 values for each of the eleven confidence levels. Even though a
large number (3844 for each confidence level, amounting to a total of
42284 values for all confidence levels) of new values of F were
simulated, values do not exist for many different degrees of freedom in
the range of 1-2000. This problem of unavailable critical values was
resolved by evaluating regression models based on simple polynomial
functions as well as those involving log-transformation of the
independent variable. New best-fit equations were thus proposed to
estimate the not-tabulated critical values as well as for the estimation
of probability of calculated F value. This methodology of log
transformations should be useful also for other kinds of applications
involving polynomial fitting. We compared these simulated results with
commercial as well as freely available software. The new precise and
accurate critical values were used to illustrate the application of
analysis of variance (ANOVA) and Fisher's F tests to geochemical data
for international geochemical reference material granite G-2 from U.S.A.
We also present the methodology to statistically compare geochemical
data for ultrabasic, basic and intermediate magmas from eight regions of
the Eastern Alkaline Province of Mexico and U.S.A. Finally, we use these
as well as the discordant outlier-free data for ultrabasic and basic
rocks in multi-dimensional discrimination diagrams to explore the
tectonic setting for this volcanic province, which was inferred to be
mainly an extensional zone or a continental rift.
Filiaciones:
Cruz-Huicochea, R:
Univ Nacl Autonoma Mexico, Inst Energias Renovables, Col Ctr, Temixco 62580, Morelos, Mexico
Verma, SP:
Univ Nacl Autonoma Mexico, Inst Energias Renovables, Dept Sistemas Energet, Col Ctr, Temixco 62580, Morelos, Mexico
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