IS THE SAMPLE LARGE ENOUGH?
One reason we should be suspicious of small samples is that they can be af- fected by runs of luck. Suppose Harold flips a Canadian quarter four times and it comes up heads each time. From this, he can hardly conclude that Canadian quarters always come up heads when flipped. He could not even reasonably conclude that this Canadian quarter would always come up heads when flipped. The reason for this is obvious enough: If you spend a lot of time flipping coins, runs of four heads in a row are not all that unlikely (the probability is actually one in sixteen), and therefore samples of this size can easily be distorted by chance. On the other hand, if Harold flipped the coin twenty times and it continued to come up heads, he would have strong grounds for saying that this coin, at least, will always come up heads. In fact, he would have strong grounds for thinking that he has a two-headed coin. Because an overly small sample can lead to erroneous conclusions, we need to make sure that our sample includes enough trials.
