FINDINGS

Looking at Standard Deviation, with Latin and Arabic known-language texts included for comparison, produced results consistent with the hypothesis that gallows characters have meaning and are not null:

Standard Deviation increases in every manipulation of the source text. The most marked increase occurs in those versions with character omissions (NO BPVF for example). The total conversion modification (WQYX to S) also shows a significant increase in Standard Deviation. It is likely that the high Standard Deviation resulting from total removal of all gallows characters (ALLGONE), when compared to the source text, reflects lexical importance in at least some of the gallows characters.

It is interesting to note that NO BV and NO PF returned quite different Standard Deviations.

The rank order of terms within the text samples may be significant. By looking at rank, rather than frequency, it is possible to differentiate between texts, looking for close pattern matches, and apply appropriate statistical measures.

The Spearman rank correlation coefficient (Spearman's rho) was used to examine differences in rank order between samples, as well as levels of significance.

The Spearman rank correlation coefficient is an outgrowth and expansion of the Pearson correlation coefficient, and is designed for use with ordinal data (Roscoe, 1969). Thus, it is an excellent tool for examining differences in rank.

To do this, the Voynich and related data was first organized from each text sample by frequency, re-ordering rank in the process. The Spearman rank correlation coefficient was then applied.

As might be expected, all the samples, when compared statistically with the source CURRIER text, returned scores well above the .01 level of significance. The lowest nonparametric correlation, NO BV, was 0.426, and they ranged as high as 0.69 (NO BVPF).

Performing a logarithmic transformation of the frequency data of the texts yielded a set of relevant graphs illustrating similarity and difference between samples. Each sample text demonstrated consistent negative correlation.

The sample texts that most closely mimic the original COURIER are NO B and W to S, with NO B diverging only slightly (less than 1%) from the source text. CURRIER has 217 more unique words than NO B, but the samples are otherwise quite similar. The character B represents 1.44% of the text, and is the 13th most common letter in CURRIER. In contrast, the character A represents 3.98% of the text, and is 7th most common in CURRIER. NO A's correspondence with CURRIER is not as close as NO B, which is most likely due to the relative importance of the letter in the Voynichese alphabet. This, in turn, argues against ascribing importance to the close correspondence between NO B and the source text.

The sample texts with the widest divergence from COURIER (excluding the known-language texts GENESIS and QU'RAN) are NO PF and ALLGONE. In the case of ALLGONE, 10.49% of the characters in the manuscript have been stripped away (every gallows variant). NO PF removes 5.86%, the two most frequent gallows variants. The wide variance between these samples and the source text suggests that the wholesale removal of the gallows characters has a profound impact on the underlying structure. This, in turn, points toward lexical significance for those characters.