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Four Levels of Measurement

In social scientific research, measurement is the process of assigning numbers or words to observations made in the real world. It is the foundation of the research process because it results in data that can be examined using mathematical operations. Because different things have different properties, what is being measured (what type of variable) determines how it is measured—or more specifically, the level at which it can be measured. That’s what the term levels of measurement, describes, and there are four recognized levels.

· 1 Ratio

· 2 Interval

· 3 Ordinal

· 4 Nominal

The level at which something will be or was measured affects the values recorded for the units of analysis and the mathematical operations that can be performed on the data collected: In general, the higher the level of measurement the less restricted researchers are in the types of mathematical operations they can perform on the data. Researchers, therefore, want to collect data at the highest level possible.

Although the levels of measurement are ranked from most to least informative, all four levels have a role in conducting social science research. Again, knowing the level of measurement is important because those at lower levels may limit the kinds of statements you can make about your results. A closer look at the pyramid, starting at the bottom or lowest level, follows.

Nominal Measurement

Merely assigning objects to unique categories is a type of measurement. For example, when researchers label participants in a study as male or female, they are performing measurement; specifically, they are measuring the variable of gender using what is known as a nominal scale. The nominal, level of measurement addresses naming—that is, identifying or categorizing objects using a name. A variable that can be named is said to meet the naming criterion of measurement, which is that two things with the same name carry the same value. Also, note that the categories for a nominal variable should be mutually exclusive.

A nominal scale is the weakest form of measurement. Again, the values for variables measured at the nominal level merely identify or name the real-world entity being measured. Numbers are not even necessary for scale values when using a nominal scale; instead, they can have descriptive names. For gender, for example, you might have two measurements: female (=1) and male (=2). There is no relationship between the two numerical values (that is, the numbers should not be interpreted that males are "one unit more or larger than are females); they just stand-in for the name of the category. You could just as easily write female and male as the scale value. Other examples of nominal variables are numbers on a baseball player's uniform, social security numbers, gender, and race.

Ordinal Measurement

Moving up the pyramid, the ordinal, level of measurement is next; it addresses ordering real-world entities. A variable that can be ordered is said to meet the ordering criterion of measurement. More specifically, this criterion requires that objects can be placed in ascending or descending order. 

Example 1: Emojis

A set of emojis can serve as a good starting point for understanding the ordinal measurement, as these scales are sometimes challenging:

The emojis of course symbolize real-world emotions ranging from very happy (left) to very sad (right). The set of emojis comprises a scale, and if you associate a number with each emotional state, the ordinal scale could look like this:

The larger the number, the happier the emotion. Note, though, that it is difficult to say that the difference between Very Sad and Sad is exactly the same as the difference between any other two consecutive values on the scale. This is a characteristic of the ordinal level of measurement: ordinal measurement allows us to assign values that are in rank order, but the distances between the values are not necessarily equal. Note, also, that there is no value that represents zero in the real world; that is, there is no such thing as zero emotion. Noting this feature is important for determining the level of measurement for a scale, which will be discussed more below in the section on ratio measurements. Researchers often treat ordinal data as being on an interval level of measurement; you will learn more about this as you continue your studies in statistics.

Example 2: Measuring the Hardness of Minerals

For now, consider a more academic example of ordinal measurement: that of measuring the hardness of minerals. Hard minerals have the property that they can scratch softer minerals, and the softer mineral cannot scratch the harder mineral. The measurement process involves taking two minerals and seeing which mineral scratches the other. Diamond is the hardest mineral and scratches all other minerals, and talc is the softest mineral and cannot scratch any other mineral. Geologists use this process, and the result is the Moh Hardness Scale, shown below.

Note that the differences in adjacent numbers do not reflect equal differences in hardness. Researchers cannot say, for example, that a diamond is ten times harder than talc. However, looking at the values above, you can say that diamond is harder than apatite, which is harder than talc. The claim is that the greater the number, the harder the mineral. The variable minerals, therefore, satisfies the ordering criterion of measurement.

Interval Measurement

The level of measurement second from the top of the pyramid is interval, measurement, which addresses differences, or intervals, between entities. The interval criterion requires that differences in the real world correspond to differences in the values a scale uses. In addition to allowing researchers to categorize and rank-order entities, interval measurement has the additional property of the intervals on the scale being equivalent. That is, variables measured at the interval level contain the properties of both nominal and ordinal variables but also have equal distance between values on the scale. It is important to note, though, that the zero value for interval scales tends to be rather arbitrary and does not correspond to a meaningful real-world observation. In other words, a zero value on an interval scale does not carry meaning.

The measurement of temperature would be considered an interval level of measurement. Considering temperature measured in both degrees centigrade and degrees Fahrenheit, as presented in the table that follows, may help you to understand interval scales of measurement:

 First, notice the differences in temperature. The temperature difference between real-world entities A and B is the same as the difference between B and C, regardless of whether you use temperature measured in degrees Centigrade or Fahrenheit.

 Alternatively, the proportions are not the same. In Centigrade, C has a value twice that of B, but in degrees Fahrenheit, C is 1.73 times greater than B. 

 Using the definition of degree, physicists would agree that neither scale measures an absolute zero, but rather that equal intervals on either scale have the same real-world meaning.

Interval scales are used in a variety of settings. They are popular, in part, because many statistical procedures are based on the premise that differences in scale values have real-world meaning. Examples of constructs that are often viewed as interval measurement include intelligence as measured by an IQ test, depression measured by a self-report questionnaire in which item scores are added together, and some subjective judgments.

Ratio Measurement

The ratio level of measurement is at the top of the pyramid. Ratio measurement addresses proportions, or ratios, between entities. It allows researchers to make a variety of statements about the data, including that scale values are in proportion to one another. The ratio criterion, then, requires that equal proportions on the measurement scale correspond to equal proportions in the real world. In short, the important test of the ratio criterion is that a measurement of zero has real-world meaning.

Here’s another way to think of it: 

 Variables that can be measured at the ratio level contain all of the properties of nominal, ordinal, and interval variables, but have the additional property that the zero value for the variable is meaningful. Throughout the process of measurement, determining whether a measurement meets the two lower levels of measurement (nominal and ordinal) is often easy, but determining whether the two higher levels (interval and ratio) are met can be more challenging.

The key is paying attention to how differences in a given real-world construct are mapped into numbers along with the real-world concept that is mapped into zero. 

For example, it’s easy to tell that weight is a ratio variable because zero means an entity weighs nothing. Measurement for the number of items correct on a math test is also easily a ratio measurement because a person can get zero items correct. However, mathematical ability as a psychological construct measured by the math test would be harder to defend as a ratio scale. The numbers on the test may order individuals according to mathematical ability and the interval criterion may also be met, but what does it mean in the real world to have zero mathematical ability? The researcher is responsible for arguing, possibly using data or other research sources, that the scale being used has the properties of measurement being claimed.

In general, if you are counting items or comparing them to a physical standard, you can use a ratio scale.

· Measures of distance, weight, dollars, and other things where zero has clear real-world meaning are also usually easily identified as ratio scale. 

· Often, you can identify a scale as a ratio scale by examining changes to different units of measurement.

· If intervals that are equal on one scale are also equal on a second scale, and zero is the same on both scales, then the measurement process is most likely ratio measurement.

The levels of measurement are, ultimately, cumulative or additive. That is, the ratio level of measurement satisfies all the measurement criteria required for the levels below it, the interval level those below it, the ordinal level the level below it. This progression is shown below, along with a summary of each level’s mathematical focus.