# Scales of measurement

## There are three primary scales of measurement in applied statistical analysis

There are three scales of measurement used in statistical analysis: Categorical, ordinal, and continuous. Categorical variables are used to group observations according to characteristics that they do or do not possess. Nominal variables are synonymous with categorical variables in that numbers are used to "name" phenomena such as outcomes or characteristics. Non-parametric statistics are used for statistical analysis with categorical outcomes.

Ordinal variables provide a sense of order and most often are used in applied research as Likert-type scales. They can provide a measure of distance, but not magnitude. Non-parametric statistics are used with ordinal outcomes.

The final and most powerful scale of measurement is continuous. Continuous level measurement possesses a "true zero," meaning that it can provide a measure of both distance and magnitude. Continuous level measurement provides the most precise and accurate level of measurement for an outcome or variable. In applied research, interval, ratio, and count variables are treated the same as continuous variables. Parametric statistics are used with continuous outcomes.

The way that researchers measure for their predictor and outcome variables in terms of scale of measurement has a drastic impact on statistical power, or the ability to detect significant treatment effects. Categorical and ordinal scales of measurement decrease statistical power due to limited precision and accuracy in measurement. Continuous measurement possesses a "true zero" that allows for both distance and magnitude to be detected, leading to more precision and accuracy when measuring for variables or outcomes. Continuous level measurement will always increase statistical power due to increased precision and accuracy in measurement.

Ordinal variables provide a sense of order and most often are used in applied research as Likert-type scales. They can provide a measure of distance, but not magnitude. Non-parametric statistics are used with ordinal outcomes.

The final and most powerful scale of measurement is continuous. Continuous level measurement possesses a "true zero," meaning that it can provide a measure of both distance and magnitude. Continuous level measurement provides the most precise and accurate level of measurement for an outcome or variable. In applied research, interval, ratio, and count variables are treated the same as continuous variables. Parametric statistics are used with continuous outcomes.

The way that researchers measure for their predictor and outcome variables in terms of scale of measurement has a drastic impact on statistical power, or the ability to detect significant treatment effects. Categorical and ordinal scales of measurement decrease statistical power due to limited precision and accuracy in measurement. Continuous measurement possesses a "true zero" that allows for both distance and magnitude to be detected, leading to more precision and accuracy when measuring for variables or outcomes. Continuous level measurement will always increase statistical power due to increased precision and accuracy in measurement.

**Categorical, ordinal, and continuous level measurement differences**

### There are three primary scales of measurement: Categorical, ordinal, and continuous

**Categorical**variables are also known as nominal in applied statistics.

**Ordinal**variables are commonly used as Likert-type scales in applied statistics.

**Continuous**variables are also known as interval, ratio, or count variables in applied statistics.

### More scales of measurement

Here are other scales of measurement.

**Nominal**variables are the same as categorical variables above.**Interval**,**ratio**, and**count**variables all fall under the guise of continuous variables but possess different measurement characteristics.Nominal variables are used to name or categorize events or phenomena.

Interval measures do not possess a "true zero" and can generate measures of distance, but not magnitude.

Ratio variables possess a "true zero" and can generate measures of both distance and magnitude.

Count variables represent the number of times that an event or phenomenon occurs.

## Hire A Statistician - Statistical Consulting for Students

**DO YOU NEED TO HIRE A STATISTICIAN?**

Eric Heidel, Ph.D.

**will provide the following statistical consultingservices for undergraduate and graduate students at $50/hour. Secure checkout is available with Stripe, Venmo, Zelle, or PayPal.**

- Statistical Analysis
- Research Design
- Sample Size Calculations
- Diagnostic Testing and Epidemiological Calculations
- Survey Design and Psychometrics