Illuminating Statistical Analysis Using Scenarios and Simulations

20Amount of Evidence

Statistical Scenario—Amount of Evidence.

When we increase our sample size, will the sample mean distribution get more compact like it did with sample proportions?

The original histogram, reproduced in Figure 20.1, shows the distribution of random sample means for a sample size of 50.

Figure 20.1

Figure 20.2 is a histogram showing the distribution of sample means when sample size is 200. Like before, we use random integers 1–7. Notice that it is more compact.

Figure 20.2

Analogous to what we saw with sample proportions:

When sample sizes are larger, sample means tend to be closer to the population mean.¹

More evidence (larger sample sizes) → less uncertainty

As we'll see, the uncertainty due to sample size is incorporated into various statistical formulas involving sample means.

Note

1. As noted in lesson 5, this principle is called the Law of Large Numbers.