Statistics For Dummies®, 2nd Edition

Chapter 10

The t -Distribution

In This Chapter

• Characteristics of the t-distribution
• Relationship between Z- and t-distributions
• Understanding and using the t-table

The t-distribution is one of the mainstays of data analysis. You may have heard of the “t-test” for example, which is often used to compare two groups in medical studies and scientific experiments.

This short chapter covers the basic characteristics and uses of the t- distribution. You find out how it compares to the normal distribution (more on that in Chapter 9) and how to use the t-table to find probabilities and percentiles.

Basics of the t-Distribution

In this section, you get an overview of the t -distribution, its main characteristics, when it's used, and how it's related to the Z -distribution (see Chapter 9).

Comparing the t- and Z-distributions

The normal distribution is that well-known bell-shaped distribution whose mean is μ and whose standard deviation is σ(see Chapter 9 for more on the normal distribution). The most common normal distribution is the standard normal (also called the Z- distribution), whose mean is 0 and standard deviation is 1.

The t-distribution can be thought of as a cousin of the standard normal distribution — it looks similar in that it's centered at zero and has a basic bell-shape, but it's shorter and flatter than the Z-distribution. Its standard deviation is proportionally larger compared to the Z, which is why you see the fatter tails on each side.

Figure 10-1 compares the ...