**Numbers are assigned to events to describe how different two events are.**

At this level we have

- an ordinal scale plus something else (or a nominal scale plus two something elses).
- What we add when we more to the interval scale of measurement is the
**unit of measurement**. Now we can say whether two events are closer together or further apart than two other events and tell exactly who much different. - A second property of this scale is that the event labeled (0) has been arbitrarily selected.
- That means you can have events with negative numbers which is different from having negative events.

- What we add when we more to the interval scale of measurement is the

**Some Examples**

**Fahrenheit and Celsius measures of temperature.**For either of the temperature scales- There is a unit, the degree. Any two temperatures which differ by the same number of degrees are equally different.
- 50°F and 100°F differ by a given amount (50 F degrees). That is the same diffference as the difference in temperature between 125°F and 175°F.

- There is a relative zero (0°F and 0°C--not the same event). There are events which can be assigned negative numbers, but they are not negative events.
- Temperature is a measure of how much the molecules of the substance are moving around: The more movement, the higher the temperature. At 0°F, movement doesn't stop because if it did then temperatures like -20°F would mean we have negative movement and what the heck would that be??

- There is a unit, the degree. Any two temperatures which differ by the same number of degrees are equally different.
- We can build an interval scale of
**Committing Offenses at Boys' School**in the following way:- Draw a horizontal line to indicate the total difference in severity. Label the ends of the lines with the least severe (status offences) and most severe (offenses against persons) offenses.
- Ask one person to indicate where on the line the other two categories go. For example,

- Now you can measure the differnces in severity between any two offenses and indicate which differences are bigger and which differences are smaller.

**Meaningful Operations**

Equality (nonequality) operation: See Nominal Scale.

Greater (Lesser) operation: See Ordinal Scale

Addition (Subtraction) operations

Because we have a unit of measure, we can determine which differences are larger and which differences in events are smaller.We can also talk about ratios of differences. The difference in temperature from 40° to 50° is twice the difference in temperature from 60° to 65°.

**Measure of Central Tendency**

Mode: See Nominal ScaleMedian: See Ordinal Scale

Mean: The mean is the number that "balances" the total distances of scores less than the mean with the total distances of scores greater than the mean.

The mean is the number that makes the total of the positive deviations the same as the total for the negtive deviations

The negative deviations total the same as the positive deviations and thus balance out (+13 and -13).

Score Mean Deviation 5 - 11 - 6 5 -11 - 6 10 - 11 - 1 15 - 11 4 20 - 11 9 To do the balancing, you have to know how far the scores are from the mean. You can't do that unless you have a unit of measure so you can count the number of units of measure the two events are.

Is Intelligence measured at the interval level?

© 2002 by BurrtonWoodruff. All rights reserved. Modified