anova1: Analysis of Variance (ANOVA)

Description Usage Arguments Details Note Author(s) References See Also Examples

Description

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

Usage

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anova1(x1, x2, xname = deparse(substitute(x1)), log = FALSE)

Arguments

x1

a column vector from a matrix or data frame, x1[1], ..., x1[n].

x2

another column vector from the matrix or data frame, x2[1], ..., x2[n]. x1 and x2 must be of identical length, n, where x2 is a duplicate measurement of x1.

xname

by default the character string for x1 is used for the title. An alternate title can be displayed with xname = "text string", see Examples.

log

if a logarithmic transformation (base 10) of the data is required to meet homogeneity of variance considerations (i.e. severe heteroscedasticity) set log = TRUE. This is also advisable if the range of the observations exceeds 1.5 orders of magnitude.

Details

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.

Note

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 NAs 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.

Author(s)

Robert G. Garrett

References

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.

See Also

anova2, ltdl.fix.df

Examples

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## Make test data available
data(ms.data1)
attach(ms.data1)

## Undertake an ANOVA for duplicate measurements on rock samples
anova1(MS.1, MS.2, log = TRUE, 
	xname = "Duplicate measurements of Magnetic Susceptibility")

## Detach test data 
detach(ms.data1)

Example output

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 

rgr documentation built on May 2, 2019, 6:09 a.m.

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