In a statistical study, four categories of data are encountered: nominal, ordinal, interval, and ratio.

Ratio data is a type of qualitative data in which variables are measured on a continuous scale. Continue reading to find out more about this type of data, including examples and analysis.

In a Nutshell: Index Ratio Data

The highest degree of measurement is ratio data, which includes a real zero.

A true zero denotes the absence of any measurement beyond it.

This data type has the following features: categories, rank order, a true zero, and equal intervals between data.

Ratio data is defined as

A type of qualitative data is ratio data. Variables in ratio data, like those in interval data, are spaced at equal intervals. This scale also has a genuine zero (which means that the zero has a meaning).

In contrast to the interval data scale, the zero in the ratio scale denotes the absence of a variable to measure. 2

Measurement levels - Ratio data

In statistics, there are four main levels of measurement. The most difficult measurement level is ratio data, which is the highest of the four measurement levels.

Furthermore, ratio data contains all of the characteristics of the other three levels. The values can be classified and sorted.

They also have equal intervals, and the distinctive feature is that the values in the ratio level take on a genuine zero. 

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

The true zero

Only the ratio data scale contains the genuine zero. It signifies that the variable of interest or the one you wish to measure is completely absent.

For example, a person's years of work experience is a ratio variable because a person can have zero years of work experience. 

A true zero in a scale indicates that the values' ratios may be calculated. So, for example, a person with six years of job experience has three times as many years as someone with two years of work experience.

Temperature, for example, can be measured on a variety of scales. Temperature measurement units such as Celsius and Fahrenheit are interval scales, but the Kelvin unit is a ratio scale.

The spacing between adjacent spots in all three measuring units are equal. So, 0 on the Kelvin scale, for example, signifies that nothing can be colder.

In the Fahrenheit and Celsius scales, however, 0 is merely another temperature value. 4

The genuine zero in ratio data

As a result, temperature ratios in Kelvin can be calculated but not in Celsius or Fahrenheit. For example, just because 40 degrees Celsius is twice as hot as 20 degrees Fahrenheit does not mean it is twice as hot.

However, because the genuine zero is the beginning point, 40 Kelvins is twice as hot as 20 Kelvins.

A genuine zero indicates that you can multiply, divide, or discover the square root of a value on a scale.

Furthermore, due to its accuracy, gathering statistical data on a ratio measurement level is preferable above other levels.

Examples of ratio data

In natural and social sciences, the ratio scale is a chosen measurement level.

Ratio data can be discrete (represented exclusively in countable figures such as integers) or continuous (can take on infinite values).

Discrete ratio data examples:

• The number of children in a family

• The number of vehicles owned at a certain period (5 years)

• the number of male students in a class

Continuous ratio data examples:

• Years of professional experience

• The number of hours spent waiting in a waiting room

• Speed of driving (MpH)

Ratio data analysis

The initial phase is to collect ratio data, followed by descriptive and inferential statistics.

The best part about ratio data is that it can be used for any mathematical process.

As a result, practically all statistical analyses can be performed on the ratio scale.

Ratio data example:

Collect information about students' travel times in a certain city. This data will be collected in real-time and recorded in minutes.

In this case, you can summarize your data by compiling the following descriptive statistics:

• Distribution of frequencies (indicate in numbers or ratios)

• The central tendency (discovered by determining the mode, median, or mean of data)

• Indicate the degree of variability (by calculating range, standard deviation, and variance)

Overview of the frequency – distribution

You may determine the frequency of the individual variables by creating a table or graph.

Tendency Central

Calculate the mean, median, or mode of the data to find the central tendency. The mean, on the other hand, is the most favored computation because it takes into account all of the values in your data collection. 5

Mode

This is the variable that appears the most frequently in a discrete data set. Because of their limitless value possibilities, continuous variables rarely have a mode. There is no mode in our example because each variable appears just once.

Median

This is the value located in the center of your data set. The median is calculated using the formula Ratio data median   (n=total number of values). The median in our example is:

The value in position 26 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

The spread of data is referred to as variability. The range, variance, and standard deviation of ratio data can be used to describe the variation.

The range is the simplest mathematical computation because standard deviation and variance are more complex but provide more information. 

Range

The range is generated by subtracting the lowest and highest values from your data collection. The range in our example is 72.5 - 7 = 65.5 minutes. 

Deviation from the mean

This is your values' average variability. Standard deviation can be calculated using computer applications.

The standard deviation in our example is 13.4.

Variance

The variance is equal to the standard deviation squared. It denotes the difference between an individual value in your data set and the mean. In our example, the variance is (13.4) x 2 = 178.04.

Variation coefficient

This standardized measure of dispersion indicates how variable your data is in comparison to the mean. It is calculated using the following formula:

In our example, the CF is

Statistical tests

Finally, using your data overview, you may make relevant statistical judgments.

Parametric tests, for example, are appropriate for evaluating hypotheses in normal ratio data distributions.

Parametric tests are more powerful inferences than non-parametric tests because they allow you to draw stronger and more exact conclusions from your data.

However, before parametric tests can be used, the ratio data must meet numerous conditions. 

The following are some frequent parametric tests for testing ratio data hypotheses:

• Comparisons of means

• Correlation

• Regression

Frequently asked questions

What is the distinction between interval data and ratio data?

The key distinction between interval and ratio data is that in the latter, zero represents the total absence of the derivative being measured. There is no actual zero in interval data.

What are the four measurement levels?

Nominal data, ordinal data, interval data, and ratio data are the four measurement levels.

What is the difference between discrete and continuous variables?

Discrete variables represent numbers or counts. Continuous variables, on the other hand, reflect quantifiable amounts.

What exactly is a measuring level?

It is a statistical technique that explains how variables are captured precisely.