Comments on the Statistical Analysis in Ken Rahn's Essay:
"NeutronActivation Analysis and the John F. Kennedy Assassination"
by Arthur Snyder
In his essay,
The relevant portion of Rahn's essay is quoted below:
Since Guinns data on heterogeneity are the only ones we have, we must base all our conclusions about separability of groups on them. What do his data show? That of 12 zones within bullets, only two differed markedly from the "pack." The other ten zones varied from one another by only 8% on the averageabout the same as Guinns anecdotal 6%. Thus for MannlicherCarcano bullets as a whole, 83% of the time (10 of 12 cases) we may expect bullets to produce highly reproducible fragments (heterogeneities of only 8%), and 17% of the time (2 of 12 cases) we will find much larger variations. Since variations of 8% will keep Guinns two groups of fragments separate to a very high confidence limit (between 95% and 99%), we may conclude that there is an 83% chance that the two groups are actually separate to the 9599% confidence level, and a 17% chance that they are not separate. This is the probabilistic result referred to earlier.
How should we view an 83% probability of having separate groups, strong support for the SBT, and all those other good things? Obviously, its not the 95% probability that a scientist would like, nor the 9095% that a jury needs in order to convict in a criminal trial. But its stronger than any other evidence for the SBT, and far better than any evidence against it. And so it controls the issue. Maybe some day someone will analyze a much larger suite of MC bullets for heterogeneity. Maybe Dr. Guinn will release his large set of analyses from so long ago. In either case, we could have more confidence in our probabilities. But until then, we may state that there is an 83% probability that the hospital bullet had first passed through Connallys wrist, that all the other fragments came from a single head shot, and that only those two bulletsboth fired from Lee Harvey Oswalds Mannlicher Carcano rifle to the exclusion of all other rifleshit Kennedy and Connally that day.
The table at end of this note contains the measurements Ken is referring to. The measurements are the antimony content (in parts per million (PPM)) for four measurements Guinn repeated on each of five bullets. The first 3 bullets in the table represent studies of heterogeneity, i.e., the same bullet sampled multiple times. The last two are studies of measurement reproducibility, i.e., the same sample from each bullet measured multiple times. As Ken notes, the measurements from three bullets studied for heterogeneity seem to cluster, e.g., bullet 6002A has three measurements ~900 and one flyer way down at 358. 6001B yielded three measurements of ~ 400 and one flyer way up at 667. The choice of what is a flyer is a bit arbitrary. Qualitatively at least his division is not unreasonable  2 flyers and 10 "in the pack."
Rahn's 83% is the fraction of Guinn's measurements that are "in the pack"  "10 out of 12 cases". His application of this "in the pack" fraction to CE 399 implicitly assumes that this same fraction applies to it. However, 83% is really only the best estimate of this fraction averaged over Guinn's samples; there is no justification for assuming it is the same for each bullet Guinn sampled much less CE 399. In the "marble cake" model Ken proposes for Carcano bullet variations one would expect that the number (there need not be just two) and sizes of regions of differing composition to vary from bullet to bullet. The probability that a bullet which was a 50/50 mixture of a component with an antimony content ~350 PPM and a component of ~900 PPM would produce the 1/3 pattern observed for 6002A is only 2/3 times smaller than the probability of the most probable 2/2 pattern. Thus, from the extremely limited statistics available there is no evidence that the ~350 PPM "flyer" component of 6002A is substantially smaller the ~900 PPM "in the pack" component. Using the average 83% average "pack" fraction for 6002A or for CE 399 is not justified.
For the sake of argument let us assume that for all Carcano bullets, 83% of the lead has one antimony content and the other 17% has another significantly different antimony content. Even in this case 83% is not the probability that two samples from the same bullet would match. In the "marble cake" model in which two samples from the "flyer" component would also expected to be near each other the probability of getting a match is given by:
P_{match}=CL x (F_{p}^{2} + F_{f}^{2})
where CL is the confidence level of the match considered to be acceptable, F_{p} is the "pack" fraction and F_{f }(=1F_{p}) is the "flyer" fraction. For a 90% confidence level and our assumed 83% "in the pack" fraction P_{match} is 0.64. This does NOT mean that there is an 64% chance that CE 399 caused the damage to Connally's wrist; but only that if CE 399 did leave the fragments in Connally's wrist, there was a 64% chance that Guinn would have found a match and 36% chance that he would not have seen a match. Even if CE 399 had not matched the wrist fragment, that would not have been strong evidence that the wound was caused by a different bullet [a]. The fact that it did match is not strong evidence that CE 399 caused the wound either.
To establish that CE 399 caused Connally's wound one needs to show that the probability of an accidental match between two different bullets is much smaller than the probability of a selfmatch. Guinn actually claimed that this is the case in his HSCA testimony, but it is not true, e.g., the Connally wrist fragment at 797 PPM using a 150 PPM tolerance (which matches ~90% of the "pack" measurements from Guinn's test samples) matches 6002A samples 3 and 4, 6003A sample 1 and measurement 4 of 6001B. The three fragments supposed to have come from the head shot with antimony content ~620 make a good match to 6003A sample 1 and to 3 out of 4 of 6001B repeated measurements. Presumably, nobody is going to claim that Guinn's 6002A caused Connally's wounds or the 6001B was used for the headshot [b]!
Based on these accidental matches we can roughly estimate that the probability of an accidental match is ~1/5 in which case the ratio of the likelihood of a selfmatch to an accidental is ~4/1. There is not enough data to get an accurate estimate of the probability of accidental matches, but it is clear from the number that occur between the wrist fragment and Guinn's sample bullets that an accidental match is not "extremely unlikely, or very improbable" as Dr. Guinn claimed in his HSCA testimony.
Quite apart from the origin of Ken's 83%, the claim that "there is an 83% probability that the hospital bullet had first passed through Connallys wrist, that all the other fragments came from a single head shot, and that only those two bulletsboth fired from Lee Harvey Oswalds MannlicherCarcano rifle to the exclusion of all other rifleshit Kennedy and Connally that day" is a statistical non sequitur. Without knowing the a priori probability of these events such a probability cannot be computed. The a priori probability Guinn's 6001B being used during the assassination is clearly zero. The probability that 6001B was used for the head shot is ZERO despite the fact that the odds were something like 4/1 against the fragments found in the car and recovered during the autopsy matching it.
Rahn's claim is similar to the nonsensical assertion made by the HSCA's acoustic experts that there was a 95% chance there was another shooter on the grassy knoll. Statistical arguments can not deliver such grand claims.
The situation could be improved if multiple precision measurements could be made of lead from the base of CE 399 [c]. Since, only lead from the base is supposed to have been deposited in Connally's wrist, the variations in antimony over the whole bullet are not relevant. It can be hoped that the variation of CE 399 base lead is substantially smaller than the variations seen in Guinn's samples. This would increase the probability of a selfmatch and decrease the probability of an accidental match. If the antimony content distribution of base lead from CE 399 turned out to be narrow enough and centered near the current measured value of 833 PPM [d], the results could even turn out to be in conflict with the single bullet theory.
With the currently available data we cannot discriminate between CE 399 causing Connally's wrist wound and the wound being caused by a different Carcano bullet that accidentally happened to have similar antimony content. However, "lone nutters" can take comfort from the fact that there is no evidence of anything other than Western Cartridge Carcano bullets. Most other bullets have antimony contents at the several percent level and would have been easily detected if they were among the fragments tested. Thus, while Guinn's measurements do not establish the SBT, they are consistent with it.
Intrabullet variations measured by Dr. Guinn
Bullet 
Sample 
Antimony 
6001C 
1 
1139± 60 

