1. Why do you need an operational definition when you already have a perfectly good conceptual definition?

In your conceptual definitions you explain what your constructs are by showing how they relate to other constructs. This explanation and all of the constructs it refers to are abstract — their existence is only as real and concrete as the thoughts you have while you watch a seagull soar past on a stiff breeze. To work with your constructs, you must establish a connection between them and the concrete reality in which you live. This process is called operationalization. Your operational definitions describe the variables you will use as indicators and the procedures you will use to observe or measure them. You need an operational definition because you can't measure anything without one, no matter how good your conceptual definition might be.

2. Why can't you skip the conceptual definition and use only an operational definition to define your concept? i.e. why is it also necessary to have a conceptual definition?

A conceptual definition tells you what the concept means, while operational definitions only tell you how to measure it. If you have only an operational definition, you may know how to measure it, but you won't know what you are measuring. This means that your measurements won't be worth much, considering that you don't know what the concept is, so you don't know what you measured. A concept defined only operationally may make a nice little ceremony as you carry out the steps described by the operational definition, but it doesn't mean anything and it is not related to other concepts.

3. What is the difference between conceptual and operational definitions?

A conceptual definition tells you what the concept means, while an operational definition only tells you how to measure it. A conceptual definition tells what your constructs are by elplaining how they are related to other constructs. This explanation and all of the constructs it refers to are abstract. On the other hand, your operational definitions describe the variables you will use as indicators for youor constructs and the procedures you will use to observe or measure the variables.

4. A professor is studying learning and academic performance and uses GPA as a measure of how much her students have learned. Discuss why (or why not) this is an adequate operational definition of learning.

In order to evaluate this operational definition, it would be useful to know what it means to "learn" something. Is it necessary to memorize the material? If it you have memorized the material but you don't understand it, have you "learned" it? Do you have to be able to reproduce the information, or is it enough that you are familiar with it? At the same time, it will be useful to know what GPA measures and to what extent it measures how much was learned. Some people get high grades because they take courses that cover material they are already familiar with, so for them, GPA measures how familiar were they with the material before the course began, rather than how much they learned in the course. For other people, low grades may indicate that they did not like the instructors of their courses, that they had to work a lot of overtime for the last several months, or their allergies were making it difficult to sleep at night and they had trouble concentrating. These other factors are all things that could be having a larger effect on grades than how much the students learned. This illustrates the need to have a good conceptual definition so you know what the concept means. A knowledge of the essential qualities of your concept will help you develop an operational definition -- a measurement strategy -- that will provide a valid assessment of the concept.

5. What role should essential qualities play in operational definitions?

Since the specification of essential qualities as part of a conceptual definition tells exactly what the concept means, it gives some very good clues about how the concept could be measured in a most straightforward way. Essential qualities should play a central role in operational definitions in that the measurement procedures should be explicitly designed to look for the presence or absence of the essential qualities.

6. What is the difference between a numeral and a number?

Numerals are symbols composed of one or more of the characters from 0 to 9, and used as labels to indicate which category something belongs to. They are only symbols, like letters, and they have no mathematical meaning. You cannot do valid arithmetic with numerals. Wayne Gretzky's "99" is an famous example.

Numbers are symbol composed of one or more of the characters from 0 to 9, possibly including a decimal point or a leading minus sign. While a numeral indicates which category something belongs to, a number can indicate how many objects there are, how much of something there is, where something is located along a continuous scale, or how many steps it is along a discrete scale. Unlike numerals, numbers have mathematical meaning and can be used in arithmetical comparisons ("greater than" or "less than") and operations (addition, subtraction, multiplication, and division).

7. What is the difference between a number and an ordinal?

Ordinals look a bit like numbers, but they only tell what order things are. Examples are 1st, 2nd, 3rd. No mathematical operations can be performed on ordinals.

Numbers are symbol composed of one or more of the characters from 0 to 9, possibly including a decimal point or a leading minus sign. Numbers have mathematical meaning, whereas ordinals only specify ordering relationships.

8. In what way is ratio scaling "stronger" than interval or ordinal scaling?

As you move from nominal to ordinal to interval to ratio, the numbers in the data contain more amounts and more kinds of information about whatever it is the numbers represent.

With ordinal scaling you can tell if one case comes before or after another case, but not how far before or after. With interval scaling you can tell both whether one case comes before or after another case, and how far apart the two values are. Ratio scaling is the most powerful. It has everything interval scaling has, as well as a fixed absolute zero point. With ratio scaling you can tell both the distance between values and the relative sizes or magnitudes of values.

The fact that any value on a ratio scale tells how far that value is from 0 ("none") makes ratio scaling stronger than interval scaling, which only places values at a point on a line.

9. How do you tell which level of scaling is appropriate for a particular situation? (What aspects of the situation do you consider? Why do these aspects matter?)

You should choose a level of scaling that matches the form of the phenomenon you are trying to measure. This is the reality isomorphism principle. "Isomorphic" is a Greek word that means "same form."

When the thing you are measuring is a dichotomy — the object is red or black; the person is a man or a woman — or if you are measuring something that has more than two categories, all you can do is sort the cases into categories. The form of the phenomenon matches categorical nominal scaling.

If the phenomenon you want to measure is a variable trait, so that some people have more than others and you can determine who has more but not how much more they have, the form of the phenomenon matches ordinal scaling. An example of this type of concept are how uncomfortable a person becomes when someone stands too close to them in a line in the supermarket.

If you are interested in the dfferences between people and if the difference between two people could be anywhere between no difference at all and a very large difference, and if you can measure the sizes of the differences between pairs of people and compare the differences to one another and tell which difference is bigger and how much bigger it is, you should use interval scaling. If you are interested in the amount of the trait individuals have, and if it is also meaningful to say that someone has none of the trait, you should use ratio scaling.

10. Under what conditions would you have to use a lower level of scaling than the one that matches the phenomenon you want to measure? Give an example.

Think about this.....

11. What can you do with interval or ratio scaling that you can't do with nominal or ordinal scaling?

With interval scaling you can measure the size of the differences between values, with ratio scaling you can also compare one value as a fraction or percentage of another value. You can't do either of these things with nominal or ordinal scaling.

12. Under what conditions does "0" not mean "none"? What are the consequences of this?

Interval scaling is what you get when you but that it has been weaken or cripple ratio scaling by moving or displacing the origin -- when you recalibrate the scale in such a way that "0" no longer means "none." The Celsius temperature scale does this. Displacing the origin means that numbers can't be used to indicate quantities. Not only does it untie the quantity "none" from the numeral "0"; it also requires you to interpret all numbers only as marks on a line, where the only information a number carries is where that number is located in relation to the other numbers.

13. If you have a ratio-scaled variable and want to compare two values, what kind of comparisons can you make?

With ratio scaling you can tell 1) whether one case comes before or after another case, as in "the red horse is heavier than the white one"; 2) how far apart the two values are, as in "the red horse weighs 274 pounds more than the white one"; and 3) the relative sizes or magnitudes of values, as in "the red horse weighs 30% more than the white one."

14. If you have an ordinal-scaled variable and want to compare two values, what kind of comparisons can you make?

With ordinal scaling you can tell if one case comes before or after another case, but not how far before or after.

15. If you have an interval-scaled variable and want to compare two values, what kind of comparisons can you make?

With interval scaling you can tell if one case is larger or smaller than another case, and how much larger or smaller.

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