In the realm of statistical research, one primarily encounters four types of data: nominal, ordinal, interval, and ratio. Ratio data, a qualitative form of data, quantifies variables on an unbroken scale. This article will delve further into the concept of ratio data, providing a comprehensive understanding through examples and in-depth analysis, all aimed at enriching your knowledge of statistics.

## Definition: Ratio data

Ratio data is a form of qualitative data. Like interval data, variables in ratio data are placed at equal distances. Also, this scale features a true zero (which means that the zero has a meaning). However, unlike in the **interval data scale**, the zero in ratio scale implies the absence of a variable for measuring.^{2}

## Levels of measurement – Ratio data

There are four main levels of measurement in statistics. Ratio data is the highest among the four measurement levels, and it is the most complex measurement level.

Also, ratio data features all the characteristics of the other three levels. The values can be categorized and ordered. In addition, they have equal intervals and the unique characteristic is that the values in the ratio level take on a true zero.

Level |
Characteristics of the values |

Nominal data |
Categories |

Ordinal data | Categories, rank/order |

Interval data | Categories, rank/order, equal spacing |

Ratio data | Categories, rank/order, equal spacing, true zero |

**Note:** **Nominal data** and **ordinal data** scales are categorical variables, while **interval data** and ratio data variables are quantitative.

### The true zero

The true zero is only found in the ratio data scale. It means there is a total absence of the variable of interest or the one you want to measure. For example, the years of work experience a person has been a ratio variable, as a person can have zero years of work experience.

A true zero in a scale means that you can calculate the ratios of the values. So, for instance, you can say that a person with six years of work experience has thrice as many years as one with two years of work experience.

Additionally, variables like temperature can be measured on various scales.

For instance, Celsius and Fahrenheit temperature measurement units are interval scales, while the Kelvin unit is a ratio scale. All three measurement units have equal intervals between adjacent points.

So, for example, zero in the Kelvin scale means nothing can be colder. On the other hand, in the Fahrenheit and Celsius scales, zero is just another temperature value.

Therefore, you can calculate temperature ratios in the Kelvin scale but not in Celsius or Fahrenheit. For example, while *40* degrees Celsius is twice *20* degrees Fahrenheit, it does not mean it is twice as hot. However, *40* Kelvins is twice as hot as *20* Kelvins because the true zero is the starting point.

A true zero means you can multiply, divide, or find square roots of values in a scale. Also, collecting statistical data on a ratio measurement level is highly preferred over other levels because of its accuracy.

### Examples of ratio data

The ratio scale is a preferred measurement level in natural and social sciences. Ratio data can be discrete (only expressed in countable figures, like integers) or continuous (can take on infinite values).

## Ratio data analysis

The first step is collecting ratio data, then gathering the descriptive and inferential statistics. The best thing about ratio data is that all mathematical operations are applicable. Therefore, almost all statistical assessments can be executed on the ratio scale.

### Overview of the frequency – distribution

By constructing a table or graph, you can determine the frequency of the various variables.

### Central Tendency

You can determine the **central tendency** by calculating the data’s **mean, median,** or **mode**. However, the **mean** is the most preferred computation because it uses all the values in your data set.

#### Mode

This is the most frequently repeating variable in a discrete data set. Continuous variables typically do not have a **mode** because of infinite value possibilities. In our example, there is no **mode** because each variable appears once.

#### Median

This is the value in the middle of your data set. The formula for calculating the median is (=total number of values). In our example, the median is:

The value in the *26th *position is *36.4 *minutes

#### Mean

The formula for calculating the mean is:

In our example, the mean is: *1883.5* divided by *52 = 36.9*

### Variability

Variability refers to how the data is spread. You can describe the variation in ratio data by finding the range, variance, and standard deviation. The easiest mathematical computation is the range because standard deviation and variance are more complex, yet more informational.

#### Range

The **range** is calculated by subtracting the lowest value from the highest in your data set. In our example, the range is * *minutes.

#### Standard deviation

This is the average **variability** in your values. You can calculate **standard deviation** using specific computer programs. In our example, the standard deviation is *13.4*.

#### Variance

The variance is the square of the standard deviation. It means the difference between a value in your data set and the mean. The variance in our example is *.*

#### Coefficient of variation

This standardized measure of dispersion tells you how variable your data is in relation to the **mean**. It is calculated using the formula:

In our example, the **CF** is

### Statistical tests

Finally, you can determine the appropriate statistical inferences with the overview of your data. For instance, parametric tests are ideal for testing hypotheses in normal ratio data distribution.

Parametric tests are powerful inferences because they allow you to draw stronger and more precise conclusions from your data than non-parametric tests. However, the ratio data must meet several requirements before parametric tests apply.

## FAQs

The primary difference between interval and ratio data is that in the latter, zero means the total absence of the derivable you are measuring. **Interval data** does not contain a true zero.

The four measurement levels are:

- Nominal data
- Ordinal data
- Interval data
- Ratio data

Discrete variables represent counts or figures. On the other hand, continuous variables represent measurable amounts.

It is a statistical technique that tells you how precisely variables are recorded.