## Operationalizing Quantitative Measurements

Your measurements are your dependent variables. In educational research, one of the dependent variables is frequently learning. To measure learning, we have to define exactly what we mean. Learning could be measured by grades on assignments, such as exams or projects, performance on standardized tests, such as concept inventories, or self-report, such as feelings of learning. All of these options are possible, though some are more defensible in scientific research (more on validity later). As a researcher, you need to **operationalize, **or clearly articulate in a way that can be applied to your research, what you mean when you say learning, or any of your other dependent variables. You might need to operationalize your independent variables, too. For example, instead of saying you’ll measure peer-to-peer interaction, you could operationalize these interactions as number of posts on a peer-to-peer forum and number of contributions during peer-to-peer discussions in class.

## Levels of Measurement for Quantitative Data

**Levels of measurement** describe the type of quantitative data that you have by categorizing the relationships among values of a variable. When we represent information as numbers, such as representing learning as grades, we must be mindful of what these numbers represent. Unlike in math, higher numbers do not always mean higher value in quantiative data. For example, if you’re recording learners’ race, you might code “Black or African American” to be 1, “Hispanic or Latino” to be 2, etc. for purposes of analysis. This coding does not mean that Hispanic or Latino is more valuable than Black or African American, but it is merely a way of distinguishing between the two. On the other hand, if you’re measuring learners’ test scores, then a score of 80 would have a higher value than a score of 70. Levels of measurement categorize these relationships to determine which statistical tests are appropriate to analyze your data. There are four levels of measurement.

### Nominal – Lowest Level of Measurement

For** nominal** data, you are basically replacing the name of a value with a number. Like in the race example from earlier, the number does not imply anything about the relationship between values. For another example, if you separated students into groups, the group number would not provide any information about the value of the group.

### Ordinal

For **ordinal **data, you can rank-order the values, but the distance between values is not meaningful. For example, you could code prior education as high school degree = 1, some college = 2, college degree = 3, etc. You could rank these values from less education to more education, but the difference between 1 and 2 isn’t necessarily the same as the difference between 2 and 3.

### Interval

For **interval **data, the difference between values is meaningful. For example, if learners rate how much they liked an activity on a scale of “0 – Not at all” to “10 – A great deal,” then the difference between 4 and 5 is equal to the difference between 5 and 6. For interval data, zero is just another number on the scale; it does not indicate an absence of something. In this example, the scale could just as easily start at “1 – Not at all,” and the meaning would be the same.

### Ratio – Highest Level of Measurement

For **ratio **data, the difference between values is meaningful and zero indicates an absolute zero, or a lack of something. For example, grades are ratio because the difference between 70 and 80 is the same as the difference between an 80 and 90, and a grade of 0 means that nothing about the topic was known (or demonstrated to be known).

Typically, you want the highest level of measurement that makes sense for the data. For example, you’d rather have numeric grade values, which are ratio, than letter grade values, which are interval or arguably ordinal. It would not make sense, however, to measure years in school, which is ratio, instead of highest level of degree earned, which is ordinal, because that information would be less meaningful. The higher that your level of measurement is, the less restricted and more sensitive your statistical analyses can be. That being said, there are few differences between analyzing interval and ratio data, so if your data don’t have an absolute zero point, that’s not a problem. The main difference between interval and ratio data is the interpretation of the results.

Level of Measurement | Definition | Example | Explanation |

Nominal | Numbers are placeholders for categories | 0 = male 1 = female | Data don’t provide information about relationship between values |

Ordinal | Numbers provide rank-order but not exact interval between categories | 1 = low 2 = medium 3 = high | Data provide information about rank but not exact differences |

Interval | Numbers provide information about interval between categories | 1 = Strongly Disagree 2 = Disagree 3 = Neutral 4 = Agree 5 = Strongly Agree | The difference between 1 and 2 are equal to the difference between 2 and 3, and 0 does not indicate an absence of agreement |

Ratio | Numbers provide information about interval between categories, and zero means an absence | 0 = 0 forum posts; 1 = 1 forum post; 2 = 2 forum posts; 3 = 3 forum posts; etc. | The difference between 1 and 2 are equal to the difference between 2 and 3, and 0 means no posts were made |

To view more posts about research design, see a list of topics on the Research Design: Series Introduction.

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