Coin catalogue section: |
Kelenderis |

Coin corpus datasets: |
Kelenderis, Group 1, Kelenderis, Group 2, Kelenderis, Group 3 |

### Summary

Although the data samples cannot yet be considered fully representative, the basic analysis so far indicates the following:

- Coins in Groups 1 and 2 were probably minted in the same (or very similar) weight standard.
- After changing the orientation of the rider on the obverse, i.e. after the transition from Group 2 to Group 3, the weight standard is reduced. Within Group 3, two further significant decreases in the weight standard can be observed. The first decrease can be observed in Types 3H.2 and 3I.1, the second in Types 3A.3, 3B.1, 3C.1, 3I.2 and 3J.1. Types 3H.2 and 3I.1 probably represent the penultimate phase of the pre-Hellenistic Kelenderis coinage, and Types 3A.3, 3B.1, 3C.1, 3I.2 and 3J.1 its final phase.
- The decrease in the weight standard from the early issues (Group 1) to the last issues (Types 3A.3, 3B.1, 3C.1, 3I.2 and 3J.1) is 7.9% in terms of average weight (from 10.73 g to 9.88 g) and 7.8% in terms of median weight (from 10.79 g to 9.95 g).
- Unlike the orientation of the rider on the obverse, the orientation of the kneeling goat on the reverse is not in itself an indicator of phases of the Kelenderis coinage, as both orientations of the goat are found on coins belonging to the final phase of the pre-Hellenistic Kelenderis coinage.

### Analysis

Box plots1 of individual coin types and basic descriptive statistics are presented in Figure 1 and Table 1 (Std. dev. denotes the standard deviation and IQR the interquartile range), respectively.

**Figure 1: **Box plots of individual coin types

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

1A.1 |
2 | 10.57 | 10.57 | 0.02 | 0.03 |

1A.2 |
2 | 10.77 | 10.77 | 0.11 | 0.15 |

1A.3 |
8 | 10.76 | 10.82 | 0.28 | 0.21 |

2A.1 |
4 | 10.78 | 10.77 | 0.09 | 0.15 |

2A.2 |
1 | 10.68 | 10.68 | 0.00 | 0.00 |

2B.1 |
2 | 10.73 | 10.73 | 0.06 | 0.08 |

2C.1 |
6 | 10.73 | 10.74 | 0.03 | 0.06 |

2D.1 |
11 | 10.71 | 10.75 | 0.13 | 0.23 |

2D.2 |
34 | 10.70 | 10.71 | 0.10 | 0.12 |

2E.1 |
11 | 10.78 | 10.81 | 0.08 | 0.12 |

2F.1 |
12 | 10.73 | 10.71 | 0.13 | 0.21 |

2F.2 |
40 | 10.74 | 10.74 | 0.09 | 0.10 |

2G.1 |
44 | 10.73 | 10.75 | 0.10 | 0.15 |

2G.2 |
49 | 10.72 | 10.72 | 0.11 | 0.16 |

3A.1 |
29 | 10.53 | 10.65 | 0.44 | 0.28 |

3A.2 |
16 | 10.69 | 10.69 | 0.05 | 0.07 |

3A.3 |
3 | 9.58 | 9.92 | 0.63 | 0.83 |

3B.1 |
4 | 10.07 | 10.05 | 0.08 | 0.11 |

3C.1 |
2 | 10.04 | 10.04 | 0.08 | 0.12 |

3D.1 |
7 | 10.51 | 10.52 | 0.23 | 0.44 |

3E.1 |
50 | 10.64 | 10.62 | 0.16 | 0.19 |

3E.2 |
30 | 10.67 | 10.71 | 0.18 | 0.18 |

3E.3 |
4 | 10.69 | 10.75 | 0.16 | 0.18 |

3F.1 |
1 | 10.35 | 10.35 | 0.00 | 0.00 |

3G.1 |
5 | 10.70 | 10.70 | 0.07 | 0.14 |

3G.2 |
2 | 10.56 | 10.56 | 0.18 | 0.25 |

3H.1 |
24 | 10.68 | 10.68 | 0.13 | 0.16 |

3H.2 |
16 | 10.29 | 10.35 | 0.50 | 0.65 |

3I.1 |
5 | 10.38 | 10.29 | 0.18 | 0.32 |

3I.2 |
6 | 9.92 | 9.91 | 0.09 | 0.16 |

3J.1 |
5 | 9.80 | 9.85 | 0.23 | 0.21 |

**Table 1:** Basic descriptive statistics of coin types

As Figure 1 and Table 1 shows, Types 3A.3, 3B.1, 3C.1, 3I.2 and 3J.1 stand out in Group 3 with their low weights. The common features of Types 3B.1, 3C.1, 3I.2 and 3J.1 are dotted borders on the reverse and broader flans. Although Type 3A.3 does not have a dotted border on the reverse, it shares a slender goat with Types 3B.1 and 3C.1. These five types can thus probably be included in the last phase of the pre-Hellenistic Kelenderis coinage. It is also worth mentioning that in Types 3A.3, 3B.1 and 3C.1 the kneeling goat is oriented to the left, while in Types 3I.2 and 3J.1 to the right. This shows that the orientation of the kneeling goat is not in itself an indicator of phases of the Kelenderis coinage. Lower median weights can also be observed for Types 3F.1, 3H.2 and 3I.1. However, since the style of the remarkable Type 3F.1 is different from Types 3H.2 and 3I.1, and this type is so far represented by a single specimen, it must be left aside for the time being.

