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:

- The division of obol types into Groups 2 and 3 probably does not reflect the chronological sequence of their production (an adjustment of the Coin Catalog will be appropriate). Based on the weight analysis, the coins in Groups 2 and 3 are tentatively divided into three subgroups denoted as Phase 2, 3 and 4 (the first phase being Group 1), which probably roughly correspond to the chronological sequence of obols production.
- The transition from the early production of obols (Group 1) to Phase 2 probably did not mean a change in the weight standard. Both Phases 3 (Types 3N.1, 3N.2 and 3N.3) and 4 (Types 2C.3 and 3L.4), however, brought a reduction in the weight standard.
- The decrease in the weight standard from the early obol issues (Group 1) to the last issues (Phase 4 comprising Types 2C.3 and 3L.4) is 26.0% in terms of average weight (from 0.77 g to 0.57 g) and 29.1% in terms of median weight (from 0.79 g to 0.56 g).

### 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 |
---|---|---|---|---|---|

1B.2 |
5 | 0.77 | 0.79 | 0.07 | 0.12 |

2B.3 |
1 | 0.85 | 0.85 | ||

2C.3 |
10 | 0.57 | 0.58 | 0.06 | 0.06 |

2H.1 |
7 | 0.83 | 0.81 | 0.04 | 0.05 |

3K.1 |
9 | 0.81 | 0.83 | 0.11 | 0.18 |

3K.3 |
1 | 0.69 | 0.69 | ||

3L.1 |
2 | 0.78 | 0.78 | 0.02 | 0.03 |

3L.2 |
16 | 0.75 | 0.77 | 0.08 | 0.11 |

3L.4 |
1 | 0.54 | 0.54 | ||

3M.1 |
8 | 0.79 | 0.79 | 0.03 | 0.05 |

3M.2 |
39 | 0.79 | 0.80 | 0.06 | 0.08 |

3N.1 |
3 | 0.71 | 0.72 | 0.03 | 0.04 |

3N.2 |
58 | 0.72 | 0.72 | 0.06 | 0.07 |

3N.3 |
4 | 0.68 | 0.68 | 0.04 | 0.06 |

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

As Figure 1 and Table 1 shows, Types 2C.3 and 3L.4 stand out with their low weights. The distinctive feature of these two types is the astragalos on the reverse, which does not occur on the other types of obols. Lower mean and median weights can also be observed for Types 3K.3, 3N.1, 3N.2 and 3N.3. Type 3K.3 is so far represented by a single specimen and its design does not connect it with Types 3N.1–3, so we leave it aside for now. The distinctive feature of Types 3N.1, 3N.2 and 3N.3 is the whole horse on the obverse, which does not occur on the other types of obols (only Type 2B.3 shows the forepart of the horse). It seems, therefore, that the obols with the whole horse belong to the penultimate phase of the Kelenderis obol coinage. The other types are comparable in weight to Group 1.

The obols of Group 1 undoubtedly represent the first phase of the Kelenderis coinage. Based on the above observations, the production of obols from Groups 2 and 3 can be tentatively divided into the following phases:

Phase 2: |
All coins in Groups 2 and 3 except Types 2C.3, 3L.4, 3N.1, 3N.2 and 3N.3. |

Phase 3: |
Types 3N.1, 3N.2 and 3N.3 (the whole horse on the obverse). |

Phase 4: |
Types 2C.3 and 3L.4 (astragalos on the reverse) |

Table 2 provides the descriptive statistics for Group 1 and the assumed obol production phases in Groups 2 and 3. The following Figures 2–4 present their box plots, relative frequency histograms (the bars represent the relative frequencies of observations ranging from 0.40 to 1.00 g in increments of 0.10 g) and cumulative distributions.

Statistics | Group 1 | Phase 2 | Phase 3 | Phase 4 |
---|---|---|---|---|

Number of coins: |
5 | 83 | 65 | 11 |

Mean: |
0.77 | 0.79 | 0.71 | 0.57 |

Standard deviation: |
0.07 | 0.07 | 0.05 | 0.06 |

Interquartile range: |
0.12 | 0.08 | 0.06 | 0.07 |

Skewness: |
-0.19 | -0.31 | -0.36 | -0.71 |

Kurtosis: |
1.49 | 3.48 | 3.64 | 3.46 |

Minimum: |
0.68 | 0.60 | 0.55 | 0.44 |

25th percentile: |
0.70 | 0.75 | 0.69 | 0.54 |

Median: |
0.79 | 0.80 | 0.72 | 0.56 |

75th percentile: |
0.82 | 0.83 | 0.75 | 0.61 |

Maximum: |
0.85 | 0.97 | 0.84 | 0.66 |

**Table 2:** Descriptive statistics of supposed phases of obol coinage

**Figure 2: **Box plots of supposed phases of obol coinage

**Figure 3: **Relative frequency histograms of supposed phases of obol coinage

**Figure 4: **Cumulative distributions of supposed phases of obol coinage

The distribution of coin weights in individual groups do not have the same shape and some seems to be asymmetrical (Group 1 and Phase 4). 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.2 Table 4 shows the differences in sample medians, their bootstrap 95% confidence intervals and p-values.3 These results also suggest that the transition from Group 1 to Phase 2 did not result in a decline in the weight standard, but that there was a decline in Phase 3 and a further decline in Phase 4.

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

0.79 | 0.68 | 0.85 | |

0.80 | 0.77 | 0.81 | |

0.72 | 0.70 | 0.73 | |

0.56 | 0.54 | 0.61 |

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

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

-0.01 | -0.12 | 0.05 | 0.774 | |

0.08 | 0.05 | 0.10 | <0.001 | |

-0.16 | 0.10 | 0.18 | <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.

2Wilcox 2022, pp. 122–3. The number of bootstrap samples was 10^{6} (one million) for each group.

3Wilcox 2022, pp. 196–7. The number of bootstrap samples was 10^{6} (one million) for each comparison.

8 July 2023 – 29 July 2023