 23 variation units in the UBS4 apparatus of Hebrews where the readings of P46 and B are both defined. Critical limits of 0 and 6 are obtained using the binomial distribution, 23 observations, a probability of “success” of 3/23, and cumulative probabilities of 0.025 and 0.975. One can therefore be 95% confident that the actual distance from P46 to B is between 0/23 (0.000) and 6/23 (0.261), inclusive.
 There remains a question concerning whether the variation units in the UBS4 apparatus represent a random sample of the entire population of variation units. If, for some reason, the UBS editors chose the variation units in a way that favoured ones with a higher or lower probability of disagreement than applies for the entire population then there would be a bias that could render invalid a confidence interval calculated from those variation units.
 As the number of variation units in a sample decreases, the range of distances covered by the corresponding confidence interval increases. If there are too few variation units, the range extends to include all possible distances, making the associated distance estimate worthless. In view of this, it is desirable to calculate the minimum sample size required to obtain an acceptable relative width for the confidence interval. One possibility is to specify a maximum acceptable relative width of 50%, corresponding to a confidence interval that covers half of all the possible distances. Should a narrower relative width be desired, a larger sample size would be required.
 As discussed above, a confidence interval can be calculated with the binomial distribution, a sample size, a probability of disagreement estimated from the sample, and cumulative probabilities reflecting the preferred confidence level. The width of the confidence interval is a maximum when the probability of disagreement is one half. Using this value for the probability of disagreement therefore provides a conservative estimate of the sample size required for a desired interval width. The following table presents a selection of sample sizes and corresponding relative widths obtained using a probability of disagreement of 0.5 and cumulative probabilities of 0.025 and 0.975:
|Sample size||Lower limit||Upper limit||Relative width|
 In summary, this section covers three statistical questions:
What range of distances between a pair of witnesses is likely to occur if readings are chosen at random from the available pool? If the actual distance is outside this range then it can be considered to be significant in a statistical sense.
What confidence interval applies to a distance between two witnesses estimated from a sample of variation units? One can be confident but not certain that that the actual distance is within an interval defined by critical limits calculated from a random sample of the entire population.
What is the minimum sample size required to obtain an acceptable relative width for the confidence interval calculated from a sample of variation units?
 A Monte Carlo calculation provides estimates for critical values which allow one to decide whether a distance between two witnesses is statistically significant. The binomial distribution is useful for calculating the confidence interval which applies to the distance between two witnesses estimated from a sample of variation units. The binomial distribution can also be used to estimate the minimum sample size required to obtain a given relative width for the confidence interval.
 A distance matrix is a table of distances between pairs of objects, which, in the present case, are textual witnesses. The distance matrix is square and symmetrical about its diagonal because its rows and columns relate to the same set of objects. The diagonal is comprised entirely of zeros because the distance from every object to itself is zero.
 The larger the sample size, the more reliable a distance estimate based on the sample. The relative width of the confidence interval associated with an estimated distance between two witnesses increases as the number of variation units in the 