Coin catalogue section: |
Kelenderis |

Coin corpus datasets: |
Kelenderis, Obols |

### Summary

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

- Two significant decreases in the weight standard can be observed, which divide the obols into three groups: Types 5.1–8 (Group 5A), Types 5.9–12 (Group 5B) and Types 5.13–14 (Group 5C). These groups probably correspond to the relative chronology of obol coinage.
- The decreases in the weight standard between these groups expressed by the differences between the average observed weights are 0.08 g and 0.14 g, respectively. The differences between the observed medians have the same values.

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

5.1 |
5 | 0.77 | 0.79 | 0.07 | 0.12 |

5.2 |
9 | 0.84 | 0.83 | 0.05 | 0.07 |

5.3 |
10 | 0.78 | 0.79 | 0.05 | 0.06 |

5.4 |
51 | 0.80 | 0.80 | 0.06 | 0.09 |

5.5 |
1 | 0.85 | 0.85 | 0.00 | 0.00 |

5.6 |
10 | 0.82 | 0.84 | 0.11 | 0.15 |

5.7 |
19 | 0.76 | 0.77 | 0.09 | 0.11 |

5.8 |
10 | 0.75 | 0.77 | 0.06 | 0.07 |

5.9 |
1 | 0.69 | 0.69 | 0.00 | 0.00 |

5.10 |
3 | 0.71 | 0.72 | 0.03 | 0.04 |

5.11 |
63 | 0.72 | 0.72 | 0.05 | 0.07 |

5.12 |
4 | 0.68 | 0.68 | 0.04 | 0.06 |

5.13 |
12 | 0.57 | 0.58 | 0.06 | 0.06 |

5.14 |
1 | 0.54 | 0.54 | 0.00 | 0.00 |

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

As Figure 1 and Table 1 show, the obols can be divided into three groups according to their weight:

Group 5A: |
Types 5.1–8; |

Group 5B: |
Types 5.9–12; |

Group 5C: |
Types 5.13–14. |

Note that Types 5.5, 5.9 and 5.14 are each represented by only one specimen. Type 5.5 is classified in Group 5A based on its weight and the fact that it is linked by the letter *heta* to Type 2.5 staters of Group 2, and this group is also characterized by a higher weight standard. Type 5.9 is linked to Type 5.11h by the reverse die and can therefore be assigned to Group 5.B. Type 5.14 is linked by design to Type 5.13 and it therefore seems safe to place both types in the same group 5C.

Table 2 shows the descriptive statistics of these groups.

Statistics | Group 5A | Group 5B | Group 5C |
---|---|---|---|

Number of coins: |
115 | 71 | 13 |

Mean: |
0.79 | 0.71 | 0.57 |

Standard deviation: |
0.07 | 0.05 | 0.06 |

Interquartile range: |
0.09 | 0.06 | 0.07 |

Skewness: |
-0.15 | -0.36 | -0.63 |

Kurtosis: |
3.29 | 3.63 | 3.30 |

Minimum: |
0.60 | 0.55 | 0.44 |

25th percentile: |
0.75 | 0.69 | 0.54 |

Median: |
0.80 | 0.72 | 0.56 |

75th percentile: |
0.84 | 0.75 | 0.61 |

Maximum: |
1.00 | 0.84 | 0.66 |

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

The following charts visualize the weight distributions of these groups. Figure 2 shows box plots and Figure 3 present relative frequency histograms (the bars represent the relative frequencies of observations ranging from 0.40 to 1.00 g in increments of 0.05 g). Cumulative distributions are shown in Figure 4.

**Figure 2: **Box plots of groups 5A, 5B and 5C

**Figure 3: **Relative frequency histograms of groups 5A, 5B and 5C

**Figure 4: **Cumulative distributions of groups 5A, 5B and 5C

The distributions of coin weights in individual groups have different shapes and, with the exception of Group 5B, 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.2 Table 4 lists all pairwise differences in sample medians, their bootstrap 95% confidence intervals and p-values.3 Since the p-values of all pairwise tests are less than the Bonfferoni correction (0.05/3 = 0.0167), we can conclude at the 5% significance level that the weight standards of Groups 5A, 5B and 5C are descending.

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

Group 5A |
0.80 | 0.78 | 0.81 |

Group 5B |
0.72 | 0.70 | 0.73 |

Group 5C |
0.56 | 0.54 | 0.61 |

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

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

Group 5A vs Group 5B |
0.08 | 0.06 | 0.10 | <0.001 |

Group 5A vs Group 5C |
0.24 | 0.18 | 0.26 | <0.001 |

Group 5B vs Group 5C |
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 – 4 June 2024