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Wednesday, October 2, 2013

How to Lie with Statistics

A recent email from a reader of this blog pointed me to a website I'd seen but forgotten about, in which the author attempted to prove that Patsy and only Patsy could have written the Ramsey "ransom" note by means of a statistical analysis. If you're curious, here's the URL:

I had to laugh, because this person's use of statistics was clearly a travesty. It reminded me of the title of a book I'd heard about, published back in the 50's by Darrell Huff, entitled How to Lie with Statistics. Here's how his little game worked:

Our "expert statistician" based his analysis on only two examples of Patsy's writing, drawn from a comparison done by journalist Frank Coffman (who later became a staunch Ramsey defender). The first, is this one:

Note that the above contains all of eleven words, not counting Patsy's signature, in cursive and the block letters at the bottom, which could have been penned by someone else.

Here's the other:
Anyone directly comparing either of these documents to the ransom note would immediately notice the complete difference in style between the hand that wrote them and the hand that wrote the "ransom" note. But our author could care less about the look of Patsy's hand -- he's interested only in making a statistical analysis of how likely it is that both Patsy and the writer of the note would form their letters in certain ways.

His Exhibit One is intended to assess the likelihood that both Patsy and the note writer  would switch "back and forth between printed block letters and cursive script letters at random when printing." Well, this is odd, because the note contains very few examples of either block lettering or cursive, and the only example of cursive I can find in Patsy's samples is in her signature. And since most people write their signature in cursive, that would be expected, no? And I see no examples of block lettering by Patsy, aside from capital letters, which are usually written that way, and the bottom of the first example, which is clearly separate from the rest, so sorry but I see no examples of Patsy going "back and forth" between block and cursive, at least not in these documents. Nevertheless our statistician sees three different possible variants:
  • Note written completely in cursive script style text.
  • Note written in completely in printed block style text.
  • Note written as shown in a combination of both styles.
And since, according to what he claims to have seen, he (falsely) concludes that both the note and Patsy's exemplars are in a combination of both styles. And since there are three possibilities, that means there is a 3 to 1 chance that the same person wrote all three documents:
There are only three possible variations the author of the ransom note could have used which are listed in the box above.  That gives us a one-in-three possibility or 3:1 odds if we were to guess which characteristic any person would use when writing an identical exemplar.
Yikes! Even if the similarities he sees were actually there, the notion that this sort of analysis gives us any sort of meaningful odds regarding the author of the note is completely unwarranted. For one thing, there is absolutely no control over the possibility of cherry picking, i.e., concentrating on the sorts of comparison that give you what you want to see and ignoring others that might give you the opposite.  For another, we have no way of knowing what the odds would be for anyone other than Patsy, because no other exemplars are compared, only hers. If we include the one example we have from John in our little game, we see that he combines block letters with manuscript letters, notably using a block letter "F" as the second letter in the word "oF". And we see something very similar in the ransom note, in the word "iF." And that's not the only place in the note where we find block "F" in the middle or end of a word. So by this reasoning, the same 1 in 3 odds also apply to John. But John is not considered in this comparison, only Patsy.

Moving on to Exhibit 2, our statistician writes: "Patsy Ramsey connects the cross stroke on the letter "t" to the following letter "e" she prints." And we are provided with examples from the ransom note in which the letter "t" is also followed by the letter "e" in a supposedly similar manner. The problem here is that the horizontal in Patsy's "t" continues smoothly to connect with the following "e" in a single stroke. Whereas if we look carefully at the note, we see that in almost every case, the cross stroke on the "t" simply abuts the cross stroke in the letter "e" -- there is no continuity between the two strokes, they just touch one another.

Now if you look really carefully at the note you'll be able to find a few examples where the two letters are connected by a single stroke, but what can that mean, statistically speaking? And here we must consider a problem completely ignored by our statistician. What can it mean if, say, Patsy connects the letters 90% of the time and the note writer connects them only 5% of the time? Does that count as a similarity or a difference? Statistically speaking, it would certainly count as a difference, and a significant one at that. But our analyst has made no effort to assess the relative frequency of any given trait, he is simply cherry picking what suits him. If he can find one single example of something that appears to be similar in some way, that's good enough for him.

