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Understanding Measurement: Properties and Scales

1. What is measurement?

2. Why is accurate measurement so critical?

3. What are the important properties of the abstract number system?

4. List and define the four scales of measurement.

5. What type of data does each scale produce?

6. What are the properties of each scale of measurement?

7. What is the concept of true zero? What is its importance in measurement?

8. What is the best way to reduce measurement error in research?

9. How do operational definitions transform theoretical concepts into concrete events?

10. What is social desirability bias in research? How might it affect research?

11. Explain the concept of convergent validity. What is its importance?

Nominal scales are at the lowest level of measurement; they do not match the number system well. Nominal scales are “naming scales,” and their only property is identity. Such dependent variables as place of birth (Chicago, Toronto, Tokyo, Nyack, Chippewa Falls), brand name choice (Ford, Honda, Volvo), political affiliation (Democrat, Republican, Socialist, Green Party, Independent), and diagnostic category (panic disorder, schizophrenia, bipolar disorder) are nominal scales of measurement. The differences between the categories of nominal scales are qualitative and not quantitative.

In nominal scales, we can assign numbers to represent different categories. For example, we could label Chicago as 1, Toronto as 2, Tokyo as 3, Nyack as 4, and Chippewa Falls as 5, but the numbers are only arbitrary labels for the categories. Except for identity, these numbers have none of the properties of the number system, and therefore, we cannot meaningfully add, subtract, multiply, or divide them. Is Chicago, with its assigned number of 1, to be understood as only one-fifth of Chippewa Falls, with its assigned number of 5? Nominal scales have no zero point, cannot be ordered low to high, and make no assumption about equal units of mea- surement. In fact, they are not numbers at all, at least not in the sense that we usually think of numbers. Nominal scales classify or categorize participants. With nominal scales, we count the frequency of participants in each category. We call the data from nominal scales nominal data or categorical data.

Ordinal Scales

Ordinal scales have the property of magnitude as well as identity. They measure a variable in order of magnitude, with larger numbers representing more of the variable than smaller numbers. How much more is unclear in an ordinal scale. For example, using socioeconomic class as a vari- able, we could categorize participants as belonging to the lower, middle, or upper socioeconomic class. There is a clear underlying concept here of order of magnitude, from low to high. Other ex- amples of ordinal scales are measurements by rankings, such as a student’s academic standing in class, or measurements by ranked categories, such as grades of A, B, C, D, or F. Data measured on ordinal scales are called ordered data. Ordinal scales give the relative order of magnitude, but they do not provide information about the differences between categories or ranks. Student ranks indicate which student is first, second, and so on, but we cannot use the ranks to determine how much each student differs from the next. That is, the numbers provide information about relative position, but not about the intervals be- tween ranks. The difference in academic achievement between students ranked 1 and 2 might be very small (or large) compared with the difference between students ranked 12 and 13. As illustrated in the example of ranking Coke, Pepsi, and vinegar on taste preference, the in- tervals in ordinal scaling are not necessarily equal. In fact, we usually assume that they are unequal.

Therefore, it is inappropriate to analyze ordered data with statistical procedures, that implicitly require equal intervals of measurement. interval scales

When the measurements convey information about both the order and the distance between values, we have interval scaling. interval scales have the properties of ordinal scales in addition to equal

What kind of statistical test (and why) would you use to answer each of the following research questions?

Validity

The third factor to consider in evaluating a measure is its validity. To say that a scale designed to measure weight is valid means that the scale measures what it is supposed to measure weight. Validity is not the same as reliability, which refers to how consistently the weight is measured. A scale for measuring weight, for example, might not be properly adjusted, perhaps giving a reading 10 pounds lighter than the object’s true weight. Although this scale would be reliable if it consistently gave that same weight, it would not be valid, because that weight is not the true weight. A measure cannot be valid unless it is reliable, but a measure can be reliable without being valid. Validity, like reliability, is not an all-or-nothing concept. Degrees of validity range from none to perfect. A correlation coefficient is typically used to quantify the degree of validity. Researchers evaluate the validity of a measure by quantifying how well the measure predicts other variables.

For example, a researcher might want to know if SAT scores predict performance in college. This would be referred to as predictive validity, because we are evaluating how well our measure predicts a future event. The variable that the researcher wants to predict is the criterionthe measure used to predict the criterion is the predictor In other instances, we may want to see if our measure is correlated with a criterion that already exists or can be measured simultaneously. This type of validity is referred to as concurrent validity. If we correlated SAT scores with current high school grades, we would be testing concurrent validity. Predictive validity and concurrent validity are two subtypes of criterion-related validity, so named because these validities are established by correlating the measure with a criterion measure.