{"id":203714,"date":"2020-08-28T16:05:11","date_gmt":"2020-08-28T14:05:11","guid":{"rendered":"https:\/\/www.scribbr.nl\/?p=203714"},"modified":"2021-09-16T11:08:34","modified_gmt":"2021-09-16T09:08:34","slug":"ratio-data","status":"publish","type":"post","link":"https:\/\/www.scribbr.com\/statistics\/ratio-data\/","title":{"rendered":"What is a ratio scale of measurement?"},"content":{"rendered":"

A ratio scale<\/strong> is a quantitative scale where there is a true zero and equal intervals between neighboring points. Unlike on an interval scale, a zero on a ratio scale means there is a total absence of the variable you are measuring.<\/p>\n

Length, area, and population are examples of ratio scales.<\/p>\n

<\/p>\n

Levels of measurement<\/h2>\n

The ratio level is the highest of four hierarchical levels of measurement<\/a>. The levels, or scales, of measurement indicate how precisely data is recorded. The higher the level, the more complex the measurement is.<\/p>\n

The ratio level contains all of the features of the other 3 levels. At the ratio level, values can be categorized, ordered, have equal intervals and take on a true zero.<\/p>\n

\"The<\/p>\n

While nominal and ordinal variables are categorical variables, interval and ratio variables are\u00a0 quantitative variables<\/a>. Many more statistical tests can be performed on quantitative than categorical data.<\/p>\n

What is a true zero?<\/h3>\n

On a ratio scale, a zero means there\u2019s a total absence of the variable of interest. For example, the number of children in a household or years of work experience are ratio variables: A respondent can have no children in their household or zero years of work experience.<\/p>\n

With a true zero<\/strong> in your scale, you can calculate ratios of values. For example, you can say that 4 children is twice as many as 2 children in a household. Similarly, 8 years is double 4 years of experience.<\/p>\n

Some variables, such as temperature, can be measured on different scales. While Celsius and Fahrenheit are interval scales, Kelvin is a ratio scale.<\/p>\n

In all 3 scales, there are equal intervals between neighboring points. However, unlike the Celsius and Fahrenheit scales where zero is just another temperature value, the Kelvin scale has a true zero (0 K) where nothing can be colder.<\/p>\n

That means that you can only calculate ratios of temperatures in the Kelvin scale. Although 40\u00b0 is twice as many degrees as 20\u00b0, it isn\u2019t twice as hot on the Celsius or Fahrenheit scales. However, in the Kelvin scale, 40 K is twice as hot as 20 K because there is a true zero at the starting point of this scale.<\/p>\n

A true zero makes it possible to multiply, divide or square root values. Collecting data<\/a> on a ratio level is always preferable to the other levels because it is the most precise.<\/p>\n

Examples of ratio scales<\/h2>\n

Many variables<\/a> in the natural and social sciences are measured using ratio scales.<\/p>\n

Like interval variables, ratio variables can be discrete or continuous.<\/p>\n

A discrete variable<\/strong> is expressed only in countable numbers (e.g., integers) while a continuous variable<\/strong> can potentially take on an infinite number of values.<\/p>\n\n\n\n\n\n\n\n\n\n\n
Ratio variable<\/strong><\/th>\nDiscrete or continuous?<\/strong><\/th>\n<\/tr>\n<\/thead>\n
Number of vehicles owned in the last 10 years<\/td>\nDiscrete<\/td>\n<\/tr>\n
Number of people in a household<\/td>\nDiscrete<\/td>\n<\/tr>\n
Number of students who identify as religious<\/td>\nDiscrete<\/td>\n<\/tr>\n
Reaction time in a computer task<\/td>\nContinuous<\/td>\n<\/tr>\n
Years of work experience<\/td>\nContinuous<\/td>\n<\/tr>\n
Speed in miles per hour<\/td>\nContinuous<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Ratio data analysis<\/h2>\n

After you\u2019ve collected ratio data, you can gather descriptive<\/a> and inferential statistics<\/a>. Almost all statistical tests<\/a> can be performed on ratio data because all mathematical operations are permissible.<\/p>\n

Ratio data example<\/figcaption>You collect data on the commute duration of employees in a large city. The data is continuous and in minutes.<\/figure>\n

To summarize your data, you can collect the following descriptive statistics:<\/p>\n