apparatus of Hebrews (Heb 1:3) reports the readings of 66 witnesses. Of these, 24 have the first reading, 6 the second, and 36 the third. The estimated probabilities of the readings are then 0.364 (24/66), 0.091 (6/66), and 0.545 (36/66), respectively. The estimated probability of random agreement is (24/66)2 + (6/66)2 + (36/66)2 = 0.438, giving an estimated probability of disagreement of 1 - 0.438 = 0.562.
 Once the probability of random disagreement is known for each variation unit, it is possible to calculate critical values of distance. To obtain the values by an exact calculation is an intensive computing exercise; performing such a calculation for the 44 variation units of Hebrews presented in the UBS4 apparatus would take a typical computer months to complete. Happily, one can instead use a “Monte Carlo” calculation to obtain the critical limits in a short time. This kind of calculation simulates a large number of trials using a program that generates pseudo-random numbers. Such a calculation that employs enough trials (say, 10,000) has a good chance of producing the same critical values as would be obtained by an exact calculation. To give an example, the estimated critical distances obtained by a Monte Carlo calculation for the set of variation units where the readings of both P46 and B are reported are 0.174 (4/23) and 0.565 (13/23), respectively. The calculated distance between P46 and B (0.130) is less than the lower critical distance (0.174) so it can be regarded as statistically significant. That is, there is less than or equal to one chance in twenty that such a distance will occur if readings are randomly chosen from variation units where both P46 and B are reported.
 The UBS4 apparatus provides 44 variation units for Hebrews. This is certainly not a comprehensive account of all variation among extant witnesses. To identify all of the variation among these witnesses would require them all to be collated, and this would still miss variations that once occurred among witnesses now lost. Extant witnesses represent a small fraction of the total number ever produced. To add to the difficulty of estimating the number of variation units, there is no agreed upon way to delimit their boundaries.
 Despite these problems, it is possible to get a rough idea of how many variation units would occur in Hebrews if a large number of the extant witnesses were compared. Since 1997, the Institute for New Testament Textual Research (INTF) in Münster, Germany, has been publishing installments of its Editio Critica Maior (ECM). The fascicles are so far limited to the Catholic Letters, where a total of 3061 variation units have been identified. Based on respective word counts of 7591 and 4953 for the Catholic Letters and Hebrews, this figure implies that the ECM installment for Hebrews will contain about 2000 variation units. It follows that the 44 variation units given in the UBS4 apparatus of Hebrews represent a small sample of the total number. In view of this, it becomes important to know what sampling error applies for a distance calculated from a selection of variation units.
 If a sample is selected from a population then a sample statistic can be calculated to estimate a population parameter. In the present case, the population is all variation units of Hebrews, the sample is those variation units presented in the UBS4 apparatus, the sample statistic is the simple matching distance (i.e. proportion of disagreements) between two witnesses calculated from the sample of variation units, and the population parameter is the actual distance that would be obtained if all variation units were considered.
 A statistical analysis can be used to obtain an interval (i.e. range) of distances that one is confident contains the actual distance. This “confidence interval” specifies minimum and maximum distances between which the actual value is expected to lie. In order to obtain a confidence interval, a “confidence level” is selected then the boundaries of an interval are computed such that if many samples were randomly chosen, a propo