Explaining Statistics – Summary Statistics: Cumulative Probability Values for DAE are presented in the form of an Interval Scale ( conventional numbers). The data are in decimal years for the Age at Attainment (AaA) of each Tooth Development Stage (TDS). [ There are up to 258 Tooth Development Stages comprising 8 TDS per Tooth Morphology Type (TMT). That is 8 Stages, by 16 Tooth Type by 2 Gender – thus 8 X 16 X 2 = 256 sets of data plus the LR8 and UL8 = 258 ] The following applies to each of these data sets. In practice there are slightly less than 256 as some stages are not represented as children of 1, 2, and 3 years do not have DPT radiographs. Summary statistics are the result of mathematical processing of a data set to provide values that allow an observer to understand the essential characteristics of the data. These summary data are the key to understanding the way in which Age at Attainment (AaA) data are presented.

**The exemplar for the whole of this DAE web is the data for LL8Gf.** The most common format for summary data are Normal distribution Statistics. Often, the Percentile format is used but it should be remembered that the percentiles are based only on the sample data. A further way of presenting the summary data is to combine the mathematical characteristics of the Normal distribution and the concept of percentiles which enables estimation of Cumulative Probability at the same data points as the Percentile values. This is achieved by using the Probability Tables relate to the Normal distribution. These tables are available in Statistics text books.

Cumulative Probability | Percentile Equivalent | Value (years) | Calculation for Cumulative Probability |
---|---|---|---|

0.005 | [0.5%] | 14.05 | 18.25 - (2.576*1.63) |

0.05 | [5%] | 15.57 | 18.25 - (1.645*1.63) |

0.1 | [10%] | 16.16 | 18.25 - (1.282*1.63) |

0.25 | [25%] | 17.15 | 18.25 - (0.674*1.63) |

0.5 | [50%] | 18.25 | 18.25 +/-(0.0*1.63) |

0.75 | [75%] | 19.35 | 18.25 + (0.674*1.63) |

0.9 | [90%] | 20.35 | 18.25 + (1.282*1.63) |

0.95 | [95%] | 20.94 | 18.25 + (1.645*1.63) |

0.995 | [99.5%] | 22.46 | 18.25 + (2.576*1.63) |

These cumulative probabilities are not often used as they require a detailed understanding of the calculations involved. Also, they are not part of the ‘standard’ output from computer programmes. However, the cumulative probabilities provide a reliable estimate of probability (similar to percentiles) of the * population *rather than the

**data. It is proposed that the cumulative probability is used in the place of percentiles for DAE data.**

*sample*~~~~~||~~~~~