Contents
1. Examined coins and rulers
AR tetradrachms of Demetrios II (1st and 2nd reigns) and Antiochos VII from Tyre mint. Data samples are presented in the corresponding sections.
2. Basic characteristics
Basic descriptive statistics and box-percentile plots are presented in Figures 1 and 2. Kernel estimations of probability density functions are presented in Figures 3 (Gaussian kernel) and 4 (Epanechnikov kernel).
Notes: The box-percentile plot is a modified version of the well-known boxplot. At any height the width of the irregular “box” is proportional to the percentile of that height, up to the 50th percentile, and above the 50th percentile the width is proportional to 100 minus the percentile. Thus, the width at any given height is proportional to the percent of observations that are more extreme in that direction. As in boxplots, the median, 25th, and 75th percentiles are marked with line segments across the box. For details see Esty and Banfield, The Box-Percentile Plot.
The bandwidth of the Gaussian kernel was computed as hGauss = 0.9 × min(σ, SIQR) × n-1/5, where σ is the standard deviation, SIQR is the standardised interquartile range (i.e. the interquartile range of the data sample divided by the interquartile range of the standard normal density) and n is the number of observations; see Silverman, Density Estimation for Statistics and Data Analysis, p. 48, formula (3.31). The bandwidth of the Epanechnikov kernel was chosen subjectively in the range from 0.75×hGauss to 1.25×hGauss.
3. Test of differences
The Kruskal-Wallis test was used to test the hypothesis that the examined weight distributions are the same, against the alternative that at least one of the distributions tends to yield larger observations than at least one of the other distributions. The test statistic of 0.241 does not exceed the critical value of 5.992 for a 95% level test (the p-value is 0.886). Thus, at the 95% level of significance, we cannot reject the hypothesis that the weight distribution of teradrachms minted in Tyre mint was stable under the reigns of Demetrios II and Antiochos VII.