Test of Equality

Suppose that the areas are the same. Even so, you'd expect there to be small differences between the number of rice grains on the loo versus the ring, just by chance. If there were no difference in the areas, however, then on average you'd expect the difference to swing evenly between the two areas: one time the ring would have more rice grains, and the next time the loo would have more rice grains.

Just like flipping a fair coin: you expect half heads, and half tails. If you flip a coin twenty times, and it came up heads each time, you (hopefully!) suspect that it isn't really a fair coin.

So we'll think of all these rice counts like coin tosses: if the loo wins, think of that as "heads"; if the ring wins, think of that as "tails".

Using the table of your rice trial results, write "heads" if the loo has more rice grains on a given trial, and "tails" if the ring has more.
If your results are half heads and half tails, then the areas appear to be about the same. But what if there are twice as many tails as heads?
Use a "binomial calculator" (like this one) to find out how odd your results are.
```
(binomial-cdf 5 5 .5)
```
If your results would only occur 5% of the time or less with "a fair coin", we'll guess that "your coin isn't" fair: there is a difference in the areas of the loo and the ring, and we didn't do a good job of choosing our radii.

Website maintained by Andy Long. Comments appreciated.