Illuminating Statistical Analysis Using Scenarios and Simulations

16Brief on Two-Tail Versus One-Tail

Statistical Scenario—Two-Tail, One-Tail

Say you want to see if a coin is fair or not, so you flip it 100 times counting the number of heads.

Use an alpha-level of 0.05 (95% confidence level).

Where do you draw the two lines for declaring the coin to be not fair? (Two lines, one toward the left and the other line toward the right.)

Where do you draw the one line for declaring the coin favors tails? (One line toward the left.)

Where do you draw the one line for declaring the coin favors heads? (One line toward the right.)

0.38	0.40	0.42	0.44	0.46	0.48	0.50	0.52	0.54	0.56	0.58	0.60	0.62
Proportion of heads

The first question asks for two lines, as we have done before. It is called a two-tailed test for this reason. Recall that “tail” in this context means the far left and far right of a histogram's distribution, which are called the tails of the distribution.

For this chapter, a simulation of 10,000 people each flipping fair coins 100 times is used. In the histogram of Figure 16.1, the lines are drawn so that about 5% is divided equally between the two tails: about 2.5% of the simulation outcomes are in the left tail and about 2.5% are in the right tail. A tested coin outside the interval 0.41–0.59 will be declared not fair (reject the two-tailed null hypothesis).

Next: Where do you draw the one line for declaring the coin favors tails? (One line toward the left.)

This asks for a one-tailed test. More specifically, ...