# 50% plus or minus 13% is good or bad guessing. How was this reached?

I made some edits to this question which are separated and inserted at the end. If anyone feels this changes the question, please let me know and I will put it in a separate question.

I watched a documentary some years back and I cant find it anymore. It was either about genetics or twins (specifically identical twins). But I recall a test was done to see statistically if identical twins could read each others minds.

Numbers quoted in such programs stay with me because I always wonder where they come from even though I am not a great mathematician. I do like to know where information comes from.

One quote in particular was something like:

Anything over 63.3% is definitely mind reading. Anything between 63.3 and 37.7% is just guessing. On the + side of 50% is a good guess, on the - side is a bad guess, but its all just guessing. I deduced from this that anything under 37.7% was definitely not mind reading.

The program concluded that as none of the the twins who were tested could get higher than something like 60% they could not say for sure that it was anything more than good guessing given how well they knew each other and their preferences in most cases. However they could also not say for definite that it was not. General population seemed to score much lower somewhere in the low 40% as far as I recall (most likely incorrectly). But again not low enough to say with certainty that it was not mind reading. Just bad guessing.

Please, if your a twin, don't take issue with this. I personally don't care if twins can or cant read minds. What I care about is how this range came about. I deduced from this that there chance that anything out side of this range was certainty of one kind or another (certain success, or certain fail), and anything inside was little better than a good or bad guess.

I want to see if I can apply this to software development. To reduce the risk of not meeting requirements. Obviously the more meetings, prototypes, and info you can get from the customer, and the more you keep the customer involved as the project develops the greater the chance that the project will meet requirements. But I am thinking of a simpler way...

Database design gives at least 40 to 60% of the requirements of any system in my experience. UI prototypes built on top of this will give between another 15% to 30%. With the business logic in between usually making up what remains of the 100%. So if this 50% + or - 13.3% rule is true. Then we can say that as long as we get the database and UI well defined, we greatly reduce the risk of the system not meeting requirements.

I'd like to see how the math community think about this. Also...if anyone else saw this documentary, can you perhaps provide the name of it if possible. Id like to watch it again and follow up on that point.

My question is, how do we know if someone is just making good guesses and what are these figures based on. Surely 13.3% either side of 50% is not just pulled out of the sky.

Also...as a side note, if anyone can remember the name of the documentary I was referring to...

Edits:

I have revisited this post several times hoping for answers. But in desperation I came up with my own way of reaching these figures (63.3%).

Taking a range 0% to 100% we can say accurately that 50% is mid way. We don't need math geniuses to work this out. So lets say it's a fact.

Now lets say we want to remove as much "risk" as possible. Risk being the chances of being wrong. This means we can say we are definitely on good ground if we can guess halfway between 50% and 100% or guess right 75% of the time.

Now lest say, that through much experimentation, its rare to guess 75% correct, so this variance is too far and we want to get a more accurate variance. Then we can accept higher risk of being wrong by taking a value half way between 50% and 75%. Or 62.5%.

If we want to close in even more, we keep moving the margins and dividing by 2 to get the mid point. If we do this correctly, we can with a few more calculations, reach 63.3%...

our margins currently stand at 62.5 and 75%. Half way is (75-62.5)/2 = 6.25.

Add this to the lower boundary... 62.5 + 6.25 = 68.75 and take this as our new upper boundary. To increase further repeat...

Margins currently stand at 62.5 and 65.625%. Half way is (65.625-62.5)/2 = 1.5625.

Add this to the lower boundary... 62.5 + 1.5625 = 64.0625 and take this as our new upper boundary.

Margins currently stand at 62.5 and 64.0625%. Half way is (64.0625-62.5)/2 = 0.78125.

Add this to the lower boundary... 62.5 + 0.78125 = 63.28125.

We can continue this process and all we do is proceed to get closer and closer to 63.3 but at this stage simple rounding will give us the same result as 63.28 rounded = 63.3.

Once we reach this on one side, it's as easy as subtracting it from 50% on the other side to give us the margin spelled out in the original question.

Now lets say I wanted, for example, to develop a software system using this to invest in the stock market, or gamble or decide if I should go for an operation based on past success rates, or whatever? Essentially something that could be life changing.

Essentially I could say that if I can eliminate definite risk of failure (below 37.7%) and get as far away from the mid range (37.7% to 63.3%) as possible, only investing when the chances are greater than 63.3% in my favour. And then weighting the amount to invest, based on the surety of the investment (very little if it's just over 63.3% to much more if it's much higher or closer to certainty).

Is this the correct way to approach the problem? Or have I just conjured up a solution to the problem and made it seem plausible with figures that fit. I guess what I am asking, is what I have done here to justify my solution, viable or dangerous?

• What's your question? Oct 28 '14 at 23:49
• If you accept the premise that twins can't read each other's minds, the highest percentage found during the experiment must be the cap for good guessing. Oct 28 '14 at 23:51
• @UserX - I updated the question to clarify. Apologies for the length. Oct 28 '14 at 23:54
• @Jonny - From what I recall of the program (not very much) they had this +- 13.3% either side of 50% quite well researched and it was based on something relating to chance. This is what has me asking. So this "limit" if you will call it that, was defined before the test. And as it turned out, no one got over it, and very few got under it. So they couldn't completely eliminate mind reading or lack thereof as everything fell well within the good / bad guess zone. Oct 28 '14 at 23:57

## 1 Answer

As you quoted it, this "anything over 63.3%" rule is nonsense. Depending on the design of the experiment, a statistical test will typically set a certain threshold for significance''. For example, the result is significant at the $5\%$ level if random guessing (the null hypothesis) would produce a result this good or better with probability at most $0.05$. But you'll never be able to say that any result is "definitely mind reading".

For example, let's say that your subject is making $100$ guesses, and (if this is done randomly) each guess has probability $1/2$ of being correct. Then a random guesser has probability approximately $0.0033$ of making more than $63$ correct guesses out of the $100$. That looks pretty impressive, and it wouldn't be surprising if you tested $100$ guessers and didn't find any that did so well. But if you tested $1000$ guessers, you'd most likely find at least three who passed the test. They're not mind readers.

For more, see e.g. Statistical hypothesis testing.

• This was my taught too. From what I very loosely recall. I believe they said it was sufficient to prove it was no longer chance. For example, if two people are able to score "consistently" above 63.3% then there has to be some mind reading or at least something else more concrete (cheating) happening that proved it was no longer just chance or good guessing. I am wondering how they reached this as half the documentary was based on such assertions. It was also a well funded / established documentary, like national geographic or discovery. Big name brand not some street joker. Oct 29 '14 at 0:14
• Misuse of probability and statistics is very common, not just in documentaries. Mind you, it could be that they were completely correct in their analysis; it's very hard to judge based on someone's imperfect recollections. Oct 29 '14 at 0:17