rtion of confidence intervals equal to the confidence level would contain the actual value. A popular confidence level for the present kind of work is 95%.
 If one had a comprehensive list of variations units for extant witnesses, the actual distance between two witnesses could be calculated by selecting the set of variation units where the readings of both witnesses are defined then calculating the proportion of disagreement for this set. For each variation unit where the readings of both witnesses are defined, it is only possible for the respective readings to agree or disagree. The set of all agreements and disagreements could therefore be represented as a set of observations, each observation signifying agreement or disagreement at the corresponding variation unit. If many random samples of a particular size were taken from this set and the number of disagreements in each sample counted then the result would be a distribution of numbers of disagreement. Provided that certain conditions are met, this “sampling distribution” is approximately the same as the binomial distribution corresponding to the given number of observations and the probability of disagreement in the selected variation units.
 Once the sampling distribution is known, the limits of the confidence interval for the number of disagreements are found as follows:
Select a confidence level (e.g. 0.95).
Select upper and lower cumulative probabilities such that the difference between them is the confidence level (e.g. 0.025 and 0.975).
Choose two witnesses to compare.
Select the set of variation units where the readings of both witnesses are defined.
Count the number of variation units (n) and calculate the probability of disagreement (p) for the set.
Using the binomial distribution for n observations and probability of “success” p, find the corresponding upper and lower critical limits.
 The resulting confidence interval includes the critical limits and all distances between them. To give an example, there are three disagreements among the sample of 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 pres