Datasheet

Chapter 1: Evaluating Data in the Real World

Interval data provides equal differences. Fahrenheit temperatures provide an

example of interval data. The difference between 60 degrees and 70 degrees

is the same as the difference between 80 degrees and 90 degrees.

Here’s something that might surprise you about Fahrenheit temperatures:

A temperature of 100 degrees is not twice as hot as a temperature of 50

degrees. For ratio statements (twice as much as, half as much as) to be valid,

zero has to mean the complete absence of the attribute you’re measuring. A

temperature of 0 degrees F doesn’t mean the absence of heat — it’s just an

arbitrary point on the Fahrenheit scale.

The last data type, ratio data, includes a meaningful zero point. For tempera-

tures, the Kelvin scale gives us ratio data. One hundred degrees Kelvin is

twice as hot as 50 degrees Kelvin. This is because the Kelvin zero point is

absolute zero, where all molecular motion (the basis of heat) stops. Another

example is a ruler. Eight inches is twice as long as four inches. A length of

zero means a complete absence of length.

Any of these types can form the basis for an independent variable or a depen-

dent variable. The analytical tools you use depend on the type of data you’re

dealing with.

A little probability

When statisticians make decisions, they express their confidence about those

decisions in terms of probability. They can never be certain about what they

decide. They can only tell you how probable their conclusions are.

So what is probability? The best way to attack this is with a few examples.

If you toss a coin, what’s the probability that it comes up heads? Intuitively,

you know that if the coin is fair, you have a 50-50 chance of heads and a 50-50

chance of tails. In terms of the kinds of numbers associated with probability,

that’s

/2.

How about rolling a die? (One member of a pair of dice.) What’s the prob-

ability that you roll a 3? Hmmm . . . a die has six faces and one of them is 3, so

that ought to be

/6, right? Right.

Here’s one more. You have a standard deck of playing cards. You select one

card at random. What’s the probability that it’s a club? Well . . . a deck of

cards has four suits, so that answer is

/4.

I think you’’re getting the picture. If you want to know the probability that an

event occurs, figure out how many ways that event can happen and divide by

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