### Summary

Pre-Hellenistic silver staters minted in the mints of Anemourion, Aphrodisias, Holmoi, Kelenderis, Nagidos, and Pseudo-Kelenderis can be divided into two major groups based on their weight. Assuming that these mints used the same weight standard during the same time periods, and assuming that the weight standard was not increased over time, these groups represent two phases in the development of the weight standard in Cilicia Trachea. These two weight standards differ in terms of average and median weight by approximately 0.7 g, representing a decrease in the weight standard in the second phase by about 6.5%.

The Holmoi, Kelenderis, Nagidos, and Pseudo-Kelenderis mints produced staters during both phases. In contrast, Anemourion and Aphrodisias only began minting staters in the second phase, adhering exclusively to the reduced weight standard. However, it is important to note that Anemourion is represented by only two coins, and the Aphrodisias coinage remains uncertain.

### Analysis

Staters minted by the Anemourion and Aphrodisias mints (the Aphrodisias coinage is somewhat uncertain, see the catalogue section devoted to Aphrodisias) form homogeneous sets. On the other hand, staters minted by the Holmoi, Kelenderis, Nagidos and Pseudo-Kelenderis mints can be divided into the following groups (see the relevant catalogue sections and, for Kelenderis and Nagidos, also their weight analyses):

Holmoi: | Group 1: |
Type 1; |

Group 2: |
Type 2. | |

Kelenderis: | Group 1: |
Types 1.1–3; |

Group 2: |
Types 2.1–12; | |

Group 3A: |
Types 3.1–3 and 3.7–12; | |

Group 3B: |
Types 3.13–14; | |

Group 3C: |
Types 3.4–6 and 3.15–17. | |

Nagidos: | Group A: |
Group 1 except Type 1.5e; |

Group B: |
Group 2 except Type 2.8; | |

Group C: |
Group 3 with Types 1.5e and 2.8. | |

Pseudo-Kelenderis: | Group 1: |
Type 1; |

Group 2: |
Type 2. |

Box plots1, cumulative distributions and basic descriptive statistics of these groups are presented in Figures 1–2 and Table 1 (Std. Dev. denotes the standard deviation and IQR the interquartile range), respectively.

**Figure 1: **Box plots of individual groups

**Figure 2: **Cumulative distributions of individual groups

Group | Count | Mean | Median | Std. Dev. | IQR |
---|---|---|---|---|---|

Anemourion |
2 | 9.68 | 9.68 | 0.19 | 0.27 |

Aphrodisias |
5 | 9.94 | 9.94 | 0.05 | 0.09 |

Holmoi, Group 1 |
9 | 10.55 | 10.66 | 0.22 | 0.18 |

Holmoi, Group 2 |
6 | 10.04 | 10.04 | 0.14 | 0.16 |

Kelenderis, Group 1 |
13 | 10.73 | 10.78 | 0.23 | 0.21 |

Kelenderis, Group 2 |
230 | 10.73 | 10.75 | 0.10 | 0.13 |

Kelenderis, Group 3A |
182 | 10.63 | 10.68 | 0.24 | 0.18 |

Kelenderis, Group 3B |
15 | 10.47 | 10.46 | 0.20 | 0.37 |

Kelenderis, Group 3C |
36 | 9.92 | 9.98 | 0.31 | 0.19 |

Nagidos, Group A |
123 | 10.52 | 10.55 | 0.22 | 0.26 |

Nagidos, Group B |
241 | 10.62 | 10.66 | 0.19 | 0.17 |

Nagidos, Group C |
209 | 9.94 | 9.99 | 0.27 | 0.30 |

Pseudo-Kelenderis, Group 1 |
16 | 10.61 | 10.70 | 0.29 | 0.33 |

Pseudo-Kelenderis, Group 2 |
1 | 10.04 | 10.04 |

**Table 1:** Basic descriptive statistics of individual groups

As Figures 1–2 and Table 1 show, the staters of these mints can be divided in terms of the similarity of their weights into two large groups, which probably correspond to the two phases of the weight standard development in pre-Hellenistic Cilicia Trachea:

Phase 1: |
Holmoi, Group 1; Kelenderis, Groups 1, 2, 3A and 3B; Nagidos, Groups A and B; Pseudo-Kelenderis, Group 1. |

Phase 2: |
Anemourion; Aphrodisias; Holmoi, Group 2; Kelenderis, Group 3C; Nagidos; Group C; Pseudo-Kelenderis, Group 2. |

Note that Anemourion is represented by only two coins and the Pseudo-Kelenderis Group 2 by only one coin. Their inclusion in Phase 2 is therefore only preliminary. It should also be noted that these two phases represent only a basic division of the mintages of staters. For example, the weight analysis of the Kelenderis staters suggests that Kelenderis Groups 2 and 3B cannot be considered weight-homogeneous. However, Group 3B is represented by only 15 coins in the corpus, so it would be premature to attempt to establish multiple phases of coin production.

