352 PART 7 The Part of Tens

This chapter provides a very short table of critical values for the t, chi-square, and

F distributions. A critical value is the value that your calculated test statistic must

exceed in order for you to declare statistical significance at the α = 0.05 level. For

example, the critical value for the normal distribution is 1.96 at α = 0.05.

The Uniform Distribution

The uniform distribution is the simplest distribution. It’s a continuous number

between 0 and 1. To generalize, it is a continuous number between a and b, with

all values within that range equally likely (see Figure 24-1). The uniform distribu-

tion has a mean value of (

) /

b

a

2 and a standard deviation of b

a / 12 . The

uniform distribution arises in the following contexts:»

» ^{Round-off errors are uniformly distributed. For example, a weight recorded}

as 85 kilograms (kg) can be thought of as a uniformly distributed random

variable between a = 84.5 kg and b = 85.5 kg. This causes the mean to be

(84.5 + 85.5)/2 = 85 kg, with a standard error of (84.4 – 84.5)/√12, which is

1/3.46 = 0.29 kg.»

» ^{In the case the null hypothesis is true, the p value from any exact significance}

test is uniformly distributed between 0 and 1.

The Microsoft Excel formula

RAND() generates a random number drawn from

the standard uniform distribution.

FIGURE 24-1:

The uniform

distribution.

© John Wiley & Sons, Inc.