Exhibit 3 is concerned with the difference between manuscript "a" and cursive "a". And here again the claim is that both the note writer and Patsy switch back and forth between the two. Sorry, Charley, but statistically speaking you have the same problem here as above. Patsy does indeed have a tendency to switch back and forth between these two forms of the letter "a," though that's more apparent in her London Letter than the examples seen above. However, the great majority of "a"s in the note are manuscript, with only a very few written in cursive. So again, statistically speaking, there is a huge difference between the two, NOT a similarity. Seeing that Patsy tends to use both forms and then searching to see if you can find both in the ransom note, even if one type is relatively rare, sorry but that's cherry picking, NOT statistics. And if in fact both forms were not found in the note, then that difference would be ignored, wouldn't it? Well, it wouldn't be ignored in a truly scientific comparison, where differences need to be given exactly the same weight as similarities. But clearly our "statistician" has no interest in spotting differences.

I don't really need to go on, but I will, because this is kinda fun. Exhibit 4 concerns the presence of the "straight letter "y" descender." "Patsy Ramsey forms the letter "y" with a u-shaped arc to the right followed by a straight line downward." And so, apparently, does the writer of the ransom note. Since he finds 6 different possible ways of forming that letter, that gives him 6 to 1 odds in favor of the note being written by Patsy.

Well, if you look carefully at the note you'll find that it contains at least two types of letter "y," one with a u-shaped arc at the top and one with a triangular shaped "v" at the top. We also see both straight line vertical descenders and descenders slanting down to the left. And lo and behold, we find both types in John's sample, the triangular, left-slanting type in the name "Ramsey" and the u-shaped, vertical descender type in the word "satisfactorily." And if you don't believe me, take a look for yourself:

So, according to the method pioneered by our intrepid statistician, the odds in this case are far more with John than Patsy, because, after all, how many times would you find BOTH ways of forming both elements in the letter "y" in the writings of any two people? Unfortunately, however, our "expert" is focused only on Patsy, and only on whatever he can find in Patsy's exemplars that might have some similarity with what he can find in the note.

In the next exhibit, we are informed that both the note writer and Patsy like to write the letters R and D with an overhang at the upper left. But once again we find the same trait in John's writing.

I could go on, but at this point I'm getting bored. As should be clear, this is not really a statistical analysis at all, but in fact a travesty of both statistics and scientific method. I'm not saying this person was deliberately "lying with statistics," because that's probably not the case. He simply has no understanding of how to actually use statistics scientifically, with some measure of control, self criticism and humility. Lacking any such skill, he comically comes up with a "One in 55 million" chance that Patsy didn't pen that note. Yeah, right.


  1. Was wondering why JB headstone reads day of death being Dec 25th? How can that be? If an intruder did it (what they want you to think) then he would wait till midnight at least to enter a home with whole family present in house.Hence she would have died on Dec 26. If JR did it he would do so before midnight cause he had to wakeup very early. I think the garrotte was not ment to kill but was part of his sexual sadistic repetitve molestation of JB.Strangulation without killing is a common fetish with the sexualy perverse.She wasn't ment to die,hence the sloppy cover up. Thanks for your work so far. You changed my mind and yes its a shame as to how society protects the monsters of the world.I still cant figure that part out.

    1. I guess someone in the family decided it would be "nicer" if she died on Christmas. I don't think it means much more than that. It's been suggested that the "intruder" entered the house while the Ramseys were partying with the Whites, so I guess it would make sense, from Patsy's perspective anyhow, to assume she was killed later that same evening.

      I understand from others with a better knowledge of knots than I have, that this type of knot wasn't really the sort of slip knot that could easily be tightened and released, so I'm skeptical of the sexual sadistic angle. I think it's more likely to be simpler than that. I think the purpose of the head blow was to suddenly knock her out, so she wouldn't feel any fear or pain, and the purpose of the ligature was to finish her off by strangling her - in such a way that her killer would never need to actually lay hands on her.

