Illuminating Statistical Analysis Using Scenarios and Simulations

2Judging Coins I

Let's start with the simplest statistical situation: that of judging whether a coin is fair or not fair. Later we'll see that this situation is statistically equivalent to agree or disagree opinion polling. A coin is fair if it has a 50% chance of coming up heads, and a 50% chance of coming up tails when you flip it. Adjusting the verdict table to the coin-flipping context gives us Table 2.1.

Table 2.1 Coin flipping outcomes.

Statistical Scenario–Coins #1

You want to see if a coin is fair or not. To gather evidence, you plan on flipping it 10 times to see how many heads come up. Beforehand, you want to set the verdict rule.

Where do you draw the two lines for declaring the coin to be not fair?

0	1	2	3	4	5	6	7	8	9	10
Number of heads

Draw one line toward the left for your threshold of “too few heads,” and another line toward the right for your threshold of “too many heads.”

Where you draw the lines represents your choice of thresholds.

Just use your intuition; don't do any arithmetic.

Intuitively, it seems extremely unlikely for a fair coin to come up heads only 0 or 1 times out of 10, and most people would arrive at the verdict that the coin is not fair. Likewise, it seems extremely unlikely for a fair coin to come up heads 9 or 10 times out of 10, and most people would arrive at the verdict that the coin ...