Technical Addendum:
The Conclusive Significance
of the Divine Name Mosaics in the Peshitta

Estimating the odds of chance occurrence of Bauscher’s findings is complicated by certain key issues. As noted in the first bulleted point regarding the comparison of ranked Z scores, the distribution of Z values from the control text is more dispersed than would be indicated if mosaics conformed to a typical bell-shaped normal curve, or any one of several other common probability distributions. As mentioned above, this is due to the presence of correlation in many of the mosaics.

Bauscher’s way of dealing with this has been to measure the degree of correlation in each mosaic and to exclude from the above comparison examples where the correlation is too high. This is helpful to a fair degree, but the problem is that the remaining examples from the control text are still too spread out to conform to a bell-shaped curve. This means that probabilities estimated by standard statistical tests that assume the presence of normally behaved phenomena will be inaccurate.

A solution to this problem is to apply a statistical test that makes no assumptions about the statistical nature of the underlying phenomenon. Such a test is termed a non-parametric test. The Wilcoxen-Mann-Whitney test is one of the most widely accepted tests of this type. As intimidating as the name of this test is, it is actually simple to understand. First we rank the Z scores of all of Bauscher’s findings for four-letter-long divine names—exactly as they appear in the left column of the first table above. Then we sum up the ranks of the Peshitta findings. That total is 2,091, and we will call it the “ranksum.” If the Peshitta results were totally unremarkable, the rankings of the Peshitta results and the control results would be randomly dispersed among one another. The sum of all of the rankings is 6,786, so the expected value of the rank sum of all the Peshitta findings should be exactly half of that, or 3,393. This makes sense because, for example, if all of the Peshitta findings had rankings that were odd numbers (i.e., 1,3,5,7,…..111,113,115) the ranksum would be 3,364. And if all of the Peshitta findings had rankings that were even numbers, the ranksum would be 3,422.

It so happens that the ranksum statistic becomes normally distributed as the sample size becomes large. So the ranksum conforms to a bell shaped curve, and the average variation from expected (commonly called the standard deviation) is the square root of (1/12)mn(m+n+1), where m and n are the number of observations from the Peshitta and the control text [see page 437 of Statistical Theory, by B.W. Lindgren, 2nd Edition, Macmillan, 1968]. Thus the standard deviation is 181.1049, and the Z-value of the Peshitta ranksum is 7.189 (=(3,393-2,091)/181.1049). Given a normal bell-shaped curve, this means that the odds of chance occurrence of the Peshitta findings are less than 1 in 3.047 trillion. So we can conclusively reject the hypothesis that the Peshitta findings are due to chance.

The Peshitta findings are far more improbable than the Wilcoxen test indicates, however. In statistical language, a non-parametric test is not very efficient. In other words, it only tells us that the odds are clearly “less than” some value, but it doesn’t provide us with an accurate estimate of the exact odds. This doesn’t really matter, however, because the odds indicated by the test are already so remote that we should conclusively reject chance as an explanation of the results.

One thing that the Wilcoxen test doesn’t measure adequately is that the Peshitta Z scores are not only higher in general than the control Z scores, they are typically far greater. To appreciate this, suppose we took all of the Peshitta Z scores and we cut them in half. The resulting Peshitta ranksum would be 2,403, still far less than the control ranksum of 4,383, and the odds of chance occurrence of the halved Peshitta Z scores would still be less than 1 in 43,454,423. We would still very conclusively eliminate chance as an explanation. In fact, we could even reduce all the Peshitta Z scores by two-thirds and the odds of chance occurrence would still be less than 1 in 27,823.

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