2 
1062± 60 

3 
1235± 93 

4 
1156± 90 

Mean/RMS 
1148/71 
6002A 
1 
358± 47 

2 
983± 51 

3 
869± 47 

4 
882± 81 

Mean/RMS 
732/281 
6003A 
1 
667± 58 

2 
395± 54 

3 
363± 39 

4 
441± 51 

Mean/RMS 
466/137 
6001B 
1 
621± 56 

2 
646± 55 

3 
646± 55 

4 
791± 55 

Mean/RMS 
676/78 
6002B 
1 
990± 60 

2 
1007± 56 

3 
942± 56 

4 
946± 56 

Mean/RMS 
971/32 



Notes:
[a] Unless the fraction had been completely outside the ~1200 PPM upper limit on Carcano antimony content  indicating a totally different type of bullet.
[b] Curiously, another "match" occurs between the bullet removed from General Walker's wall and the unfired round found in the Carcano rifle found on the 6th floor of the Texas School Book Depository. Guinn in the report he submitted to the HSCA (not his testimony) uses this match to establish that the Walker bullet is from a Carcano!
[c] If such a program of measurements could be undertaken it would be important to carefully characterize the antimony distribution for unrelated sample bullets like Guinn's with high precision measurements and adequate statistics. Nearby samples need to be compared to confirm the "marble cake" model. The protocol for establishing a match should be developed using data on the samples before the data on CE 399 is examined in order to avoid pernicious ex post facto biases, e.g., if CE 399 had measured 646 (like the notquite matches of 6001B) instead of 833 PPM, this would probably have been considered a good enough match. In the unlikely event that the opportunity to make these measurements should arise, they should be done blind, so that which fragments come from which bullets is not known to the experimenters till after measurement and matching are complete.
[d] I don't know where Guinn sampled CE 399. Probably not the base as he had no reason to expect the inhomogeneity that afflicts these bullets. A sample from the base might turn out to be quite different from the one Guinn measured.