Part 4: Full Statistical Calculation of a Matrix
by Roy A. Reinhold April 20, 2000

We will fully evaluate the statistical significance of the Sid Roth life matrix using the methods shown in parts 2 and 3 of this 4-part article series on statistics. One should keep in mind that this is a post-matrix-development calculation rather than having been done before the matrix was found. However, the method used can be applied predictively in the future. Besides, the method used to find a life matrix allows much further development after the correct matrix area is localized. For example, in developing the Sid Roth life matrix, my method is to use the CodeFinder program and search for the last name as the main/center term and about 15-20 unique terms about that person. The other terms include first and middle names, spouse, applicable dates, etc.

After the correct location for the life matrix is found, then we assume that all other relevant information on the life of that person is within the matrix. In that sense it is predictive. In the Sid Roth life matrix, all 8 relevant clusters were developed after finding the correct matrix location. Viewers can see the entire Sid Roth Life matrix elsewhere on this site in the Hebrew matrixes section, and further discussion of it in the 3-part article on it in the Articles section.

The overall equation for statistical calculation of the matrix is shown in part 3 of this article and is:

matrix probability = (probability from sum of positive matrix R-values) x (overall probability calculated for all clusters after calculating the probability for each cluster)

We will recalculate the expected occurrences for terms in each cluster and arrive at a cluster R-value for each term. Then we sum the positive individual cluster R-values to arrive at an overall cluster R-value. All 8 clusters are calculated in the same way, and then the overall cluster R-values are summed to arrive at the matrix clusters R-value. In order not to double count the significance of terms, we only use non-cluster term's R-values for the first part of the equation above. At the end we apply a number of corrections to more conservatively state the probabilities. Finally, we will arrive at a single number for the probability of the matrix. The other equation used in the calculations is for R-values.

R-value = log (1/E) (where E is the expected occurrences), and therefore E = 1 / antilog (R-value)

Anyone can do these calculations in minutes with a scientific calculator. To take the antilog, just use INV --- LOG, and then use the 1/x key to get E.

Data: the Sid Roth life matrix is made up of 118 rows and 115 columns, or 13,570 letters. It has 73+ terms and 8 clusters within the matrix.

Let's start with cluster 1, the date of birth area. Below are the Matrix Report and matrix sub-area for cluster 1.  As seen above, we can count the numbers of rows and columns for the cluster area, and we get 47 columns and 20 rows. There are 940 letters in the cluster area, therefore, cluster 1 comprises 940/13,570 = 0.0692704 of the area of the entire Sid Roth life matrix. We will use that to recalculate the expected occurrences for the cluster area and the cluster R-value for each term. The column in the Matrix Report above merely shows the R-value for each term where they would be expected to occur anywhere in the entire Sid Roth life matrix, and we need to recalculate them for the cluster sub-area. We use the equation above for R-value and for E, to get the new cluster R-values. This is relatively easy with an inexpensive scientific calculator. The calculation results are shown below in the graphic. We could have eliminated some of the duplicates and made a smaller cluster area size, but I chose to demonstrate the procedure using all terms in cluster 1 from the Sid Roth life matrix. As you can see, the R-values are more positive for each term in cluster 1, because the area in which they are found is smaller than the overall Sid Roth life matrix.

The next step is to sum the positive cluster R-values to get an R-value for the cluster, and that is 2.258. I have chosen to more conservatively state the cluster R-value by reducing it for the number of clusters within the overall Sid Roth life matrix that are the same size. That is I reduced it by 13,570/940=14.436. This has the effect of reducing the cluster R-value from 2.258 to 1.099. I will do that for all 7 of the remaining clusters in the Sid Roth life matrix. The cluster R-values are:

cluster 1 has a cluster R-value of 1.099 (47 columns, 20 rows, and 940 letters)
cluster 2 has a cluster R-value of 1.396 (39 columns, 28 rows, and 1452 letters)
cluster 3 has a cluster R-value of 3.837 (28 columns, 9 rows, and 252 letters)
cluster 4 is not meaningful (74 columns, 21 rows, and 1554 letters)
cluster 5 has a cluster R-value of -0.779 (37 columns, 20 rows, and 740 letters)
cluster 6 has a cluster R-value of -0.246 (52 columns, 21 rows, and 1092 letters)
cluster 7 has a cluster R-value of 0.899 (63 columns, 16 rows, 1008 letters)
cluster 8 has a cluster R-value of 2.938 (64 columns, 11 rows, and 704 letters)
NOTE: on some clusters I reduced the number of terms to arrive at the matrix size.

Once we have calculated the cluster R-values for each cluster, we sum those with positive cluster R-values to get the overall clusters R-value for the entire matrix. Summing them above, we get an overall clusters R-value of 10.169.

In order not to double count terms when calculating statistical probability, we examine the entire Matrix Report to see which terms in the overall matrix are not in clusters. We then use the equation near the beginning of this article to arrive at a final R-value for the matrix. Ignoring the R-value of the main term, we see that there is only one term not in clusters, and it has an R-value of 1.736.

Our overall matrix R-value is now = 1.736 + 10.169 = 11.905

the antilog of 11.905 = 8.0352612 times 10 to the 11th power.

Now we apply a conservative correction factor to account for how many times the main term (Rothbaum) appears in the search text (entire Tanakh) for the ELS range from -4478 to +4478, which is 13.4005 expected occurrences of RothBaum in the Tanakh. We divide 8.0352612 times 10 to the 11th power by 13.4005 and we get, 5.996 times 10 to the 10th power.

And to be even more conservative, we apply the row-split correction for use of a row-split of 6 to apply the multi-dimensional design aspect of the Bible code and arrive at the optimal matrix display. Divide 5.996 times 10 to the 10th power by 6, and we get 1 chance in 9.994 times 10 to the 9th power.

Restated, there is 1 chance in 9,994,000,000 of the matrix occurring by chance, or 1 chance in approximately 10 billion.

The reader should note that the boundary box method for clusters was proposed by Dr. Robert Haralick. While it provides an easy to calculate method for clusters of terms within a boundary box enclosing the terms in the cluster, it will always understate the probability. The reason can be easily seen in cluster 8 of the Sid Roth life matrix. In that cluster, we have the names for two long-time employees named Bob Duval and Janie Duval, and the cluster shows their association with the Messianic Vision radio program. The boundary box method assumes that all terms are random in the cluster, while visually one can see that Bob crosses Duval and Janie is also close to Duval. Proper application of proximity of related terms within the cluster would account for crossing or closely parallel terms. The boundary box method doesn't fully account for all relevant proximity information about terms within the cluster, since it assumes random appearance of terms in the matrix.

We hope to see commercial Bible code software programs build a system to arrive at a single number for the probability of a matrix. (CodeFinder and Keys to the Bible now do this). The above system could be built into these programs today, and give the user an almost automatic method for arriving at a single measure. Although it understates probability, it is a useful means for the average person looking at a matrix, to gauge whether it is meaningful.

What are the ramifications for skeptics? A matrix with a statistical probability of 1 chance in approximately 10 billion is powerful in saying that the Bible code is a real phenomena, and this Sid Roth has been and can be duplicated for the lives of others. I'm not claiming that there is a life matrix for every person, however, one might make that assertion after seeing that after doing many of them, they are all in the Bible code.

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