Summary Analysis

Coin catalogue sections:	Holmoi, Kelenderis, Nagidos, Pseudo-Kelenderis Mints
Coin corpus datasets:	Holmoi, Group 1, Holmoi, Group 2, Kelenderis, Staters – Group 1, Kelenderis, Staters – Group 2, Kelenderis, Staters – Group 3, Nagidos, Staters – Group 1, Nagidos, Staters – Group 2, Nagidos, Staters – Group 3, Pseudo-Kelenderis Mints

Summary

Pre-Hellenistic silver staters minted at Holmoi, Kelenderis, Nagidos and Pseudo-Kelenderis mints can be divided into three large groups based on their weight, which probably correspond to the three phases of the weight standard development in Cilicia Trachea. Assuming that these mints used the same weight standard in the same time periods, and assuming that the weight standard was not increased over time, these groups represent the basic relative chronology of pre-Hellenistic staters in this region.

Analysis

Based on the Coin Catalogue and the weight analyses of Holmoi, Kelenderis, Nagidos, and Pseudo-Kelenderis mints, silver staters can be divided into the following groups, which group together coin types with the same weight standard:

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
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	0.00	0.00

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 three large groups, which probably correspond to the three phases of the weight standard development in pre-Hellenistic Cilicia Trachea:

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

Note that Phase 2, represented only by Kelenderis Group 3B, is represented by only 15 coins in the corpus. It cannot therefore be ruled out that it can be merged with Phase 1. However, the weight analysis of the Kelenderis staters suggests that Kelenderis Groups 2 and 3B cannot be considered weight-homogeneous. Therefore, the possibility of a possible merger of Phases 1 and 2 is left open for the time being until the data sample of Kelenderis Group 3B is enlarged.

It should also be noted that the Pseudo-Kelenderis Group 2 is represented by only one coin. Its inclusion in Phase 3 is therefore only preliminary and unreliable.

Box plots and descriptive statistics of these three assumed phases are presented in Figure 3 and Table 2, respectively. In Table 2, note the large negative skewness of Phases 1 and 3, 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	Phase 3
Number of coins:	814	15	252
Mean:	10.64	10.47	9.94
Standard deviation:	0.20	0.20	0.27
Interquartile range:	0.18	0.37	0.29
Skewness:	-2.44	0.13	-1.80
Kurtosis:	16.03	1.62	7.47
Minimum:	8.70	10.20	8.71
25th percentile:	10.58	10.26	9.85
Median:	10.68	10.46	9.99
75th percentile:	10.76	10.63	10.14
Maximum:	11.07	10.77	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 hypotheses that the mean weight of Phase 1 is equal to the mean weight of Phase 2 and the mean weight of Phase 2 is equal to the mean weight of Phase 3 against the alternative that the mean weight in the earlier phase is higher than in the later phase (p-value equal to 0.002 for the first test and less then 0.001 for the second test). In addition, the two-sample Kolmogorov-Smirnov test rejects the hypothesis of the equality of the weight distributions in Phases 1 and 2, and in Phases 2 and 3 (p-value equal to 0.002 for the first test and less then 0.001 for the second test).

The distributions of coin weights in individual groups 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, 2 and 3 are significantly different at the 5% significance level.

	median	95% confidence interval
Phase 1	10.68	10.67	10.69
Phase 2	10.46	10.25	10.64
Phase 3	9.99	9.97	10.02

Table 3: Medians and their confidence intervals

	medians difference	95% confidence interval		p-value
Phase 1 vs Phase 2	0.22	0.05	0.42	0.008
Phase 1 vs Phase 3	0.69	0.65	0.72	<0.001
Phase 2 vs Phase 3	0.47	0.27	0.64	<0.001

Table 4: Differences in medians