Work with me here! If you want me to make a predition, and least give me some data to use!
(If you want to modify your selection click here to go back).
|Box A||Box B|
|(Missing data)||(Missing data)|
|I can't make a prediction unless you complete both boxes!||I can't make a prediction unless you complete both boxes!|
Spooky huh? go back and repeat the test. See if you can modify your random guessing to beat the random rolling.
Well, it probably worked on you because people are particulalry bad at generating random numbers; they often over think the concept.
There is a subtle, but important, difference between random and uniformaly distributed. Any truly independent event that happens (such as flipping a coin) has no knowledge of past history – the chances of it landing heads, or tails, is the same each time it is flipped. Even though people realize this, they get uncomfortable with repeated runs and sequences that, statistically, should occur quite frequently.
The chances are that, when you made up your half of the data, you probably did not include as many sequences of three in a row, four in a row, five in a row … that probably occur in natural random data.
Here's another example. Which of these images below shows the black dots distributed in the most “Random” way? The image on the left, or the image on the right?
It's tempting to go for the image on the left, but that's wrong. It's the image on the right that is the most random. To the eye, the image on the left appears random because the dots are scattered around the grid, but in reality, this is a pattern. In truly chaotic and random systems, clusters and big gaps happen.
Because of independance, each dot is placed randomly on the picture with no knowledge of the dots that are already present. To generate the image on the left you need knowledge of the positions of the other dots in order to "randomly" space them out.
If you shuffle a deck of cards it's not uncommon for cards of the same suite and/or the the correct numeric order to appear. If you arranged a deck such that no card was next to the card of the same suite or number, it might look random, but actually, it has a fair amount of structure.
And remember, for independent events, history of the past has no influence on future events. If you flip a head ten times in a row, the chances of getting another head on the next flip are still 50:50. Similarly if you pick lottery numbers, you are just as (un)likely to win if you select all your numbers in sequence 1-2-3-4-5-6, or at random. (The balls about to be drawn have no intelligence about the balls already drawn and their chances at being drawn is not changed by the earlier drawn numbers).
To produce this webpage, I implemented the Pearson Chi-Squared test.
For each of your inputs, I counted the number of occurences of doubles, triples, quadruples … in the input. I then compared the frequency of incidence of these against the theoretically expected values (using the Chi-Squared test). The input that more closely matched the theoretical value (lowest Chi-Squared), was the input I predicted as the one most likely to have been generated from the real coin.
So that's it, there is no magic … unless, that is, you believe that math is magic … and that's a good thing …
Check out other interesting blogarticles.