Submitted by Petr Vesely on

Founded 1-Nov-2003

Last update 15-Apr-2007

Examined coins and rulers Basic characteristics Test of differences References

### 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 plots1 are presented in Figures 1 and 2. Kernel estimations of probability density functions are presented in Figures 3 (Epanechnikov kernel) and 4 (Gaussian kernel).

**Note:** The bandwidth of the Gaussian kernel was computed as h_{Gauss} = 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×h_{Gauss} to 1.25×h_{Gauss}.

### 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.

### References:

**Esty, Warren W.; Banfield, Jeffrey D.:***The Box-Percentile Plot.*Journal of Statistical Software, Volume 8, Number 17, 2003, pp. 1-14.**Silverman, B.W.:***Density Estimation for Statistics and Data Analysis*. Chapman and Hall, London - New York - Tokyo - Melbourne - Madras, 1993 (reprint of the first edition published in 1986).