Monday, January 9, 2017

Subtraction Priming

You may have come across a viral video on Facebook from "deception expert" Rick Lax, who invites you to participate in a little pop quiz involving numbers. If you haven't seen it, watch the 1-minute-plus video right now. (I'd embed the video in this post for you but I'm not sure I'm allowed to do so.)

If you were like me, you thought of  the number 7 at the end. Of course, this is exactly the number Lax wanted you to come up with. 

So how does it work? Or does it work at all? There was some discussion about this urgent matter on Facebook in the Psychological Methods Discussion Group. The moderator of that group, Uli Schimmack, who also thought of 7, suggested this was the result of priming. But then he questioned his explanation: "We don't know because we don't know how often he gets it right? We just see 1 million shares. It is like reading Psych Science. We only see the successes."

This makes sense. In theory there could be a massive file drawer of unshared videos by people who didn't pick 7 and the whole thing could be the result of the social media version of publication bias, sharing bias. Uninteresting.

Others in the group provided links to papers showing that people pick 7 here simply because it's the most popular number. Also uninteresting.

But is our world really this mundane? I refused to believe this, and so did Uli. So what else could be going on?

I hypothesized that I got the number 7 because it was the only number between 5 and 12 that was not mentioned. Here are the numbers we get to see in the video:

 5 + 3 = 8
 9 + 2 = 11
10 - 4 = 6

My thinking was that people have a desire to be autonomous. This would then, ironically, direct them toward the number 7, as all the other electable numbers had already been "suggested." I was heartened to see that moving people away from numbers by mentioning them is indeed a trick mentalists use.

I decided to test my mentalist hypothesis. I created a simple version of the pop quiz, using similar timing to the original video. I thought that if the mentalist trick works, I should be able to shift people's preference to a different number, namely 8. I used the following numbers:

 5 + 1 = 6
 9 + 2 = 11
10 - 3 = 7

So now 8 is the number that is left out. I ran my experiment on Mechanical Turk. Here is what I found a few hours later.

Experiment 1: No 8 in sequence

So my mentalist hypothesis clearly got the finger. People still went for 7 and my 8 didn't even outperform that lousy 6.

Uli had a different hypothesis. He reasoned that people were primed by the question: pick a number between 5 and 12. After all, 12 - 5 = 7. If this priming hypothesis is right, then it should be possible to shift people's preference by changing the final question to: pick a number between 5 and 13. So I went ahead and ran that experiment on MTurk. And what do you know:

Experiment 2: Range 5 to 13

So clearly it is possible to shift preferences away from 7. Priming lives!

Obviously, there are more experiments one could do on this topic. I suspect we'll be discussing them in the Psychological Methods Group soon.

And indeed, we collected new data. If the pattern shown in the previous figure is due to subtraction priming, then we should find people reverting to the baseline preference for 7 when all they need to do is pick a number between 5 and 13, without a sequence preceding it. Tat's the idea we tested and here is what we found.

Experiment 3: Baseline

That looks like the pattern we got the first time (7 beats 8) and not like what we got last time. So there is something about having number selection be preceded by the additions and subtraction. Subtraction priming survives!

There are many variants of the experiment one could run. However, the best one to further isolate subtraction priming as a factor is one that uses exactly the same numbers as the second experiment but removes subtraction from the opening sequence. This can be achieved by using the sequence:

5 + 1 = 6            
9 + 2 = 11          
7 + 3 = 10

The key difference with the second experiment is the absence of a subtraction sign. And apparently, this makes a big difference. As in experiments 1 and 3, 7 is now the preferred number, albeit by a small margin, as in all the other experiments except the first one.

Experiment 4: Addition only

So the only experiment in which the number 8 was the preferred choice was Experiment 2, in which the final trial in the opening sequence was a subtraction and in which subtraction of the endpoints of the range yielded the number 8: subtraction priming.

Next step: thinking of some confirmatory experiments.

*Thanks to Uli Schimmack, Laura Scherer, Robin Kok, and James Heathers for some of the references and comments used in this post.


  1. I would have a bet on 7 being a particularly salient number in many Western cultures for its association worth luck. You could run a control group who were exposed to either no priming or random priming and see if that changed anything. With Chinese and maybe some other Asian participants, I would expect more 8s. And judging by the number plates that 25-year-old drivers of 13-year-old BMW 325s choose, I would expect plenty of 6s in Germany. ☺

    1. Thanks Nick. Someone on Facebook also mentioned cultural differences involving the Chinese. The preference shift to 8 in the second experiment here shows that context can overcome the base rate at least to some extent. I suspect the same would be true for Chinese subjects: if they have a preference for 8, the task may shift it to 7, or 9 for that matter.

  2. Interesting (I got tricked too). I'd suspect another mechanism at work, apart from subtraction priming, may be scanning across the numberline: people may prefer lower numbers because they are scanning from 5 to 12. It would be interesting to see whether people would come up with a larger number if the question is phrased as "pick a number between 12 and 5". Of course, double-digit numbers may be less preferred, so one could try "2 and 9" vs. "9 and 2".

    1. Interesting point. We'll keep this in mind.