Submitted by Petr Vesely on

Founded 27-Jul-2003

Last update 15-May-2006

Examined coins and rulers Basic characteristics Test of differences References

### 1. Examined coins and rulers

AR tetradrachms of Antiochos VII (Nike left), Demetrios II (2nd reign), Alexander II, Antiochos VIII (1st and 3rd reigns in Antioch), Antiochos IX (3rd reign in Antioch), Seleukos VI, Antiochos X, Philip I and Antiochos XIII from Antioch 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. Time series of mean weights is presented in Figure 3 and time series of medians of weight is presented in Figure 4.

### 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 186.732 exceeds the critical value of 16.919 for a 95% level test (the p-value is nearly zero). Thus, at the 95% level of significance, we reject the hypothesis that Antioch tetradrachms of these rulers have the same weight distribution.

**Note:** The Jonckheere-Terpstra test might be used because we can probably suppose the weight standard was decreasing as a consequence of the decline of the Seleukid state (the Jonckheere-Terpstra test is intended for the null hypothesis that all samples came from the same distribution against the ordered alternative that the distributions differ in a specified direction). The Kruskal-Wallis test was chosen to avoid this assumption.

As the hypothesis was rejected, the multiple comparisons were done at the 95% confidence level to test which pairs of samples of consecutive rulers tend to differ. These multiple comparisons were performed using the Wilcoxon rank sum test with the Bonferroni correction (it means that an adjusted criterion of significance α' = α/9 = 0.05/9 = 0.56% was used). Results are presented in Table 1.

Rulers | Hypothesis of identical distribution | ||
---|---|---|---|

p-value | conclusion | ||

Antiochos VII | Demetrios II, 2nd reign | 52.08% | not possible to reject |

Demetrios II, 2nd reign | Alexander II | 20.21% | not possible to reject |

Alexander II | Antiochos VIII, 1st reign | 96.71% | not possible to reject |

Antiochos VIII, 1st reign | Antiochos VIII, 3rd reign | 0.00% | rejected |

Antiochos VIII, 3rd reign | Antiochos IX, 3rd reign | 2.37% | not possible to reject |

Antiochos IX, 3rd reign | Seleukos VI | 26.33% | not possible to reject |

Seleukos VI | Antiochos X | 1.30% | not possible to reject |

Antiochos X | Philip I | 78.82% | not possible to reject |

Philip I | Antiochos XIII | 0.00% | rejected |

We can conclude that there is a statistically significant difference between the weight standards of the 1st and 3rd reign of Antiochos VIII and between the weight standards of Philip I and Antiochos XIII. These differences were probably caused by the decline of the Seleukid state.

### 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).