Introduction to the

Scales of Measurement

For a more technical discussion of measurement, click here

There are many different scales of measurement. We will cover only a handful. It is important to know what scale of measurement was used for a variable, because it determines what statistics are appropriate to use in analyzing the data.

Some people don't regard nominal as a form of measurement at all. They call it, simply, classification. In nomimal data, there are numbers, but they don't have numeric properties. For example, if we ask each person what state they were born in, we could assign a number to each state (Alabama = 1, Alaska = 2, etc) for the convenience of data processing, but we wouldn't want to interpret the number in any way (e.g., we would not want to compute the average value!).

Respondent | State Born In |
---|---|

James Woods | 18 |

Steve Borgatti | 0 |

Bluejay Earthling | 17 |

Sometimes, all we record about a variable is the presence or absence of the trait in question. For example, we might ask people:

- Do you color your hair in any way? YES or NO
- Do you currently have a girlfriend/boyfriend/spouse? YES or NO

The data are recorded as ones and zeros, as follows:

Respondent | Color Hair? | Involved? |
---|---|---|

Steve Borgatti | 0 | 1 |

Roberta Chase | 0 | 1 |

Sylvester Stallone | 1 | 1 |

Joe Student | 1 | 0 |

We could think of presence/absence data as nominal, but it is a little different in the sense that a "1" always means presence (more of something) and a "0" always means absence (less of something). In contrast, in truly nominal data, the numeric value is completely arbitrary -- it's just a label.

Presence/absence data are actually ordinal-scale (see below). However, we choose to separate them because of the limited range of values (just 0s and 1s) and because they are used so often.

In ordinal measurement, the numbers have one key numeric property: the bigger the number, the more that case has of the attribute being measured. Technically, we are using an ordinal scale whenever we ask people to rate things on a 1 to 5 scale, such as:

----1---- | ----2---- | ----3---- | ----4---- | ----5---- |

disagree strongly |
disagree | neutral | agree | agree strongly |

For example:

- I enjoy dating: (circle one) ..................................... 1 2 3 4 5
- I enjoy my playstation: (circle one) ........................ 1 2 3 4 5

Note that if a person circles "2" for dating and "4" for playstation, we cannot assume that he likes the playstation TWICE as much as dating. It just means he liked it more than dating.

Rank order data are really a kind of ordinal data. We get rank order data by asking people to rank statements or objects or anything else of interest. For example, suppose we ask people to rank order comedians according to how funny they are. It might go like this:

Please rank order the following people in terms of how funny they are. Put a "1" next to the name of the person who is the funniest of the group. Put a "2" next to the name of the second funniest person, and so on. Ties are not allowed.

Person | Rank |
---|---|

Paul Reiser | ____ |

John Lithgow | ____ |

Jane Curtin | ____ |

Cybill Shepherd | ____ |

Jerry Seinfeld | ____ |

Unlike other ordinal data, in rank order data there are no ties, and there are no gaps between numbers: if there is a "7", then there is also a 6, a 5, a 4, etc. So, in a way, the interval between values always has a constant meaning of "one rank", but at the same time, the difference in funnyness between the 1st ranked person and the 2nd could be much greater than the difference between the 4th and 5th.

In interval-scaled data, the gaps between the numbers are comparable, unlike with ordinal data. For example, if we measure the boiling point of different liquids in degrees Fahrenheit, we might get data that looks like this:

Liquid | Boiling Point |
---|---|

Pure water | 212 |

Ocean water | 200 |

Pond water | 211 |

Oxygen | -150 |

Petroleum | 450 |

If these numbers of measured on an interval scale, then a difference of 1 degree (as in 212 versus 211), means the same thing anywhere along the scale (as in, say, -2 and -1).

It is important to note, however, that a value of zero on an interval scale has no particular meaning. Zero degrees fahrenheit does not mean the total absence of heat! Furthermore, if it is 20 degrees one day, and only 10 another, it is NOT twice as hot the first day. To understand why, you'll have to read the other handout on measurement.

Ratio-scaled data looks a lot like interval-scaled data. However, the zero point has a special meaning in ratio-scaled data: it indicates the absence of whatever property is being measured. For example, if we are measuring the amount of money that a person has on them at a given moment, we might get data like this:

Person | Money |
---|---|

Jack | 120 |

Steve | 5 |

Jane | 50 |

Dan | 0 |

Mary | 1 |

A zero means no money. Also, the fact that Jane has $50 while Steve has $5 means that Jane has 10 times as much money as Steve, just as Jack has 2.4 times as much money as Jane.

Ratio-scaled data always have the flavor of counting: when you measure the amount of money that Steve has, you are counting up coins and bills. When you are measuring Steve's height, you are counting the number of inches off the ground that his head is.