Silver content of Byzantine coins from A Handbook of Small Data Sets by D.J. Hand, F. Daly, A.D. Lunn, K.J. McConway and E. Ostrowski, London: Chapman & Hall, 1994. Originally from: Hendy, M.F. and Charles, J.A. (1970) The production techniques, silver content and circulation history of the twelfth-century Byzantine Trachy. Archaeometry, 12, 13-21. I remembered the data set and found it discussed on the WEB here: http://renoir.vill.edu/~short/STATS/MA/materials/datasets.html
The silver content (% Ag) of a number of Byzantine coins discovered in Cyprus was determined. Nine of the coins came from the first coinage of the reign of King Manuel I, Comnenus (1143-1180); there were seven from the second coinage minted several years later and four from the third coinage (later still); another seven were from a fourth coinage. The question arose of whether there were significant differences in the silver content of coins minted early and late Manuel's reign.
Period_1 5.9 Period_1 6.8 Period_1 6.4 Period_1 7.0 Period_1 6.6 Period_1 7.7 Period_1 7.2 Period_1 6.9 Period_1 6.2 Period_2 6.9 Period_2 9.0 Period_2 6.6 Period_2 8.1 Period_2 9.3 Period_2 9.2 Period_2 8.6 Period_3 4.9 Period_3 5.5 Period_3 4.6 Period_3 4.5 Period_4 5.3 Period_4 5.6 Period_4 5.5 Period_4 5.1 Period_4 6.2 Period_4 5.8 Period_4 5.8Macro for Welch's ANOVA:
GMACRO
Welch
# Lables MUST be in C1
# Data MUST be in C2
Name k1 "I"
Let I = 1
Let k3 = N(c1) - 1
Do k2 = 1 : k3
If c1(k2) ~= c1(k2 + 1)
Let I = I +1
ENDIf
EndDo
Name c3 'Mean' c4 "ByVar" c5 "Variance" c6 "N"
Statistics C2;
By C1;
Mean 'Mean';
GValues 'ByVar';
Variance 'Variance';
N 'N'.
Name c7 'weights'
Let 'weights' = 'N'/'Variance'
Name c8 'WeightedMean'
Let k3 = I
Do k2 = 1:k3
Let c8(k2) = sum('weights'*'Mean')/(sum('weights'))
EndDo
Name c9 'F'
Name c10 'numerator df'
Name c11 'denominator df'
Let 'F' = sum('weights'*('Mean' - 'WeightedMean')**2)/(I - 1)
Let 'F' = 'F'/( 1 + (2*(I-2)/(I**2 - 1))*sum( (1/('N' -1))*(1 - 'weights'/sum('weights'))**2))
Let c10 = I -1
Let c11 = (I**2 -1)/(3* sum( (1/('N' -1))*(1 - 'weights'/sum('weights'))**2))
Name c12 'p-value'
Let k2 = I -1
Let k3 = Floor(c11(1), 0)
CDF 'F' 'p-value';
F k2 k3.
Let c12 = 1 - c12
ENDMACRO