nse to compare the encoded states on any basis except equivalence. (In the present case, objects are witnesses and states are readings.) Comparisons on the basis of order, magnitude, or ratio are usually meaningless for nominal data.
 A measure called the “simple matching distance” is suitable for quantifying the dissimilarity between two witnesses whose readings are encoded as nominal data. This distance is calculated by operating on the data matrix as follows:
Extract the rows corresponding to the two witnesses being compared.
Extract the columns where both witnesses are defined (i.e. neither has
Count the number of extracted columns where the readings disagree.
Divide this number of disagreements by the number of extracted columns to obtain the distance.
 As an example, in the rows of the Hebrews data matrix devoted to witnesses P46 and B, there are 23 columns in which the readings of both are defined. Of these, three have different readings. The simple matching distance between P46 and B based on this sample of variation units is therefore 3/23, or 0.130.
 The significance of a distance between two witnesses is affected by certain statistical considerations. Firstly, a range of distances can be expected to occur if the readings of two witnesses are randomly selected from the available pool. Only distances outside this range are significant in a statistical sense. Secondly, the distance between a pair of witnesses calculated from a sample of variation units is only an estimate of the actual distance that would be obtained if every variation unit was counted. A statistical analysis gives a range of values that is likely to include the actual value. Finally, the relative size of the range of values increases as the sample size decreases. (In the present case, the sample size is the number of variation units.) For this reason, the utility of a distance estimate decreases as the the sample size becomes smaller.
 A range of numbers of disagreements can be expected to occur between two witnesses that have no genetic relationship if their readings are, in effect, random selections from the available pool. To illustrate, consider two randomly generated “witnesses” with ten variation units where each variation unit has two equally probable readings:
 The distance between these two is 0.7, corresponding to seven out of ten disagreements. If the same kind of trial is performed many times then the resulting distribution of disagreements conforms to the binomial distribution:
 Plotting the distribution for ten trials and a probability of disagreement of 0.5 shows the nature of the distribution:
 Any number of disagreements between zero and ten out of ten is possible, but numbers near the centre of the range are more likely to occur than those in the upper (i.e. right-hand) or lower (i.e. left-hand) “tails” of the distribution.
 Given a knowledge of the distribution of distances, it is possible to calculate how often a particular distance is likely to occur by chance. By choosing a sufficiently small probability level, one can assert that any distances with an even smaller probability of chance occurrence are significant from a statistical point of view. This small probability is called an alpha level, and for this kind of study is often chosen to be 0.05 (i.e. 5%). Once the alpha level is selected, it is possible to calculate corresponding minimum and maximum distances called critical limits. The probability of a smaller or greater distance occurring by chance is then less than or equal to the alpha level. Thus, choosing an alpha level of 0.05 means that distances more extreme than the critical limits have less than or equal to one chance in twenty of occurring.
 The following table gives critical limits of distance calculated for various numbers of variation units by assuming that each one has two equally probable readings:
|Number||Lower limit||Upper limit|
|10||0.200 (2/10)||0.800 (8/10)|
|50||0.360 (18/50)||0.640 (32/50)|
|100||0.400 (40/100)||0.600 (60/100)|
|500||0.456 (228/500)||0.544 (272/500)|
|1000||0.469 (469/1000)||0.5