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For each of the variables described below, indicate whether it is a quantitative or a categorical (qualitative) variable. Also, indicate the level of measurement for the variable: nominal, ordinal, interval, or ratio. Make sure your responses are the most specific possible. Variable Type of variable Level of measurement (a)Favorite TV game show Quantitative Categorical Nominal Ordinal Interval Ratio (b)Temperature (in degrees Fahrenheit) Quantitative Categorical Nominal Ordinal Interval Ratio (c)Playing time (in seconds) of a DVD Quantitative Categorical Nominal Ordinal Interval Ratio Updated on 20 Oct 2021 We can classify data in two ways: based on its type and on its levels of measurement. If you want to figure out how to do it based on its type, that’s something we covered in this tutorial. We've also made a video on the topic. You can watch it below or scroll down if you prefer reading. Levels of Measurement: Qualitative and Quantitative DataNow, it’s time to move onto the other classification – levels of measurement. These can be split into two groups: qualitative and quantitative data. They are very intuitive, so don’t worry. Qualitative DataQualitative data can be further divided into nominal and ordinal. Nominal variables are categories like car brands – Mercedes, BMW or Audi, or like the four seasons – winter, spring, summer and autumn. They aren’t numbers and cannot be ordered. Ordinal data, on the other hand, consists of groups and categories which follow a strict order. Imagine you have been asked to rate your lunch and the options are: disgusting, unappetizing, neutral, tasty, and delicious. Although we have words and not numbers, it is obvious that these preferences are ordered from negative to positive, thus the level of measurement is qualitative, ordinal. Quantitative DataSo, what about quantitative variables? Well, as you may have guessed, they are also split into two groups: interval and ratio. Intervals and ratios are both represented by numbers but have one major difference. Ratios have a true zero and intervals don’t. RatiosMost things we observe in the real world are ratios. Their name comes from the fact that they can represent ratios of things. For instance, if I have 2 apples and you have 6 apples, you would have 3 times as many as I do. How did I find that out? Well, the ratio of 6 and 2 is 3. Other examples are a number of objects in general, distance and time. IntervalsIntervals are not as common. Temperature is the most common example of an interval variable. Important: It cannot represent a ratio of things and doesn’t have a true 0. For instance, temperature is usually expressed in Celsius or Fahrenheit. They are both interval variables. Say today is 5 degrees Celsius, or 41 degrees Fahrenheit. And yesterday was 10 degrees Celsius, or 50 degrees Fahrenheit. In terms of Celsius, it seems today is twice colder, but in terms of Fahrenheit - not really. The IssueThe issue comes from the fact that 0 degrees Celsius and 0 degrees Fahrenheit are not true 0s. These scales were, artificially created by humans for convenience. Now, there is another scale, called Kelvin, which has a true 0. 0 degrees Kelvin is the temperature at which atoms stop moving and nothing can be colder than 0 degrees Kelvin. This equals -273.15 degrees Celsius, or -459.67 degrees Fahrenheit. Variables shown in Kelvin’s are ratios, as we have a true 0, and we can make the claim that one temperature is 2 times more than another. Celsius and Fahrenheit have no true 0 and are intervals. Side note: Numbers like 2, 3, 10, 10.5, 3.14(Pi) can be both interval or ratio. However, you have to be careful with the context you are operating in. The Different Levels of MeasurementTo conclude, the levels of measurement can be either qualitative or quantitative. Qualitative data is split into two, as well. It can be nominal or ordinal, depending if there is any strict order or not. Quantitative data also consists of 2 groups – ratios and intervals. Here, the key difference is whether or not there is a true 0. So, now that you know all levels of measurement, you will be able to move onto deeper statistics subjects. Understanding how to visualize data seems like the perfect beginning to that journey. *** Interested in learning more? You can take your skills from good to great with our statistics tutorials! Next Tutorial: Visualizing Data with Bar, Pie and Pareto Charts
In the 1940s, Stanley Smith Stevens introduced four scales of measurement: nominal, ordinal, interval, and ratio. These are still widely used today as a way to describe the characteristics of a variable. Knowing the scale of measurement for a variable is an important aspect in choosing the right statistical analysis. NominalA nominal scale describes a variable with categories that do not have a natural order or ranking. You can code nominal variables with numbers if you want, but the order is arbitrary and any calculations, such as computing a mean, median, or standard deviation, would be meaningless. Examples of nominal variables include:
OrdinalAn ordinal scale is one where the order matters but not the difference between values. Examples of ordinal variables include:
