A main concept in statistics is level of measure of variables. It’s for this reason

important to every little thing you perform with data the it’s normally taught in ~ the an initial week in every intro stats class.

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But even something so an essential can be tricky once you begin working with genuine data. The same variable deserve to be thought about to have various levels of measure up in various situations. It sounded favor an absolute in the intro stats class because your way professor didn’t want to confuse beginning students.

But currently that you’re a more sophisticated practitioner of data analysis, ns will display you just how the same variable have the right to be taken into consideration to have various levels that measurement. Yet first, permit me review some definitions.

### A review of the level of measure up of Variables

Nominal:

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

Ordinal:

Ordered categories. Tho categorical, yet in one order. Likert items with responses like: “Never, Sometimes, Often, Always” space ordinal.

Interval:

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

Ratio:

Numerical values with a true zero point.

Interval and Ratio variables deserve to be further split into two types: discrete and continuous. Discrete variables, choose counts, have the right to only take on totality numbers: variety of children in a family, number of days missed from work. Continuous variables can take on any number, even beyond the decimal point.

Not constantly obvious is the these levels of measurement space not only about the variable itself. Likewise important room the meaning of the variable within the research study context and how it to be measured.

### An Example: Age

A an excellent example that this is a variable choose age. Period is, technically, consistent and ratio. A person’s period does, after ~ all, have a systematic zero suggest (birth) and also is consistent if you measure up it specifically enough. The is coherent to say that someone (or something) is 7.28 year old.

That said, you might not be able to treat it as consistent in your analysis. It relies on just how you measure it and whether there room qualitative implications around age in your study context. Here are 5 examples in which period has one more level of measurement:

Age as Ordinal

For example, it’s not unusual to give civilization age category as possible responses on a survey. Typical reasons are that civilization don’t desire to expose their actual age or because they don’t remember the actual period at which some occasion occurred.

I functioned with a client whose dependent variable to be the period at i m sorry adult smokers began smoking. It would have been good to get an accurate date on which each person smoked their very first cigarette, yet it’s a big burden on respondents to ask them a very certain number from a lengthy time ago.

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

Ordinal response variables require a design like one Ordinal Logistic Regression.

Age as Discrete Counts

Likewise, a consistent variable may be calculation discrete because of the method people think around and measure up it.

For example, take into consideration the example of period measured in days on i beg your pardon germinated seeds of a specific types begin to sprout leaves. Many will do so within a couple of days, and it may range from 2-9 days.

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

Age as Multinomial

Sometimes numerical variables room rendered categorical because of the absence of values.

In one study I analyzed, the vital independent variable to be the period of a angry in a trial. If technically, eras are continuous, in this research there were only 4 values: 49, 69, 79 and 89.

So even though one could use statistics that treated this variable as continuous, lock don’t make a most sense. In a linear model, if girlfriend treat this age variable together a number predictor, the design will to the right a regression line across these four ages. If girlfriend treat it together categorical, the will estimate way and permit you to compare the average of Y at every age.

The effect of age in this context is far better measured through a difference in the mean of Y in ~ two different ages than with a slope—the distinction in Y for 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 examining math abilities in first grade children. The vital independent variable to be whether the child had actually reached a specific cognitive developmental milestone and the dependent variable was math score. Age was a manage variable and it was mildly associated to, however not confounded with, attainment the the milestone.

Because each son was asked just how old they were, it was measured in whole years. The would have been ideal to collect an ext specific data on ages—such together their birth days from their parents or institution records. For everything reason, that wasn’t possible.

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

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

Age as Binary category (another one)

In a research comparing the work-life balance that men and women, the result variable was variety of hours functioned per week. One an essential predictor because that women, however not men, was the age of their youngest child.

There is a qualitative difference between a 5 year old, who may only be eligible because that part-time kindergarten and a 6 year old, that is old sufficient to go to permanent school.

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

Notice the both of this binary instances are an extremely different case from act a median break-up on a consistent variable.

That type of categorizing isn’t a good idea because you’re throw away great information based upon an arbitrary cutoff.

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