      I'm glad I've changed your mind. Thanks for letting me know.

    2. I noticed the paint of paintbrush completely stripped to wood. if you look at PRs art caddy, the broken brush handle looks like new and its bright blue.I believe this garotte handle had to be used before. Maybe it wasn't a garotte but some sort of device inserted into JB to create tension. Just a homeade device. It would go along with the records of previous digital penitration. I know you say it would tear her but if done gently it wouldn't. Not all sexual crimes are done in a brutal force kind of way. Especially molestation vs rape. Remember the fist report stated death from strangulation.
      Thanks for replying,Alexandra

    3. I do think she probably died of strangulation, which leads me to believe the strangulation came last, after the head blow. As to whether or not the brush handle was ever used for anything else, I have no idea. Some things we'll probably never know.

  2. DocG,
    I read over your post Ruled Out -- Part 3: Courier New and thought you nailed how the ransom note was written. My own experience with using source material to create a new font, has always resulted in a new handwriting style that is somewhere between the source material and my natural inclination. Creating a chart which shows the courier letter, to a RN letter to John's writing and for comparison Pasty's writing, I think would show help show that John was the writer and quiet the Patsy nonsense. Excellent work, by the way...Nira

    1. Thanks, Nira. But I'm not sure exactly what type of chart you have in mind. I've already produced comparison charts for both John and Patsy.

      And I'm afraid that no matter what anyone does, nothing is ever going to quiet the Patsy nonsense. Once people make up their minds to see things a certain way it's very hard to get them to change.

  3. A nice take down. I'm very far from being a statistician but it's basic that one should at least acknowledge that both types of "ys" are found in the note and JR's exemplar. But of course figuring out who wrote the note isn't the point, the point is to pretend great mathematical certainty that PR wrote the note.

  4. Thank you for your blog. It's the most convincing explanation I have seen. I have a few comments and questions.

    1. I think that JonBenet was unconsciously set up by Patsy to be her replacement for JR during her illness and in case she died. That is why she was so sexualized.

    2. JR may have sexually abused her out of a sick desperation and a need to act out power and control during a time of a huge loss of control.

    3. I think he hit her on the head when she protested the abuse. (Didn't neighbors hear a scream?). Maybe that is when he duct-taped her after the scream and then hit her when she struggled. I think his abuse involved asphyxiation and bondage.

    4. When she did not come to, JR may have stayed there in the basement trying to make a decision. He probably realized then that JonBenet would eventually tell the doctors if he called 911 or they would see signs of sexual abuse.

    5. I think he blamed her for "making" him kill her and strangled her violently. The photos of her neck show intense rage and violence. It would have been just as easy to suffocate her with a pillow or put a plastic bag over her head. The garrote has a sexual significance, IMO. think the RN unconsciously refers to the strangulation by mentioning beheading her.

    5. I think he had to discard the underwear because they had too much of his DNA on them.

    6. What are your thoughts about the duct tape?

    1. I'm glad you find my thinking convincing, thanks.

      As for the details, I try to avoid speculating any more than necessary, because there is really no way of knowing what happened and in what order. You make a valid point regarding the strangulation though, because it's true, it would have been easier to simply place a plastic bag over her head, or suffocate her with a pillow. On the other hand, there is nothing erotic about being strangled with a ligature. That sort of thing is usually done by hand, I would suppose.

      I think it possible that some of his sperm could have dripped onto her panties, and that's why he needed to change them. Her body was wiped clean, but it wouldn't have been possible to wipe the panties clean.

      The duct tape is an interesting aspect of this case. It's just one small strip over her mouth, which would have been very easily displaced if she'd been conscious when it was applied. So it looks a lot like staging. I think it possible that he applied that tape at some point in the morning, after the police had been called, in a desperate attempt to make it look like she'd been attacked by an intruder.

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