# Ward & Wilson 
# Case I of Ward & Wilson (1978)
# alternative hipothesys: "determinations are significantly different"
WW <- function(ages, errors) {
    PM <- sum(ages / errors^2) / sum(1 / errors^2)              # pooled mean 
    TS <- sum((ages - PM)^2 / errors^2)                         # statistic
    PSD <- sqrt(solve(sum(1 / errors^2)))                       # pooled sd
    p.value <- pchisq(TS, df=length(ages)-1, lower.tail=F)      # p.value 
    return(list(PM=PM, TS=TS, PSD=PSD, p.value=p.value))
}

### Structure 10.023 -----------------------------------------------
# accepted
C14Age <- c(4150, 4150, 4200, 4220, 4170, 4140, 4180, 4170, 4170, 4140, 4200, 4180, 4150, 4200, 4190, 4140)
C14SD <- c(30, 30, 30, 30, 30, 35, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30)
WW(C14Age, C14SD)
# unaccepted
C14Age <- c(4150, 4150, 4200, 4220, 4170, 4140, 4180, 4170, 4170, 4140, 4200, 4180, 4150, 4200, 4190, 4140, 4230, 4240, 4100)
C14SD <- c(30, 30, 30, 30, 30, 35, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 25, 30, 35)
WW(C14Age, C14SD)

### Structure 10.028 -----------------------------------------------
# accepted
C14Age <- c(4180, 4112, 4108)
C14SD <- c(35, 22, 22)
WW(C14Age, C14SD)
# unaccepted
C14Age <- c(4180, 4112, 4108, 4077)
C14SD <- c(35, 22, 22, 22)
WW(C14Age, C14SD)

### Structure 10.031 -----------------------------------------------
# accepted
C14Age <- c(4100, 4094)
C14SD <- c(68, 36)
WW(C14Age, C14SD)

### Structure 10.032 -----------------------------------------------
# accepted
C14Age <- c(4196, 4147)
C14SD <- c(25, 23)
WW(C14Age, C14SD)

### Structure 10.044 -----------------------------------------------
# accepted
C14Age <- c(4190, 4240, 4200)
C14SD <- c(35, 35, 35)
WW(C14Age, C14SD)

### Structure 10.060 -----------------------------------------------
# accepted
C14Age <- c(4220, 4180)
C14SD <- c(35, 35)
WW(C14Age, C14SD)

### Structure 10.071 -----------------------------------------------
# accepted
C14Age <- c(4222, 4192, 4147)
C14SD <- c(28, 27, 37)
WW(C14Age, C14SD)
# unaccepted
C14Age <- c(4222, 4192, 4147, 4277)
C14SD <- c(28, 27, 37, 30)
WW(C14Age, C14SD)

### Structure 10.073 -----------------------------------------------
# accepted
C14Age <- c(4160, 4120) 
C14SD <- c(35, 35)
WW(C14Age, C14SD)

### Structure 10.075-10.078 ----------------------------------------
# accepted
C14Age <- c(4190, 4150)
C14SD <- c(35, 35)
WW(C14Age, C14SD)

### Structure 10.040 -----------------------------------------------
# unaccepted
C14Age <- c(4200, 4090)
C14SD <- c(35, 35)
WW(C14Age, C14SD)

### Structure 10.042 -----------------------------------------------
# unaccepted
C14Age <- c(4277, 4161)
C14SD <- c(31, 34)
WW(C14Age, C14SD)