As far as I'm concerned, if it's on a historical marker, it really happened. |

I am very good at asking questions like this, but not very good at answering them. That's why it's a very good thing that I have a wonderful reader who sent me this amazing letter after reading my Left-Handed blog posts. Here's what this reader had to say about my observations:

I'm a long-time reader of your blog (and your book, which I greatly enjoyed). I'm also a mathematician, and for once that's actually relevant. Regarding the surplus of lefts in the Hill case, there are mathematical tests that can determine if this kind of pattern is statistically significant:

https://en.wikipedia.org/wiki/Binomial_test

I was pretty amazed by this explanation, but, sadly, my reader's "pretty straightforward" math did not appear so straightforward to me. So, my reader kindly wrote again to explain further, and I reprint it here in the hopes that it might trigger some thinking among more of my readers:For a situation like this, the math would actually be pretty straightforward. The tricky part would be designing the rules for doing the data collection without introducing subconscious bias. (Ideally, one would get some undergraduates who don't know what you're expecting to find to do the actual counting.) But if you're interested in pursuing this rigorously, the math exists.

Still fascinating, but still a a few levels of complexity above my non-mathematical mind. The part I did understand, about getting grad students to make sense of the Hills' data without needing to be paid, is outside my present capabilities. So, my wonderful reader sent a third letter:We can never prove that any sequence of lefts and rights isn't anything more then a weird coincidence, at least not with math alone. But we can calculate what the probability that we would see a sequence that extreme is if left and right are equally likely. If that probability is very low, we can conclude that left and right are probably not equally likely. By tradition, a probability of 5% is usually used as the threshold for rejecting the hypothesis that they're equally likely.It's basically like flipping a coin. We can never prove that the coin is bad from coin flips alone. But while a hundred heads in a row could be coincidence, we would still be justified at that point in deciding that the coin is bad.

The tricky part is designing the rules to decide what counts as a left and what counts as a right, and implementing them in a fashion that avoids subconscious bias. For example:

1. If an event occurs in the book that has no direct relationship to the Hills - e.g., John Fuller mentions passing a diner on the left as he's driving home - is it counted?

2. If a left occurs that implies another left - e.g., the alien stands at her left side and then touches her left arm - is that one left or two?

3. If the same event occurs in two different sources - e.g., the alien stands at her left side in two books - is that one left or two?

4. Which sources do you use?

These questions really need to be answered before doing any counting. In an ideal world one would get hold of some undergraduates willing to work for course credit and have them do the counting without knowing what you expect to find, but I'm assuming that resource constraints prohibit true double-blinding.

To be completely open about my own views, I'm about 95% convinced that the Hills' experience was entirely the product of false memories induced by hypnosis. But given my tendency to grumble about insufficient scientific rigor, I felt it would be hypocritical not to make the suggestion.

The math part of the analysis really isn't hard to do. There are online calculators that will do it in your web browser - I've done some Googling to see if I can find a good one, but most also include a bunch of extra bells and whistles that make it seem more complicated then it really is. For example, there's this one:http://www.socscistatistics.com/tests/binomial/Default2.aspxTo use that, enter:

1. The total number of both lefts and rights under n.

2. The number of lefts under k.

3. 0.5 under p.

And hit calculate. The number you're looking for is "the probability of exactly, or more then, K out of N". So for example, if there were 15 lefts and 5 rights, then n=20, k=15, and the probability of observing this event by chance is 0.02069. Meaning that, if the pattern is not real, there is a roughly 2% chance that we would observe that many lefts by pure coincidence. That's under the threshold of 5%, so we can conclude that this may be a real phenomenon.

The tricky part, like I said, is deciding what to count as a left or a right. For the most part it shouldn't really matter what you decide as long as you're consistent.

Strangely enough, by the time I read this third letter, I felt myself starting to understand, if even just a little bit. Knowing that Dr. Mark Rodeghier, the scientific director of the J. Allen Hynek Center for UFO Studies, did a lot of work with statistics, I ran this saga past him, to get his take on it. Mark did not let me down:

This makes sense to me, and when I read through the thoughts of these two very smart people, I can start to see some way to study what I perceive to be the left-handed bias of the Hill case. Not sure where I'll ultimately go with this, but there's a lot to think about, and I'd love to hear from other readers on this.I haven’t come across any bias such as this before with the case details in an abduction (or any case, for that matter). Your statistician can dream up methods to test this, but as another data/stats guy, I say you need more data, i.e., you need to look at other abduction cases to see if you can find something similar, or not. You would need to choose cases with lots of detail, such as Travis Walton, or Pascagoula, or maybe a few of Budd Hopkins’ more detailed cases. Or the Allagash abduction from Maine.

Before I do anything more on this, though, there's another twist to the story that I need to process. The other day I was searching for a reference in

*The Edge of Reality,*the 1975 UFO book co -authored by Dr. J. Allen Hynek and Dr. Jacques Vallee, and I came across a fascinating comment from Dr. Hynek. He was describing his experience in 1966 when he had the opportunity to interview the Hills after they had been hypnotized by Dr. Benjamin Simon. Barney and Betty were seated side-by-side on a sofa while under hypnosis, with Betty seated to Barney's left. As the questioning began, Barney was recounting his and Betty's drive home on the night of their alleged abduction, with Barney behind the wheel of their Chevy and Betty in the passenger's seat, watching an odd light in the sky...

Wow... I don't know about you, but I find this detail arresting. This right-left switcheroo may not help to understand the apparent left-handed bias in the Hill case, but it tells us a lot about the efficacy of hypnosis. This interview took place in Boston in 1966, but"In the experience I had when they were hypnotized for an hour and a half, a remarkable thing was the incident in which Betty was sitting to Barney's left, and Barney said to Dr. Simon, 'Something is funny. I know that Betty is sitting here [to his right, where she would have been since he was driving] but why is her voice coming from the other side?' So, he arranged their seats and Barney was happy."

*Barney was also back in his car driving along that New Hampshire highway in 1961...*