Signals and Noise

I love to do experiments. As you know, I started experiments at a very young age--2--when I got to do some sinks versus floats experiments. Since that time, I've done lots of other experiments. Here is the most complex experiment I've done yet. It's called signal versus noise.

To do this experiment, you need poker chips in three different colors. I have red, white, and blue chips. You make two stacks of chips. One stack contains 2 blues, 1 red, and a variable number of white chips. The other contains 2 reds, 1 blue, and the same number of whites. The experimenter then decides which stack to put in the "urn" (my pumpkin basket) and which to hide in a nearby drawer. The other person, then draws chips from the urn, records their color on the data sheet, and then puts them back. After 5 draws, the goal is to guess whether the urn contains 2 reds or 2 blues.

When there are no white chips, it's not that hard to guess correctly. If more reds come up, you should guess red. If more blues come up, you should guess blue. Adding white chips makes things more interesting. The white chips are "noise"--you don't learn anything about the reds and the blues from the whites. After a bunch of trials, Daddy and I learned the following.

The more white chips there are in the urn, the more data you need to make a correct guess. We tried drawing 5, 7, 9, even up to 20 times and making guesses. It gets pretty hard when there are a lot of white chips. The more noise, the harder it is to guess correctly.

Now, for an even more surprising experimental finding. We tried the following comparison. 2 red, 1 blues and 6 whites versus 1 red, 2 blues, and 4 whites. Interestingly, when the number of whites is not the same in the two stacks, you can use the "noise" (the whites) to guess whether there are mostly reds or mostly blues. Amazingly, even without seeing any reds or blues, you can make a good guess. For instance, suppose you draw 7 whites and nothing else. We learned that this is a good indication that the urn contains mostly reds since there are more whites when there are more reds. Daddy says that this is because the whites are "correlated" with the reds.

This is maybe the coolest experiment ever!

A postcript: I've started thinking up and designing more of my own experiments. Yesterday's experiment asked the following question: Do you get more soap bubbles when you add the soap before adding the water or after. To conduct this experiment, I got two identical Dixie cups. In the first cup, I put in one squeeze of liquid soap, filled to the top with water, and observed the number of bubbles. I then filled the second cup to the same level and added one squirt of liquid soap after it was filled. I observed that the second cup had a lot fewer bubbles than the first.

Conclusion: Soap first produces more bubbles than soap added after.

Daddy was very impressed at the quality of this experimental design.