Summary Obols Lower silver denominations

Coin catalogue section: |
Nagidos, Silver fractions |

Coin corpus datasets: |
Nagidos, Silver fractions |

### Summary

The data suggest that obols can be divided into three groups based on their weight: Types 5.9–10 (Group 5A), Types 5.1–8 and 5.12 (Group 5B), and Type 5.11 (Group 5C). These groups probably correspond to the relative chronology of obol coinage. The reduction of the weight standard between Group 5A and Group 5B and between Group 5B and Group 5C is in both cases 0.18 g. The differences between the observed medians are very similar: 0.17 g and 0.18 g, respectively.

It seems that hemiobols and tetartemorions were minted before the second lowering of the weight standard for obols, i.e. before the minting of obols of Type 5.11. However, the corpus of lower denominations contains very little data so far, and any conclusions are therefore highly speculative.

### Obols

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 |
27 | 0.76 | 0.75 | 0.08 | 0.11 |

5.2 |
7 | 0.69 | 0.68 | 0.12 | 0.17 |

5.3 |
6 | 0.72 | 0.72 | 0.04 | 0.03 |

5.4 |
3 | 0.62 | 0.60 | 0.07 | 0.10 |

5.5 |
12 | 0.74 | 0.74 | 0.04 | 0.05 |

5.6 |
56 | 0.67 | 0.68 | 0.07 | 0.09 |

5.7 |
34 | 0.69 | 0.69 | 0.07 | 0.09 |

5.8 |
27 | 0.70 | 0.69 | 0.06 | 0.06 |

5.9 |
12 | 0.87 | 0.87 | 0.07 | 0.08 |

5.10 |
1 | 0.98 | 0.98 | 0.00 | 0.00 |

5.11 |
19 | 0.53 | 0.54 | 0.05 | 0.07 |

5.12 |
16 | 0.75 | 0.74 | 0.08 | 0.07 |

**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 5.9–10; |

Group 5B: |
Types 5.1–8 and 5.12; |

Group 5C: |
Type 5.11. |

Table 2 shows the descriptive statistics of these groups.

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

Number of coins: |
13 | 188 | 18 |

Mean: |
0.88 | 0.70 | 0.52 |

Standard deviation: |
0.07 | 0.08 | 0.05 |

Interquartile range: |
0.08 | 0.09 | 0.07 |

Skewness: |
0.61 | 0.21 | 0.08 |

Kurtosis: |
2.92 | 3.58 | 1.77 |

Minimum: |
0.78 | 0.51 | 0.45 |

25th percentile: |
0.83 | 0.66 | 0.49 |

Median: |
0.87 | 0.70 | 0.52 |

75th percentile: |
0.92 | 0.75 | 0.56 |

Maximum: |
1.04 | 0.95 | 0.61 |

**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 0.45 to 1.05 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 Group 5C is 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 |
0.87 | 0.84 | 0.91 |

Group 5B |
0.70 | 0.69 | 0.72 |

Group 5C |
0.52 | 0.49 | 0.56 |

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

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

Group 5A vs Group 5B |
0.17 | 0.13 | 0.22 | <0.001 |

Group 5A vs Group 5C |
0.35 | 0.30 | 0.41 | <0.001 |

Group 5B vs Group 5C |
0.18 | 0.14 | 0.22 | <0.001 |

**Table 4:** Differences in medians

### Lower silver denominations

The coin corpus on this website so far contains only three hemiobols and one tetartemorion. Moreover, the weight of one of these three hemiobols is not known, and the weight of one of the remaining two hemiobols is known only to one decimal place. Therefore, no statistically based conclusions can be made and we must confine ourselves to preliminary unreliable observations.

The design of the so far known types of hemiobols (Types 6.1 and 6.2) corresponds to the obols of Types 5.1 and 5.3. The mean and median weights of the obols of these two types are equal to 0.75 g and 0.74 g, respectively. Assuming that the weight of hemiobol no. 3 in the coin corpus is equal to 0.40 g (i.e., the author of the auction catalogue just simplified the entry of the numerical value), a preliminary estimate of the mean and median weight of hemiobols is equal to 0.41 g. This corresponds to approximately 55% of the mean and median weight of obols of Types 5.1 and 5.3, while one would rather expect a value of below 50%. The value of 0.41 g is also relatively close to the mean and median of Group 5C, which are equal to 0.52 g (see Table 2). Thus, these hemiobols were probably struck earlier than the obols of Group 5C, which were struck at a reduced weight standard.

The weight of the tetartemorion is 0.23 g, which would correspond to an obol weighing 0.92 g. This might suggest that this tetartemorion was struck in the same weight standard as the obols of Group A, i.e. obols of Types 5.9 and 5.10. However, no conclusions can be drawn on the basis of a single coin.

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.

23 August 2024 – 14 September 2024