Based on these observations, let us divide Group 3 into the following three subgroups:

Group 3a: |
Group 3 except Types 3B.1, 3C.1, 3H.2, 3I.1, 3I.2 and 3J.1. |

Group 3b: |
Coins of Types 3H.2 and 3I.1. |

Group 3c: |
Coins of Types 3A.3, 3B.1, 3C.1, 3I.2 and 3J.1. |

Table 2 shows the descriptive statistics of Groups 1, 2, 3a, 3b and 3c. There are four significant outliers in Groups 1, 3a, 3b and 3c. In Group 1, the coin no. 6 (Type 1A.3a, ANS Collection 1944.100.53201) stands out from the other coins, weighing only 10.11 g. Although this coin is struck from worn dies, it appears to be well preserved and without signs of serious metal degradation. It was therefore probably indeed struck on a lighter flan.2 In Groups 3a, 3b and 3c, the coins nos. 5 (3A.1a), 180 (Type 3H.2b) and 48 (Type 3A.3b) stand out from the other coins, weighing only 8.91 g and 8.86 g, respectively. Again, these coins seem to show no signs of serious metal degradation.

Statistics | Group 1 | Group 2 | Group 3a | Group 3b | Group 3c |
---|---|---|---|---|---|

Number of coins: |
12 | 214 | 168 | 21 | 20 |

Mean: |
10.73 | 10.73 | 10.63 | 10.31 | 9.88 |

Standard deviation: |
0.24 | 0.10 | 0.24 | 0.44 | 0.29 |

Interquartile range: |
0.25 | 0.14 | 0.19 | 0.60 | 0.16 |

Skewness: |
-1.44 | -0.43 | -3.78 | -1.52 | -2.55 |

Kurtosis: |
4.85 | 3.48 | 29.35 | 5.77 | 9.44 |

Minimum: |
10.11 | 10.42 | 8.70 | 8.91 | 8.86 |

25th percentile: |
10.63 | 10.66 | 10.56 | 10.08 | 9.86 |

Median: |
10.79 | 10.74 | 10.68 | 10.29 | 9.95 |

75th percentile: |
10.88 | 10.80 | 10.75 | 10.68 | 10.02 |

Maximum: |
11.01 | 11.02 | 11.07 | 10.75 | 10.19 |

**Table 2:** Descriptive statistics of coin groups

The following charts visualize the weight distributions of all these groups. Figure 2 shows box plots. Figures 3 and 4 present the relative frequency histograms (for clarity, the histograms were divided into two charts). The bars represent the relative frequencies of observations ranging from 8.70 to 11.10 g in increments of 0.10 g. The three isolated bars between 8.70 and 9.00 g in Figures 3 and 4 and the isolated blue bar between 10.10 and 10.20 g in Figure 3 represent the three outliers mentioned above. The cumulative distributions are shown in Fig. 5.

**Figure 2: **Box plots of coin groups

**Figure 3: **Relative frequency histograms of Groups 1, 2 and 3

**Figure 4: **Relative frequency histograms of Groups 3a, 3b and 3c

**Figure 5: **Cumulative distributions of coin groups

These results suggest that the coins from Groups 1 and 2 were probably struck in the same (or very similar) weight standard. In Group 1, Type 1A.1 stands out as having the lowest mean and median weight of all the types in Groups 1 and 2 (see Figure 1 and Table 1). However, this type is represented by only two coins, so nothing can be deduced from it. Group 3a shows a certain decrease in the weight standard, although the heaviest coins in Group 3a match the weight of the heaviest coins in Groups 1 and 2. This decrease continues significantly in Groups 3b and 3c. This indiciates that Group 3c corresponds to the last phase of the pre-Hellenistic Kelenderis coinage and Group 3b to its penultimate phase. This is consistent with the late style of these coins.

The distributions of coin weights in individual groups have different shapes and, with the exception of Group 2, are asymmetric. 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.3 Table 4 shows the differences in sample medians, their bootstrap 95% confidence intervals and p-values.4 These results confirm the conclusions presented in the previous paragraph. However, it should be emphasized that this is not a statistically significant confirmation at the 5% confidence level, as this would require a multiple testing method for comparison of random samples from different asymmetric distributions.5

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

10.79 | 10.63 | 10.88 | |

10.74 | 10.72 | 10.76 | |

10.68 | 10.66 | 10.70 | |

10.29 | 10.19 | 10.66 | |

9.95 | 9.88 | 10.01 |

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

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

0.05 | -0.11 | 0.14 | 0.577 | |

0.06 | 0.03 | 0.09 | <0.001 | |

0.39 | 0.01 | 0.50 | 0.027 | |

0.34 | 0.19 | 0.73 | <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.

2John Thomassen (Collections Manager, American Numismatic Society), email to author, 13 July 2023.

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

4Wilcox 2022, pp. 196–7. The number of bootstrap samples was 10^{6} (one million) for each comparison.

5If we merged Groups 1 and 2 and tested the decrease in the weight standard in Groups 1+2, 3a, 3b and 3c, then a total of 6 comparisons between these 4 samples would be needed. The Bonferroni correction would be too conservative in this case and I am not yet aware of another suitable method whose assumptions are met for these data.

8 July 2023 – 27 August 2023