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Lesson 02: Developing the Research Hypothesis and Numerical Descriptions
Chapter 4: Numerical Description of Behavior
Basics of Measurement
The whole idea of measurement is taking some idea and putting a number to it. A concept is just a concept, just an idea, but when you decide to somehow apply numbers to that concept, it becomes a new, different thing. Of course, you might arbitrarily put numbers to any number of concepts, and while those would then become measured things, technically, the quality of that measurement is somewhat in question.
At this point in your education, you should have some idea of what a variable is, at least in the very basic sense that it is a symbolic representation of a changeable value in an equation. For our purposes, we're going to think about variables in a very broad sense. There are conceptual variables, which refer to the idea that you want to get at, and then there are measured variables, which actually put numbers to that idea. This distinction may seem unimportant, but if you think about how things actually work in the world, people think about things in terms of concepts and relationships between those concepts. When it comes time to actually investigate or use these relationships, then we turn to measurements. But the rules of the world are generally described in terms of concepts. For an example, think about the relationship between how happy a busy worker is with their job and how well they do at their job. We don't describe this relationship as "an employee who rates their job satisfaction as high on a scale from 1 to 10 generally ships more units or creates more profit for the company." No, we just say that greater job satisfaction leads to better job performance.
The first version of this relationship, "an employee who rates their job satisfaction," describes the relationship in terms of measured variables, while the second version describes it in terms of conceptual variables.
So if we think about things in terms of conceptual variables, what's the point of even having measured variables? Well, in order to uncover the relationships between conceptual variables, and in order to use those relationships, we have to have some way of measuring them or turning them into numbers. This is what sets scientists apart from philosophers and any number of other types of scholars. We use math as another language through which to understand the world. Our numbers and statistics are what set us apart from other fields, not any fancy devices. As such, we have to come up with a rigorous method of creating measured variables. For this purpose, we have operational definitions to turn conceptual variables into measured variables.
For example, if we wanted to look at the concept of intelligence, we could operationally define intelligence as a score on an IQ test. We could define strength as the maximum amount a person can bench press. For job performance, we could look at an individual's productivity, their number of sales, the number of sick days taken, or any number of other alternatives. Here is the problem: any given conceptual variable can typically be operationally defined in a large number of different ways. Similarly, the same measurement can often tap into a number of different concepts. This is usually one of the biggest hurdles in research—just coming up with the right operational definition.
Types of Variables: Measurement Scales
A useful way to think about variables is in terms of measurement scales, which refer to the degree of granularity or resolution that the variable has. Think of it as what the variable allows you to do with it in terms of mathematical operations.
Nominal scales name or identify a particular characteristic about something. A good way to remember this is that nominal begins with n, as does name. For our purposes, think about nominal scales as a particular characteristic of an individual, such as race, gender, religion, or other demographic variables. When we do analyses with these labels, we may give them numbers as shorthand, but they are categories—not numbers in the usual sense. Hence, we sometimes call them categorical variables.
Ordinal scales rank order things along a continuum, or give the order in which the scores line up based on some dimension. A good way to remember this scale is that ordinal begins with ord, as does order. Examples of ordinal scales include class rank or football rankings. You know from football rankings that one team is higher than the other, but it is not necessarily the case that the difference between team 1 and team 2 is the same as the difference between team 2 and team 3. All you know is that team 1 is better than 2, and team 2 is better than 3. Ordinal scales do allow for more precision and resolution than nominal scales; instead of just knowing identity or category, you have some idea of which scores are greater than others.
The interval scale provides both the rank order and relative distance along a single continuum. Unlike an ordinal scale, on an interval scale, the difference between 1 and 2 is the same as the difference between 2 and 3. Interval scales do not necessarily give you a meaningful zero value though, as zero may be some relatively arbitrary point. Think of it as being like Celsius temperature measurement. On the Celsius scale, zero degrees does not mean that you have zero heat.
The final type of scale to be discussed here is the ratio scale, which provides rank order and relative distance, as well as a zero point (none of whatever the scale is attempting to measure). In contrast to the Celsius scale, a zero on the Kelvin temperature scale means that you have zero heat. Also, think about measuring mass. If you have zero grams of something, it means that you truly have none of it whatsoever.
As a quick summary, think about scales in terms of what they tell you:
