Reduced chi-square test or mean square weighted deviation (mswd) test

Usage

mswd.test(age, sd)

Arguments

age: A vector of age radiometric age estimates
sd: A vector of the standard deviation corresponding to each element in age

Value

A numeric vector of length one with the p-value corresponding to the test.

Details

From Ludwig (2003:646): "By convention, probabilities of fit greater than 0.05 are generally considered as arguably satisfying the mathematical assumptions of an isochron, while lower probabilities are generally taken as indicating the presence of “geological” scatter, and hence a significant possibility of bias in the isochron age.". The null hypothesis is that the isochron conditions hold.

Examples

data(laventa)
# Do the age estimates for the boundaries of the Honda Group (i.e., samples at meters 56.4
# and 675.0) conform to the isochron hypothesis?
hondaIndex <- which(laventa$elevation == 56.4 | laventa$elevation == 675.0) 
mswd.test(age = laventa$age[hondaIndex], sd = laventa$one_sigma[hondaIndex])
#> [1] 3.697832e-11
# The p-value is smaller than the nominal alpha of 0.05, so we can reject the null
# hypothesis of isochron conditions

# Do the age estimates for the samples JG-R 88-2 and JG-R 89-2 conform to the isochron hypothesis?
twoLevelsIndex <- which(laventa$sample == "JG-R 89-2" | laventa$sample == "JG-R 88-2")
dataset <- laventa[twoLevelsIndex, ]
# Remove the values 21 and 23 because of their abnormally large standard deviations
mswd.test(age = dataset$age[c(-21, -23)], sd = dataset$one_sigma[c(-21, -23)])
#> [1] 0.993701
# The p-value is larger than the nominal alpha of 0.05, so we can
# not reject the null hypothesis of isochron conditions