Your task in this assignment is to determine whether variables are measured at the nominal, ordinal, interval, or ratio level. For Part I, you need the Consumer Sentinel Network’s 2020 Data File. Thi

Tips for Determining a Variable’s Level of Measurement

Try using this decision tree to decide which level a variable is measured at:

Finally, ask if there are equal distances between intervals. If no, then we have an ordinal-level variable. STOP. If yes, then we have either an interval or a ratio-level variable. Now, ask if there are equal distances between intervals. If no, then we have a nominal-level variable. STOP. If yes, then we have at least an ordinal-level variable. If no, then we have an interval-level variable. STOP. If yes, then we have a ratio-level variable. STOP. If no, then we do not have a variable. (Instead, what we have is a constant.) STOP. Next, ask if we can use the variable’s different values to distinguish between cases that have more or less of the variable. If yes, then we have a variable, and the variable is measured at least at the nominal level. Start by asking if the variable has different values that we can use to distinguish between cases that are the same or different in terms of the variable?

For more guidance, check out the details that follow . . . .

1. There are exactly four levels of variable measurement: nominal, ordinal, interval, and ratio. When asked to identify a variable’s level of measurement, the answer has to be one and only one of these words. You can remember this list of levels of variable measurement with the acronym NOIR.

2. As we go from the first level (nominal) to higher levels, we are using increasingly complex and powerful ways of measuring variables. In other words, a nominal-level variable is the simplest, most basic type of variable, while a ratio-level variable is the most complicated type of variable. (The acronym NOIR can also help us here to remember the order: Nominal is simpler than ordinal, ordinal is simpler than interval, and interval is simpler than ratio.)

3. All variables will at least meet the criteria for a nominal-level measurement. That is, if it is a variable we are talking about, that variable will have categories that allow is to distinguish between cases that are the same or different.

a. Look at the variable’s codes and categories. Figure out what they mean and what they tell us about different cases.

b. Suppose we’ve surveyed U.S. adults to learn about the experience of serving on a jury. We might have a variable in our study that tells us which region people live in. We could name this variable REGION and give it the following codes and categories: 1 = North, 2 = East, 3 = South, and 4 = West. Well, at what level is REGION measured?

c. We know REGION at least nominal, because it does have categories and codes, and those categories and codes tell us which of the four regions of the United States each survey respondent lives in. This variable allows us to know and account for differences in which region people live. Someone scored “1” on REGION would be different from someone scored “2” on REGION in terms of where they live.

d. The question becomes: Is REGION measured at the ordinal level? If a variable is measured at the ordinal level, then its different codes and categories would tell us not only is cases are similar or different in that regard but also if one case has more or less of that variable than another case. Here, we need to look close at what those codes and categories mean: Does “2” mean more REGION than “1” (i.e., Does someone who lives in the region coded “3” have more region than someone who lives in the region coded “2” or “1”)?

i. If we answer this question affirmatively—that is, by saying yes, these different categories and codes allow us to distinguish between quantity not just quality—then what we have is at least an ordinal-level variable. We would then go on to ask if the variable meets the criteria for an interval-level variable.

ii. If we answer this question negatively—that is, by saying no, these categories and codes allow us to distinguish between quality but not quantity—then what we have is a nominal-level variable. We can stop here; we do not need to ask any more questions to determine this variable’s level of measurement.

4. We know a variable’s level of measurement is not nominal if the variable’s categories and codes allow us to distinguish between cases in terms not only of (i) same or different but also (ii) more or less. It is this more or less power that separates ordinal from nominal variables.

a. With an ordinal-level variable, there is some inherent logical ordering to the categories, and that ordering should be reflected in the codes assigned to the categories. Categories that reflect more of the variable should have higher codes than categories that reflect less of the variable. Thus, the numbers used for the codes have some meaning beyond just telling us same or different. For example, in our jury survey, we might want to know each person’s level of education. We could name this variable EDUCATION and give it categories and codes such as:

As we go from cases coded “4” on EDUCATION to cases coded “3” on EDUCATION, we are going from people with more education to people with less education.

b. To determine whether a variable is measured at the ordinal level, think about what it would mean for someone to be coded “2” on EDUCATION and someone else be coded “3” on EDUCATION. We know these people are different in terms of EDUCATION (i.e., the sole criteria for a nominal-level variable). But what else do we know about these people’s education based on these codes? We also know that the person coded “3” has more education than the person coded “2,” as we see in the table above. Because EDUCATION’s categories and codes allow us to determine more or less education as well as same or different education, EDUCATION is at least an ordinal-level variable.

