Types of Data in Statistics — Statistical Symphony Series
Welcome to the part#2 of Statistical Symphony Series. I hope you’re enjoying it ! In this article let’s understand what are types of data and understand the various scales of measurement of data — nominal, ordinal, interval and ratio scaled data.
In case you’ve missed the earlier articles in this series, please do read them for better continuity.
II. Data Types
There are two main types of data: qualitative data and quantitative data.
A. Qualitative Data
Qualitative data is data that describes characteristics or attributes of a variable, such as color, shape, and size. It is non-numerical data and cannot be measured. It can be further divided into two types:
- Nominal Data: Nominal data is data that assigns a name, label or category to a variable without any order or ranking. For example, gender, hair color, religion, and nationality are all examples of nominal data. In other words, nominal data is data that can be put into categories, but the categories do not have any order or ranking.
- Ordinal Data: Ordinal data is data that assigns a name, label or category to a variable with a specific order or ranking. For example, educational level (high school, college, graduate), job title (entry-level, mid-level, senior-level), and survey response options (strongly agree, agree, neutral, disagree, strongly disagree) are all examples of ordinal data. In other words, ordinal data is data that can be put into categories, and the categories have a specific order or ranking.
B. Quantitative Data
Quantitative data is data that describes a variable in terms of numbers. It is also known as numerical data. There are two broad types types of quantitative data: Discrete and Continuous, Interval and Ratio.
Discrete Data: Discrete data is data that can only take on specific, separate values. For example, the number of children in a family, the number of students in a class, and the number of cars sold in a month are all examples of discrete data. Another example, if a researcher wants to know the number of siblings of students in a school, they would use discrete data as the number of siblings can only take certain values (0, 1, 2, 3, etc.). In other words, discrete data can only take on specific, separate values, and the values are not infinite.
Continuous Data: Continuous data are data that can take any value within a given range, such as weight or height. For example, if a researcher wants to know the height of students in a school, they would use continuous data as height can take any value within a given range (i.e. 5 feet 2 inches to 6 feet 2 inches). In other words, continuous data can take on any value within a certain range, and the values are infinite.
Interval Data
- Interval data is a type of quantitative data that has a consistent scale, meaning the difference between two units on the scale is the same, but the zero point on the scale is arbitrary and does not represent the absence of the quantity being measured, thus ratios between values are not meaningful.
- For example, temperature measured in degrees Celsius is interval data. The difference between 20 degrees and 30 degrees is the same as the difference between 30 degrees and 40 degrees, but you can’t say that 20 degrees is twice as hot as 10 degrees, because zero point on the scale doesn’t represent the absence of the quantity being measured.
Interval data allows us to compare temperatures and understand the difference between them, but it doesn’t allow us to make statements about the absolute temperature.
- In simpler terms, think of it this way: the difference between “I’m kinda warm” and “I’m really warm” is the same as the difference between “I’m too hot” and “I’m about to pass out from heat stroke”, but that doesn’t mean “I’m kinda warm” is half as hot as “I’m about to pass out from heat stroke.”
- This is why temperature is considered as an interval data rather than ratio data and why we can’t say 20 degrees is twice as hot as 10 degrees, because zero point on the scale doesn’t represent the absence of the temperature.
- Interval data can also be used in measuring things like pH levels, where a pH of 7 is neutral, but we can’t say that a pH of 14 is twice as basic as a pH of 7.
- Interval data can also be used in measuring things like IQ scores, where a difference of 15 points is the same regardless of whether it is between an IQ of 100 and 115 or between an IQ of 130 and 145.
- Interval data can also be used in things like measuring income, where a difference of $10,000 is the same regardless of whether it is between $50,000 and $60,000 or between $100,000 and $110,000.
- Interval data, which does not have a true zero point, can have negative values. For example, temperature measured in degrees Celsius can have negative values, as it is possible to have temperatures below freezing.
So, next time you’re wondering why you can’t say “I’m 20 degrees hotter than you” to your friend, remember it’s because temperature is interval data, not ratio data.
Ratio Data
- Ratio data is a fancy type of quantitative data that has a consistent scale, like a ruler that’s not been stretched out, and a meaningful zero point, like a starting point of a race.
- Real-world examples: Height measured in meters, weight measured in kilograms, time measured in seconds.
- Ratios between values are also meaningful: Like how 4 meters is twice as tall as 2 meters, or how 2 kilograms is twice as heavy as 1 kilogram.
- Zero point is meaningful: Like how 0 meters means no height and 0 kilograms means no weight.
- Negative Values: Ratio data does not allow for negative values. It is a scale of measurement that has a true zero point, meaning that the absence of the quantity being measured is represented by zero. It is not possible to have negative values for these measurements as it would not make sense to say that something is -5 meters tall or -10 kilograms heavy.
- Bonus: We can also make statements about relative proportions, like how 4 meters is twice as tall as 2 meters.
- Uses: Useful for measuring things like weight, height, time, and distance. Just like measuring how tall a giraffe is, or how heavy a bag of potatoes is or how much time you spent on your phone today.
Interval Vs Ratio Scaled — Summary View
Summary of Scales of Measurement
Now that we understand the different scales of measurement, it is also important to understand it’s relationship with various arithmetic operations, descriptive statistical measures, analysis techniques.
It is quite important to know which statistical operation is to apply what type of data ! This table would act as a cheat sheet to various operations. We will learn about plenty of jargons in the above table in the future articles in series. So Stay Tuned !
Q: What do you get when you mix together nominal, ordinal, interval and ratio scaled data? A: A data party with a lot of confusion! haha…
Q: What do you call four friends who all measure data differently? A: Nominal, ordinal, interval and ratio buddies!
In conclusion, becoming familiar with nominal, ordinal, interval and ratio scaled data can help you become a better data analyst and make more informed decisions. Whether you use it for research or your day-to-day work, understanding these four data scales can give you a powerful tool for understanding the world around you.
In the next part of #StatisticalSymphonySeries we will discuss about measures of central tendency and its nuances. I promise to keep it super interesting !
That’s a wrap! Clap if you like :) I’m Arun Prakash Asokan, follow me on Medium for more such content on AI, Statistics, Tech & Personal Finance. See you soon !
