Measurement

Measurement

• The process of assigning numbers to objects in such a way that specific properties of the objects are faithfully represented by specific properties of the numbers.

• Such ways of assigning numbers do not attempt to measure the total phenomenon, but only a specific set of attributes.

• Measurement is used to capture some “construct” - For example, if research is needed on the construct of “depression”, it is likely that some systematic measurement tool will be needed to assess depression.

Measurement--defined as the application of rules to assign numbers to objects (or attributes).

Measurement rules--the procedures used to transform the qualities of attributes into numbers (e.g., type of scale used).

Why bother assigning numbers?

quantifying something that is expected to vary.

individual differences -- premise that people will vary (get different scores) on the attribute

Scales of measurement

Three important properties:

Magnitude--the property of “moreness”.  Higher score refers to more of something.

Equal intervals--is the difference between any two adjacent numbers referring to the same amount of difference on the attribute?

Absolute zero--does the scale have a zero point that refers to having none of that attribute?

Levels of Measurement

1. Nominal

2. Ordinal

3. Interval

4. Ratio

Levels of Measurement

Nominal Scales - there must be distinct classes but these classes have no quantitative properties.  Therefore, no comparison can be made in terms of one category being higher than the other.

For example - there are two classes for the variable gender -- males and females.  There are no quantitative properties for this variable or these classes and, therefore, gender is a nominal variable. 

Other Examples:

country of origin

biological sex (male or female)

animal or non-animal

married vs. single

Sometimes numbers are used to designate  category membership

Example:

Country of Origin

1 = United States  3 = Canada

2 = Mexico  4 = Other

However, in this case, it is important to keep in mind that the numbers do not have intrinsic meaning

Ordinal Scales  - there are distinct classes but these classes have a natural ordering or ranking.  The differences can be ordered on the basis of magnitude.

For example - final position of horses in a thoroughbred race is an ordinal variable.  The horses finish first, second, third, fourth, and so on.  The difference between first and second is not necessarily equivalent to the difference between second and third, or between third and fourth.

Interval Scales  - it is possible to compare differences in magnitude, but importantly the zero point does not have a natural meaning.  It captures the properties of nominal and ordinal scales -- used by most psychological tests.

Designates an equal-interval ordering - The distance between, for example, a 1 and a 2 is the same as the distance between a 4 and a 5

Example - Celsius temperature is an interval variable.  It is meaningful to say that 25 degrees Celsius is 3 degrees hotter than 22 degrees Celsius, and that 17 degrees Celsius is the same amount hotter (3 degrees) than 14 degrees Celsius.  Notice, however, that 0 degrees Celsius does not have a natural meaning.  That is, 0 degrees Celsius does not mean the absence of heat!

Ratio Scales  - captures the properties of the other types of scales, but also contains a true zero, which represents the absence of the quality being measured. 

For example - heart beats per minute has a very natural zero point.  Zero means no heart beats.  Weight (in grams) is also a ratio variable.  Again, the zero value is meaningful, zero grams means the absence of weight.

Example:

the number of intimate relationships a person has had

quite literally means none

a person who has had 4 relationships has had twice as many as someone who has had 2

• Each of these scales have different properties (i.e., difference, magnitude, equal intervals, or a true zero point) and allows for different interpretations.

• The scales are listed in hierarchical order.  Nominal scales have the fewest measurement properties and ratio having the most properties including the properties of all the scales beneath it on the hierarchy.

• The goal is to be able to identify the type of measurement scale, and to understand proper use and interpretation of the scale.