CHAPTER 3 Getting Statistical: A Short Review of Basic Statistics 33

Some Random Thoughts about

Randomness

When discussing probability, it is also important to define the word random. Like

the word probability, we use the word random all the time, and though we all have

some intuitive concept of it, it is hard to define with precise language. In statis-

tics, we often talk about random events and random variables. Random is a term

that applies to sampling. In terms of a sequence of random numbers, random

means the absence of any pattern in the numbers that can be used to predict what

the next number will be.

The important point about the term random is that you can’t predict a specific out-

come if a random element is involved. But just because you can’t predict a specific

outcome with random numbers doesn’t mean that you can’t make any predictions

about these numbers. Statisticians can make reasonably accurate predictions

about how a group of random numbers behave collectively, even if they cannot

predict a specific outcome when any randomness is involved.

Selecting Samples from Populations

Suppose that we want to know the average systolic blood pressure (SBP) of all the

adults in a particular city. Measuring an entire population is called doing a census,

and if we were to do that and calculate the average SBP in that city, we would have

calculated a population parameter.

TABLE 3-1

The Relationship between Probability and Odds

Probability

Odds

Interpretation

1.0

Infinity

The event will definitely occur.

0.9

9

The event will occur 90% of the time (it is nine times as likely to occur as

to not occur).

0.75

3

The event will occur 75% of the time (it is three times as likely to occur as

to not occur).

0.5

1.0

The event will occur about half the time (it is equally likely to occur or not occur).

0.25

0.3333

The event will occur 25% of the time (it is one-third as likely to occur as

to not occur).

0.1

0.1111

The event will occur 10% of the time (it is 1/9th as likely to occur as to not occur).

0

0

The event definitely will not occur.