Subject: Re: Bob Schact's stats Date: Sun, 25 Oct 1998 20:30:21 -0700 From: Bob Schacht To: miser17@epix.net, crosstalk@info.harpercollins.com At 06:23 PM 10/24/98 -0400, Stevan Davies wrote: >BOB [October 21, 1998, 02:32 PM PST] >> I'm gonna attempt to actually pin numbers to this problem. >> First of all, this is basically a probability problem of sampling without >> replacement. Therefore the probability of *any particular* three-saying >> sequence would be (1/90) times (1/89) times (1/88) = 1.418681193962e-6 = >> .000001418681193962 if the sayings were drawn at random. > >STEVE >OK. But the question is NOT "any particular" but ANY AT ALL. The >argument is made that if ANY three saying sequence is found then >there probably is dependence. As I recall from >Patterson's book there was ONE three saying sequence // in GTh and >a synoptic gospel. Now, the question is NOT >whether THAT ONE is likely to have happened by chance but whether ANY >one is likely to have happened by chance because the argument is >that if any one happened dependence is likely. And the ANY one could >be in Mt or Mk or Lk. > In the message quoted above, I tried to address this concern as follows: >Since the usual impression is >that GThomas is the random one, you need to enumerate >exactly how many three-saying sequences in Matthew (or >Luke, or Q) are there in this list of 90 sayings? Suppose the >answer is "88" (Take the 90 sayings; order them as they are >in Matthew; how many ADJACENT sequences of 3 sayings >in Matthew?) Adjacency makes the math simpler. What I >mean by adjacency is that if we sort the 90 sayings in order >by their appearance in Matthew and number them >consecutively from 1 to 90, then "1,2,3" forms an adjacent >sequence, but "1,4,5" does not. In this sense, there would be >88 triplets in Matthew, and the question would then be the >probability that they would appear in the same sequence in >Thomas should be 88 x 1.418681193962e-6 = >1.248439450687e-4 = >.0001248439450687 which is still a pretty small probability. > The problem here is that I only considered the three-saying sequence from Matthew's gospel, whereas you want to consider ANY [synoptic?] gospel. I continued: >If you wanna count "1,4,5" sequences (i.e., same order in >Matthew and Thomas, even if separated by intervening >sayings in Thomas), then the number of possible matching >sequences multiplies quite a bit, but at the cost of making the >matching sequences seem less dependent. > You wrote: >From Rene we have 30 Mk 77 Mt 70 Lk for A sayings. > >Thus we need an ANY statistic for ALL three (not each of the three >separately). What odds that three would be in sequence anywhere >in any of the three? OK, given your citation from Rene, 30 Mk => 28 possible sequences of 3 sayings; 77 Mt => 75 possible sequences of 3 sayings; 70 LK => 68 possible sequences of 3 sayings -------------------------------------------- ANY = 171 possible sequences of 3 sayings. Now, if you don't like my count, or the reasoning by which I get it, you can let me know. But what I get from this is 171 x 1.418681193962e-6 = 2.425944841675e-4 =.0002425944841675 Now, remember that the null hypothesis here is that GThomas represents a RANDOM sample of sayings from the Synoptics. Or, more precisely, that when a saying in Thomas has a synoptic parallel, its placement in Thomas is RANDOM, being completely unaffected by its placement in the synoptic gospel which it parallels. >From which I still conclude from the above computations that, given the null hypothesis, the probability that a three-saying sequence would appear in GThomas in the same order as the parallel three saying sequence in any of the synoptics, by chance, is extremely small. The most logical alternative hypothesis, that the three-saying sequence in GThomas that parallels the same three-saying sequence in one of the synoptics did not happen at random, is therefore strengthened. But what would that mean? The following possibilities may be considered: 1. Thomas borrowed the sequence directly or indirectly from that synoptic Gospel. 2. Thomas borrowed the sequence directly or indirectly from *the same source* as the synoptic gospel. Add other hypotheses as desired. Bob Robert Schacht Northern Arizona University Robert.Schacht@nau.edu "This success of my endeavors was due, I believe, to a rule of 'method': that we should always try to clarify and to strengthen our opponent's position as much as possible before criticizing him, if we wish our criticism to be worth while." [Sir Karl Popper, The Logic of Scientific Discovery (1968), p. 260 n.*5]