Multivariate Analysis, Mass Balance Techniques, and Statistical Tests as Tools in Igneous Petrology: Application to the Sierra de las Cruces Volcanic Range (Mexican Volcanic Belt)

Table 8

Results of the application of significance tests of Fisher 𝐹 and Student 𝑡 to the acid rock data from the Sierra de las Cruces at the strict 99% confidence level (CL) prepared from Excel output of UDASYS [37].

Element	Group A	Group B	𝑛A	𝑛B	Df	Sign	𝑡_calc	𝑡_criteria; One-sided	H0; One-sided	CL_𝑡; One-sided	𝑡_criteria; Two-sided	H0; Two-sided	CL_𝑡; Two-sided
(a) Major elements
[SiO2]adj	Gr 2	Gr 1	32	11	41.0	−	0.471	2.421	True	<50	2.701	True	<50
[TiO2]adj	Gr 2	Gr 1	32	11	41.0	−	0.509	2.421	True	<50	2.701	True	<50
[Al2O3]adj	Gr 2	Gr 1	32	11	41.0	−	0.687	2.421	True	72.5	2.701	True	44.9
[Fe2O3]adj	Gr 2	Gr 1	32	11	41.0	+	0.571	2.421	True	<50	2.701	True	<50
[FeO]adj	Gr 2	Gr 1	32	11	41.0	+	0.575	2.421	True	<50	2.701	True	<50
[MnO]adj	Gr 2	Gr 1	32	11	12.0	+	1.599	2.680	True	93.2	3.053	True	86.4
[MgO]adj	Gr 2	Gr 1	32	11	41.0	+	0.612	2.421	True	<50	2.701	True	<50
[CaO]adj	Gr 2	Gr 1	32	11	41.0	+	0.602	2.421	True	<50	2.701	True	<50
[Na2O]adj	Gr 2	Gr 1	32	11	41.0	−	1.877	2.421	True	96.6	2.701	True	93.2
[K2O]adj	Gr 2	Gr 1	32	11	41.0	+	0.917	2.421	True	81.7	2.701	True	63.3
[P2O5]adj	Gr 2	Gr 1	31	11	40.0	+	0.431	2.423	True	<50	2.705	True	<50
(b) Trace elements
La	Gr 2	Gr 1	32	10	39.1	+	2.661	2.425	False	99.4	2.707	True	98.9
Ce	Gr 2	Gr 1	32	11	41.0	+	1.915	2.421	True	96.9	2.701	True	93.8
Pr	Gr 2	Gr 1	32	10	40.0	+	2.507	2.423	False	99.2	2.705	True	98.4
Nd	Gr 2	Gr 1	31	10	38.9	+	2.117	2.426	True	98.0	2.708	True	95.9
Sm	Gr 2	Gr 1	31	10	37.9	+	1.454	2.429	True	92.3	2.713	True	84.6
Eu	Gr 2	Gr 1	30	10	37.6	+	0.909	2.430	True	81.4	2.713	True	62.8
Gd	Gr 2	Gr 1	31	11	40.0	+	0.096	2.423	True	<50	2.704	True	<50
Tb	Gr 2	Gr 1	31	11	40.0	+	0.144	2.423	True	<50	2.704	True	<50
Dy	Gr 2	Gr 1	31	11	40.0	+	0.331	2.423	True	<50	2.704	True	<50
Ho	Gr 2	Gr 1	31	11	40.0	+	0.503	2.423	True	<50	2.704	True	<50
Er	Gr 2	Gr 1	31	11	40.0	+	0.147	2.423	True	<50	2.704	True	<50
Tm	Gr 2	Gr 1	31	11	40.0	+	0.243	2.423	True	<50	2.704	True	<50
Yb	Gr 2	Gr 1	31	11	40.0	+	0.590	2.423	True	<50	2.704	True	<50