Note the differences between adjacent categories do not necessarily have the same meaning. For example, the difference between the two income levels “less than 50K” and “50K-100K” does not have the same meaning as the difference between the two income levels “50K-100K” and “over 100K”. Make more informed and accurate analysis choices with Prism. Start your free Prism trial. IntervalAn interval scale is one where there is order and the difference between two values is meaningful. Examples of interval variables include:
RatioA ratio variable, has all the properties of an interval variable, and also has a clear definition of 0.0. When the variable equals 0.0, there is none of that variable. Examples of ratio variables include:
When working with ratio variables, but not interval variables, the ratio of two measurements has a meaningful interpretation. For example, because weight is a ratio variable, a weight of 4 grams is twice as heavy as a weight of 2 grams. However, a temperature of 10 degrees C should not be considered twice as hot as 5 degrees C. If it were, a conflict would be created because 10 degrees C is 50 degrees F and 5 degrees C is 41 degrees F. Clearly, 50 degrees is not twice 41 degrees. Another example, a pH of 3 is not twice as acidic as a pH of 6, because pH is not a ratio variable. Learn more about the difference between nominal, ordinal, interval and ratio data with this video by NurseKillam
Does measurement scale matter for data analysis?Knowing the measurement scale for your variables can help prevent mistakes like taking the average of a group of zip (postal) codes, or taking the ratio of two pH values. Beyond that, knowing the measurement scale for your variables doesn’t really help you plan your analyses or interpret the results. Note that sometimes, the measurement scale for a variable is not clear cut. What kind of variable is color? In a psychological study of perception, different colors would be regarded as nominal. In a physics study, color is quantified by wavelength, so color would be considered a ratio variable. What about counts? There are occasions when you will have some control over the measurement scale. For example, with temperature, you can choose degrees C or F and have an interval scale or choose degrees Kelvin and have a ratio scale. With income level, instead of offering categories and having an ordinal scale, you can try to get the actual income and have a ratio scale. Generally speaking, you want to strive to have a scale towards the ratio end as opposed to the nominal end. Save time performing statistical analysis with Prism. Try Prism for free. Test your understanding of Nominal, Ordinal, Interval, and Ratio ScalesEach scale is represented once in the list below.
Each scale is represented once in the list below.
Answers: N,R,I,O and O,R,N,I Quantitative (Numerical) vs Qualitative (Categorical)There are other ways of classifying variables that are common in statistics. One is qualitative vs. quantitative. Qualitative variables are descriptive/categorical. Many statistics, such as mean and standard deviation, do not make sense to compute with qualitative variables. Quantitative variables have numeric meaning, so statistics like means and standard deviations make sense.
This type of classification can be important to know in order to choose the correct type of statistical analysis. For example, the choice between regression (quantitative X) and ANOVA (qualitative X) is based on knowing this type of classification for the X variable(s) in your analysis. Quantitative variables can be further classified into Discrete and Continuous. Discrete variables can take on either a finite number of values, or an infinite, but countable number of values. The number of patients that have a reduced tumor size in response to a treatment is an example of a discrete random variable that can take on a finite number of values. The number of car accidents at an intersection is an example of a discrete random variable that can take on a countable infinite number of values (there is no fixed upper limit to the count). Continuous variables can take on infinitely many values, such as blood pressure or body temperature. Even though the actual measurements might be rounded to the nearest whole number, in theory, there is some exact body temperature going out many decimal places That is what makes variables such as blood pressure and body temperature continuous. It is important to know whether you have a discrete or continuous variable when selecting a distribution to model your data. The Binomial and Poisson distributions are popular choices for discrete data while the Gaussian and Lognormal are popular choices for continuous data. Test your understanding of Discrete vs ContinuousThe list below contains 3 discrete variables and 3 continuous variables:
Answers: d,c,c,d,d,c Note, even though a variable may discrete, if the variable takes on enough different values, it is often treated as continuous. For example, most analysts would treat the number of heart beats per minute as continuous even though it is a count. The main benefit of treating a discrete variable with many different unique values as continuous is to assume the Gaussian distribution in an analysis. Start your free trial of Prism. Keywords: levels of measurement |