Box plots and descriptive statistics of these two assumed phases are presented in Figure 3 and Table 2, respectively. In Table 2, note the large negative skewness of both datasets, which is manifested in Figure 3 by high numbers of outliers below the bottom whiskers. The weight distributions of these two phases are considerably left-skewed.

**Figure 3: **Box plots of phases of weight standard development

Statistics | Phase 1 | Phase 2 |
---|---|---|

Number of coins: |
829 | 259 |

Mean: |
10.64 | 9.94 |

Standard deviation: |
0.20 | 0.27 |

Interquartile range: |
0.19 | 0.28 |

Skewness: |
-2.36 | -1.78 |

Kurtosis: |
15.34 | 7.49 |

Minimum: |
8.70 | 8.71 |

25th percentile: |
10.57 | 9.85 |

Median: |
10.68 | 9.99 |

75th percentile: |
10.76 | 10.13 |

Maximum: |
11.07 | 10.48 |

**Table 2:** Descriptive statistics of phases of weight standard development

Figure 4 presents relative frequency histograms. The bars represent the relative frequencies of observations ranging from 8.70 to 11.10 g in increments of 0.10 g and the continuous curves represent approximations of the data by the Weibull distribution2 based on maximum likelihood estimates. Cumulative distributions are shown in Figure 5.

**Figure 4: **Relative frequency histograms of phases of weight standard development

**Figure 5: **Cumulative distributions of phases of weight standard development

The one-sided Welch’s t-test3 rejects the null hypothesis that the mean weight of Phase 1 is equal to the mean weight of Phase 2 against the alternative that the mean weight in the earlier phase is higher than in the later phase (p-value less than 0.001). In addition, the two-sample Kolmogorov-Smirnov test rejects the hypothesis of the equality of the weight distributions these two phases (p-value less then 0.001).

The distributions of coin weights in individual phases have different shapes and are asymmetric due to many factors influencing the weights of coins in the period from their minting to the present. Instead of comparing means, it is therefore statistically more appropriate to compare medians. Since the analyzed data have many tied values, the percentile bootstrap method was chosen. Table 3 shows the observed sample medians and bootstrap 95% confidence intervals.4 Table 4 shows the differences in sample medians, their bootstrap 95% confidence intervals and p-values.5 These results confirm that, like the mean weights, the median weights in Phases 1 and 2 are significantly different at the 5% significance level.

median | 95% confidence interval | ||
---|---|---|---|

Phase 1 |
10.68 | 10.67 | 10.69 |

Phase 2 |
9.99 | 9.96 | 10.02 |

**Table 3:** Medians and their confidence intervals

medians difference | 95% confidence interval | p-value | ||
---|---|---|---|---|

Phase 1 vs Phase 2 |
0.69 | 0.66 | 0.72 | <0.001 |

**Table 4:** Differences in medians

1The bottom and top of each box are the 25th and 75th percentiles of the dataset, respectively (the lower and upper quartiles). Thus, the height of the box corresponds to the interquartile range (IQR). The red line inside the box indicates the median. Whiskers (the dashed lines extending above and below the box) indicate variability outside the upper and lower quartiles. From above the upper quartile, a distance of 1.5 times the IQR is measured out and a whisker is drawn up to the largest observed data point from the dataset that falls within this distance. Similarly, a distance of 1.5 times the IQR is measured out below the lower quartile and a whisker is drawn down to the lowest observed data point from the dataset that falls within this distance. Observations beyond the whisker length are marked as outliers and are represented by small red circles.

2The probability density function of the Weibull distribution is *f(x;a,b)* = *b*/*a*×(*x*/*a*)^{b-1}×exp(-(*x*/*a*)^{b}) for *x*≥0, and *f(x;a,b)* = 0 for *x*<0, where *a*>0 is the shape parameter and *b*>0 is the scale parameter of the distribution. The estimated values of these parameters for Phases 1, 2 and 3, respectively:

*a*: 10.719, 10.052;

*b*: 75.048, 52.983.

3The two-sample t-tests with the effective degrees of freedom approximated by the Welch–Satterthwaite equation. The variances are significantly different at the 5% significance level (the p-value of F-test is less than 0.001).

4Wilcox 2022, pp. 122–3. The number of bootstrap samples was 10^{6} (one million) for each group.

5Wilcox 2022, pp. 196–7. The number of bootstrap samples was 10^{6} (one million) for each comparison.

6 January 2024 – 30 October 2024