Description Usage Arguments Details Note Author(s) References See Also Examples
Undertakes a random effects model Analysis of Variance (ANOVA) on a set of duplicate measurements to determine if the analytical, or combined sampling and analytical, (within) variability is significantly smaller than the variability across the duplicates. For data stored in alternate form use anova2
1 | anova1(x1, x2, xname = deparse(substitute(x1)), log = FALSE)
|
x1 |
a column vector from a matrix or data frame, |
x2 |
another column vector from the matrix or data frame, |
xname |
by default the character string for |
log |
if a logarithmic transformation (base 10) of the data is required to meet homogeneity of variance considerations (i.e. severe heteroscedasticity) set |
In field geochemical surveys the combined sampling and analytical variability is more important than analytical variability alone. If the at site (within) variability is not significantly smaller than the between duplicate sites variability it cannot be stated that there are statistically significant spatial patterns in the data, and they are likely not suitable for mapping. This may not mean that the data cannot be used to recognize individuals with above threshold or action level observations. However, under these conditions there also may be above threshold or action level instances that the survey data have failed to detect (Garrett, 1983).
A random effects ANOVA is undertaken, the ANOVA table is displayed, together with estimates of the variance components, i.e. how much of the total variability is between and within the duplicate measurements, and the USGS mapping reliability measures of V and Vm (Miesch et al., 1976). Additionally, the data are investigated through a two-way model following the procedure of Bolviken and Sinding-Larsen (1973).
If the data are as a single concatenated vector from a matrix or data frame as x1[1], ..., x1[n]
followed by x[n+1], ..., x[2n]
, or alternated as x[1]
and x[2]
being a pair through to x[2*i+1]
and x[2*i+2]
, for the i in 1:n
duplicate pairs use function anova2
.
The script does not follow a standard computation of Mean Squares, but is based on a procedure developed after Garrett (1969) for use in the field in the 1970s when pocket calculators first had mean and standard deviation functions.
Any less than detection limit values represented by negative values, or zeros or other numeric codes representing blanks in the data, must be removed prior to executing this function, see ltdl.fix.df
.
Duplicate pairs x1,x2
containing any NA
s are omitted from the calculations.
If a log transformation is undertaken and any less than or equal to zero values occur in the data the function will halt with a warning to that effect.
Robert G. Garrett
Bolviken, B. and Sinding-Larsen, R., 1973. Total error and other criteria in the interpretation of stream sediment data. In Geochemical Exploration 1972, Institution of Mining and Metallurgy, London, pp. 285-295.
Garrett, R.G., 1969. The determination of sampling and analytical errors in exploration geochemistry. Economic Geology, 64(4):568-569.
Garrett, R.G., 1983. Sampling methodology. In Chapter 4 of Handbook of Exploration Geochemistry, Vol. 2, Statistics and Data Analysis in Geochemical Prospecting (Ed. R.J. Howarth), Elsevier, pp. 83-110.
Miesch, A.T. et al., 1976. Geochemical survey of Missouri - methods of sampling, analysis and statistical reduction of data. U.S. Geological Survey Professional Paper 954A, 39 p.
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Loading required package: MASS
Loading required package: fastICA
Combined Sampling and Analytical, or Analytical Variability, Study,
Utilizes Field Sampling or Laboratory Duplicates. In ANOVA Tables,
the variability:
Between would be between sampling sites or analysed samples, and
Within would be at sampling sites or due to duplicate analyses
Data have been Log10 transformed for the ANOVA
Two-Way Random Effects Model for Duplicate measurements of Magnetic Susceptibility
Source SS df MS F Prob
Between 37.272 15 2.4848 5447.94 0.0106
Within 0.018874 1 0.018874 41.38 0
Residual 0.0068415 15 0.0004561
Total 37.298 31 1.2032
One-Way Random Effects Model for Duplicate measurements of Magnetic Susceptibility
Source SS df MS F Prob
Between 37.272 15 2.4848 1546.06 0
Within 0.025715 16 0.0016072
Total 37.298 31 1.2032
Source MS Var Comp %age
Between 2.4848 1.2416 99.9
Within 0.0016072 0.0016072 0.1
1.2432
Summary Statistics for Duplicate measurements of Magnetic Susceptibility
Grand Mean = 1.0064 Variance = 1.2032
'Error' S^2 = 0.0016072 Std. Dev. = 0.04009
'Error' RSD% = 4
Miesch's V = 772.53 Vm = 1545.06
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