# Objective Measurement of Subjective Phenomena

## 5. Items, Levels of Measurement, and Methods of Scale Construction

### Exercise 2

In this exercise, you are asked to decide which level of measurement of correct (Nominal, Ordinal, Interval, or Ratio) for each example.

Instructions:
Decide what the correct level of measurement is for each of the examples below.

Levels of Measurement:
Nominal
Ordinal
Interval
Ratio

Examples:
1.  Course grades (A, B, C, D)
2.  Commute times (minutes)
3.  Health status (Excellent, Average, Poor)
4.  Gender
5.  Age
6.  High school test scores (such as 78, 80, or 95 percent correct)
7.  Type of surgery
8.  Difficulty (Impossible, Difficult, Easy)
9.  Hours spent exercising in one week
10.  Body temperature in degrees Fahrenheit (F)
11.  Race/ethnicity
12.  Breast cancer rates in geographic regions (cases per 100,000) people
13.  Test scores, such as an IQ score of 90 or 115 on an intelligence test

1.  Course grades (A, B, C, D)
[Ordinal]  Course grades (A, B, C, D) are indicators of the quality of a student’s performance and are ordered, so this is an example of an ordinal level of measurement.

2.  Commute times (minutes)
[Ratio]  Minutes (or some other unit of time, like days, hours, or seconds) is at the ratio level of measurement because it has an absolute zero value and the difference between values is meaningful.  Thus, the difference between 60 and 70 minutes is the same magnitude of time as the difference between 10 and 20 mninutes.  And, 20 minutes is twice as long as 10 minutes.

3.  Health status (Excellent, Average, Poor)
[Ordinal]  This is an example of an ordinal level of measurement because it consists of levels in order of magnitude, but the distance between levels is not quantifiable.  So, it is not possible to determine whether the difference between Excellent and Average is the same magnitude as the difference between Average and Poor.

4.  Gender
[Nominal]  Gender is at the nominal level of measurement.  Nominal variables allow a researcher to distinguish between 2 or more classes of an attribute by name.  There is no order associated with values on nominal variables.

5.  Age
[Ratio]  Age is at the ratio level of measurement because it has an absolute zero value and the difference between values is meaningful.  For example, a person who is 20 years old has lived (since birth) half as long as a person who is 40 years old.

6.  High school test scores (such as 78, 80, or 95 percent correct)
[Ratio]  Test scores on course examinations are often recorded as percent correct.  Such scores are at the ratio level of measurement because there is an absolute zero value (0% correct) and differences between values can be compared meaningfully.

7.  Type of surgery
[Nominal]  Type of surgery would be classified by names, so this is a nominal level of measurement.

8.  Difficulty (Impossible, Difficult, Easy)
[Ordinal]  This is an example of an ordinal level of measurement because it consists of levels in order of magnitude, but the distance between levels is not measureable per se.

9.  Hours spent exercising in one week
[Ratio]  Hours is a ratio level of measurement because it has an absolute zero value and differences between values can be compared.  Thus, the difference between 20 and 30 minutes of exercise is the same as the difference between 50 and 60 minutes.

10.  Body temperature in degrees Fahrenheit (F)
[Interval]  Temperature in degrees F is at the interval level of measurement because there is no absolute zero and values of temperature cannot be expressed as ratios.  For instance, it is incorrect to say that 70 degrees F is twice as hot as 35 degrees F.  But, temperature on the Kelvin (K) scale is on a ratio level.

11.  Race/ethnicity
[Nominal]  Race/ethnicity would be classified by names so this is a nominal level of measurement.  For instance, numeric codes may be used to distinguish participants who are Black, White, Hispanic, non-Hispanic, etc., but the numbers used do not imply magnitude of an attribute (ethnicity) or any ordering of the groups.

12.  Breast cancer rates in geographic regions (cases per 100,000) people
[Ratio]  A rate of disease is at the ratio level of measurement because it has an absolute zero value and the difference between values is meaningful.  Furthermore, a breast cancer rate of 10 per 100,000 is twice as high as a rate of 5 per 100,000.

13.  Test scores, such as an IQ score of 90 or 115 on an intelligence test
[Interval]  An IQ score (or a standardized score on many other kinds of tests, such as achievement tests) is probably best considered as falling at an interval level of measurement.  Some argue that such scores are at the ordinal level, providing only an ordering of performance.  But, given the large number of potential values (95% of the population falls between 70 and 130 on an IQ scale), the scores function well as interval-scaled values.