5. Nominal and ordinal variables are called categorical (or qualitative) variables. They are measured by dividing them into categories, and then assigning numerical values (i.e., codes) to those categories.

a. With nominal variables, the assigning of codes is arbitrary, because there is no quantitative meaning to the categories. This makes it hard to guess how a variable’s categories are coded.

b. With ordinal variables, the assigning of codes should be logical, because the coding should reflect the nature of the variable: Higher codes should be assigned to categories that represent more of the variable. We might be able to guess the ordering of an ordinal variable’s categories, but we still might have a hard time guessing how the variable was divided up (e.g., EDUCATION could have been broken up differently) and which number starts the coding (e.g., is the lowest category 0 or 1?).

c. With both nominal and ordinal variables, the numbers used as codes usually do not mean the same thing as the categories they represent. Thus, for example, a “2” on the variable EDUCATION above does not mean and cannot properly be interpreted as meaning “2 years of education.” Instead, “2” means anywhere between 1 and 5 years of formal education.

6. Interval and ratio variables are called continuous (or quantitative) variables. Continuous variables are different from categorical variables in two key ways.

a. With continuous variables, the numbers do mean exactly what they say. So, we aren’t really talking even about “codes” anymore. If we have a variable called AGE, where a “code” of “18” truly means “18 years of age” and a code of “45” truly means “45 years of age” (and so on), then we have a continuous variable. This has to be the case for every single category/value of the variable. If even one value is coded to mean something else, or if values are combined together (like we saw with EDUCATION), then we do not have a continuous variable.

b. Unlike categorical variables, with continuous variables, there are equal distances between all values throughout the scale. Take DOLLARS EARNED, for example, where “1” means “$1 dollar earned,” “2” means “$2 dollars earned,” and so on. Measured this way, DOLLARS EARNED is a continuous variable. We can take any two adjacent points on the DOLLARS EARNED SCALE—say $11 and $12. And we can move up or down the scale and pick any two more adjacent points—say $98 and $99. By equal distances, I mean that there is the same distance between $11 and $12 as there is between $98 and $99. (We don’t get these nice and neat equal distances with categorical variables.)

7. If we can tell (i) same or different as well as (ii) more or less, then we know the variable is at least ordinal and want to determine whether the variable is interval. Few social science variables are measured at the interval level, so we’re not likely to come across many of them. Still, we want to make sure we have a continuous variable, and then we want to make sure that the continuous variable is not measured at the ratio level. If we satisfy these two criteria, then we have an interval-level variable.

a. If a variable is interval, then as discussed in #6 above, it doesn’t really have “categories” and “codes”; rather, it has values that reflect different measurement increments. This is true of both interval and ratio variables.

b. If a variable is interval, then the “0” (zero) we see in its values does not reflect the complete absence of the variable. In other words, interval-level variables do not have an absolute zero; this is the key characteristic that sets interval variables apart from ratio variables. Temperature if an excellent example of an interval-level variable, because a temperature of 0.0 degrees does not mean there is an utter, absolute lack of heat. Instead, it can get colder than 0.0 degrees (i.e., there can be even less of the variable than what we get with zero).

i. If the zero value does not indicate the utter/absolute absence of the variable, then the continuous variable is interval. We don’t need to any more questions.

ii. If the zero value does indicate the utter/absolute absence of the variable, then the continuous variable is ratio. We should ask a couple more questions just to confirm.

8. If we can tell (i) same or different, (ii) more or less, and (iii) equal distances, then we know the variable it at least interval and want to determine if the variable is ratio. If we think the zero value indicates the variable’s complete absence, then we might have a ratio-level variable (see above).

a. Ratio-level variables have the same properties as internal-level variables—except that ratio-level variables also have a true zero point (or absolute zero point).

b. Rate variables (e.g., unemployment rate, crime rate, poverty rate) are examples of ratio-level variables. Variables like AGE, NUMBER OF PRIOR CONVICTIONS, and NUMBER OF VICTIMS also are ratio-level variables.