A central concept in statistics is level of measure of variables. It’s therefore

important to every little thing you do with data the it’s generally taught in ~ the very first week in every intro stats class.

You are watching: The number of children in a family is a discrete variable.

But even something so basic can be tricky as soon as you begin working with genuine data. The very same variable deserve to be thought about to have different levels of measure in various situations. That sounded choose an absolute in that intro stats class since your way professor didn’t want to confuse start students.

But now that you’re a much more sophisticated practitioner the data analysis, ns will present you just how the exact same variable have the right to be thought about to have various levels that measurement. Yet first, let me testimonial some definitions.

A review of the level of measurement of Variables


Unordered categorical variables. These can be either binary (only 2 categories, favor gender: masculine or female) or multinomial (more than 2 categories, like marital status: married, divorced, never married, widowed, separated). The vital thing right here is the there is no reasonable order to the categories.


Ordered categories. Still categorical, but in one order. Likert items v responses like: “Never, Sometimes, Often, Always” room ordinal.


Numerical worths without a true zero point. The idea here is the intervals between the values room equal and meaningful, but the numbers themselves are arbitrary. 0 walk not indicate a complete lack of the quantity being measured. IQ and also degrees Celsius or Fahrenheit space both interval.


Numerical values with a true zero point.

Interval and Ratio variables deserve to be further separation into 2 types: discrete and continuous. Discrete variables, like counts, can only take on whole numbers: number of children in a family, number of days missed from work. Continuous variables can take on any number, even past the decimal point.

Not always obvious is that these level of measurement space not only about the change itself. Also important space the meaning that the variable within the research context and how it to be measured.

An Example: Age

A an excellent example of this is a variable prefer age. Period is, technically, constant and ratio. A person’s period does, ~ all, have a meaningful zero point (birth) and also is continuous if you measure up it specifically enough. That is coherent to say that someone (or something) is 7.28 year old.

That said, you may not be able to treat it as consistent in your analysis. It relies on how you measure up it and whether there room qualitative implications about age in your research context. Right here are 5 instances in which period has an additional level of measurement:

Age together Ordinal

For example, it’s not uncommon to give people age category as possible responses ~ above a survey. Common reasons space that world don’t desire to disclose their actual age or due to the fact that they don’t psychic the actual age at i m sorry some occasion occurred.

I worked with a customer whose dependency variable was the age at which adult smokers began smoking. That would have been an excellent to get specific date on which each person smoked their first cigarette, however it’s a large burden on respondents to ask castle a very particular number native a long time ago.

Rather than have actually respondents guess: v inaccurately or leaving the answer blank, the researchers provided them a collection of ordered period categories: 0 to 10, 11-12, 13-15, 16-17, etc. They offered up precision to gain accuracy.

Ordinal solution variables require a design like an Ordinal Logistic Regression.

Age together Discrete Counts

Likewise, a constant variable may be calculation discrete since of the method people think about and measure it.

For example, take into consideration the instance of age measured in work on which germinated seeds of a specific varieties begin come sprout leaves. Most will execute so within a couple of days, and it may selection from 2-9 days.

In this context, period is definitely a discrete count—the variety of days. If it is used as result variable, a Poisson (or related) regression would certainly be appropriate, no a linear model.

Age together Multinomial

Sometimes number variables space rendered categorical as result of the lack of values.

In one examine I analyzed, the key independent variable was the period of a evil in a trial. When technically, periods are continuous, in this examine there were only four values: 49, 69, 79 and 89.

So also though one could usage statistics that treated this variable as continuous, they don’t do a lot of sense. In a direct model, if you treat this age variable as a number predictor, the design will fit a regression line throughout these four ages. If girlfriend treat it together categorical, the will estimate means and allow you to to compare the mean of Y at each age.

The impact of period in this context is far better measured through a difference in the average of Y in ~ two different ages than v a slope—the distinction in Y because that each one year increase.

Now if her multinomial period variable is the response, you’ll require a multinomial logistic regression.

Age as Binary Categories

In a similar example, a researcher was studying math abilities in very first grade children. The vital independent variable to be whether the child had actually reached a particular cognitive developmental milestone and the dependent change was mathematics score. Period was a manage variable and also it was mildly connected to, yet not confounded with, attainment that the milestone.

Because each child was asked how old lock were, it was measured in whole years. It would have been ideal to collect much more specific data on ages—such as their birth dates from their parents or institution records. For whatever reason, that wasn’t possible.

So the only two worths for age were 6 and also 7. So as with in the last example, it just made feeling to law this predictor variable together categorical in the analysis.

If you had actually a binary result variable, you’d most likely need a binary logistic regression.

Age as Binary category (another one)

In a examine comparing the work-life balance the men and women, the result variable was number of hours functioned per week. One vital predictor for women, but not men, was the age of your youngest child.

There is a qualitative difference in between a 5 year old, who might only be eligible for part-time kindergarten and also a 6 year old, who is old sufficient to go to permanent school.

This qualitative difference exists in this context in between 5 and 6 the doesn’t exist at other one-year age differences*. This qualitative difference is in truth the most essential feature of the youngest child’s age. Treating period as constant actually ignores this necessary qualitative difference.

Notice the both of this binary examples are really different instance from doing a median split on a constant variable.

That sort of categorizing isn’t a great idea because you’re throw away an excellent information based on an arbitrary cutoff.

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*It likewise doesn’t exist in other contexts. The difference in between ages 5 and 6 wouldn’t be essential if you’re researching drug usage or retirement planning.