Lu	Gr 2	Gr 1	32	11	41.0	+	0.996	2.421	True	83.7	2.701	True	67.5
Ba	Gr 2	Gr 1	32	11	41.0	+	1.433	2.421	True	92.0	2.701	True	84.0
Be	Gr 2	Gr 1	31	9	38.0	+	1.070	2.429	True	85.5	2.712	True	70.9
Co	Gr 2	Gr 1	32	10	40.0	+	1.330	2.423	True	90.5	2.705	True	80.9
Cr	Gr 2	Gr 1	30	11	39.0	+	0.511	2.423	True	<50	2.708	True	<50
Cs	Gr 2	Gr 1	32	11	41.0	+	1.297	2.421	True	89.9	2.701	True	79.8
Cu	Gr 2	Gr 1	27	11	36.0	−	0.180	2.434	True	<50	2.720	True	<50
Ga	Gr 2	Gr 1	32	11	41.0	+	0.817	2.421	True	78.5	2.701	True	57.0
Hf	Gr 2	Gr 1	32	11	41.0	+	1.305	2.421	True	90.0	2.701	True	80.1
Nb	Gr 2	Gr 1	30	11	39.0	+	1.425	2.426	True	91.9	2.708	True	83.8
Ni	Gr 2	Gr 1	27	9	34.0	+	0.583	2.441	True	<50	2.728	True	<50
Pb	Gr 2	Gr 1	31	11	40.0	+	1.226	2.423	True	88.6	2.704	True	77.3
Rb	Gr 2	Gr 1	32	11	41.0	+	0.735	2.421	True	75.2	2.701	True	50.5
Sb	Gr 2	Gr 1	32	11	41.0	+	0.809	2.421	True	78.2	2.701	True	56.5
Sc	Gr 2	Gr 1	32	11	41.0	+	1.282	2.421	True	89.7	2.701	True	79.3
Sr	Gr 2	Gr 1	32	10	40.0	+	1.528	2.423	True	93.3	2.705	True	86.6
Ta	Gr 2	Gr 1	32	10	40.0	+	1.528	2.423	True	93.3	2.705	True	86.6
Th	Gr 2	Gr 1	32	10	40.0	+	2.216	2.423	True	98.4	2.705	True	96.8
Tl	Gr 2	Gr 1	32	11	41.0	−	0.509	2.421	True	<50	2.701	True	<50
U	Gr 2	Gr 1	32	10	40.0	+	1.954	2.423	True	97.1	2.705	True	94.2
V	Gr 2	Gr 1	32	11	41.0	+	0.533	2.421	True	<50	2.701	True	<50
Y	Gr 2	Gr 1	31	10	39.0	−	0.018	2.426	True	<50	2.708	True	<50
Zr	Gr 2	Gr 1	32	11	41.0	+	0.478	2.421	True	<50	2.701	True	<50
(c) Geochemical ratios ^a
LILE4_LREE3	Gr 2	Gr 1	32	11	41.0	−	0.787	2.421	True	77.4	2.701	True	54.8
LILE4_HFSE4	Gr 2	Gr 1	32	11	41.0	+	0.091	2.421	True	<50	2.701	True	<50
Nb_anomaly	Gr 2	Gr 1	31	11	40.0	+	0.421	2.423	True	<50	2.705	True	<50

aLILE4_LREE3 = [(K + Rb + Ba + Sr)/4]/[(La + Ce + Nd)/3]; LILE4_HFSE4 = [(K + Rb + Ba + Sr)/4]/[(Ti + P + Nb + Zr)/4]. Nb_anomaly = {Nb/Nb*}_pm = [2 ×(Nb_sa/Nb_pm)]/[(Ba_sa/Ba_pm) + (La_sa/La_pm)]; the subscript sa stands for the sample and pm for the primitive mantle; the superscript * refers to the Nb concentration that would result from a smooth pattern for Ba to La on a primitive mantle-normalized multielement diagram [38].