Which characteristic is a key difference between ratio and interval scales group of answer choices?

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.

Nominal

A 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:

• genotype, blood type, zip code, gender, race, eye color, political party

Ordinal

An ordinal scale is one where the order matters but not the difference between values.

Examples of ordinal variables include:

• socio economic status (“low income”,”middle income”,”high income”), education level (“high school”,”BS”,”MS”,”PhD”), income level (“less than 50K”, “50K-100K”, “over 100K”), satisfaction rating (“extremely dislike”, “dislike”, “neutral”, “like”, “extremely like”).

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”.

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Interval

An interval scale is one where there is order and the difference between two values is meaningful.

Examples of interval variables include:

• temperature (Farenheit), temperature (Celcius), pH, SAT score (200-800), credit score (300-850).

Ratio

A 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:

• enzyme activity, dose amount, reaction rate, flow rate, concentration, pulse, weight, length, temperature in Kelvin (0.0 Kelvin really does mean “no heat”), survival time.

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.

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Test your understanding of Nominal, Ordinal, Interval, and Ratio Scales

Each scale is represented once in the list below. 

• Favorite candy bar
• Weight of luggage
• Year of your birth
• Egg size (small, medium, large, extra large, jumbo)

Each scale is represented once in the list below. 

• Military rank
• Number of children in a family
• Jersey numbers for a football team
• Shoe size

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 Continuous

The list below contains 3 discrete variables and 3 continuous variables:

• Number of emergency room patients
• Blood pressure of a patient
• Weight of a patient
• Pulse for a patient
• Emergency room wait time rounded to the nearest minute
• Tumor size

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. 

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Keywords: levels of measurement

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While collecting data from various types of surveys and questionnaires, marketers often make use of 4 types of data measurement scales, namely: Nominal, Ordinal, Interval, and Ratio Scale.  Among all, the ratio scale adequately serves the purpose as it possesses all the qualities of other measurement scales (Nominal, Ordinal, and Interval scales).

However, the classification among the four is crucial because they determine the characteristics of the variables and the type of statistical analysis you are planning to do as per your business needs.

Therefore, in this article, we’ve discussed the ratio scale about what it is, how it can be used, its characteristics, advantages, and ratio scale examples.

What is a Ratio Scale

Ratio scale is an interval scale with a true zero or origin characteristic. The measurable variables taken by the ratio scale can be counted, ranked, added, or subtracted to make the difference. Also, it has an exact numerical difference, ratios, and specific order between the two variables. Meaning, the data collected via ratio scales can not only be easily categorized but also have equal intervals.

When working with ratio variables, the ratio of two measurements represents a meaningful interpretation. Let’s take “weight”, which is a ratio variable. A weight of 8 grams is twice as heavy as a weight of 4 grams.

Ratio scale examples:

 “For how many years have you been working with this company?”

• Less than 5 years
• 5 years – 10 years
• 11 years – 15 years
• 16 years – 20 years
• More than 20 years

“How much time do you spend on Social Media?”

• Less than 1 hour
• 1 to 2.5 hour
• 2.5 to 4 hour
• More than 4 hour

Some other use cases of ratio scale are length, height, duration, money, mass, and revenues. Hence, ratio scales are widely used in marketing research tools to evaluate sales, price, share, revenues, and the number of customers/stakeholders.

The ratio scale is the most informative scale that allows the researchers to apply any statistical technique, such as geometric mean, harmonic mean, and coefficient of variation. Apart from that, one can also measure the central tendency via any of the statistical tools – Mean, Median or Mode.

Characteristics of Ratio Scale

The ratio scale possesses almost all characteristics to be considered as an ideal scale for research purposes. Despite encompassing all the characteristics of an interval scale, it also has an additional advantage of having a well-defined zero.

• Absolute Zero Origin Makes it Most Informative

Since ratio data is measured on the ratio scale, it, therefore, complies with the distinctive characteristic of this scale i.e true absolute zero point. This makes the data more informative and meaningful – making it easy to define the difference of “how much”. For example, “one man is twice as old as the other” or “6 has twice the value as 3”.

• All Forms of Calculations

Researchers can perform almost every statistical calculation for ratio scale data.  The values can either be subtracted, added, multiplied, or divided. With ratio scale data, other unique statistical calculations such as Chi-square, mean, mode, and median can also be calculated.

Just because the ratio scale has a true zero origin, it doesn’t have any negative numerical value. For example, the age cannot be -10 years.

Ratio scale units permit unit conversion which is also useful in interpreting symbolic notation used in equations. Units of energy including Joules, gram-calories, kilogram-calories, British thermal units are ratio scale units and hence they can be easily converted to calculate energy flow through a system, for example.

Ratio Scale Examples

Surveyors/researchers can make use of the few ratio scale survey example to capture ratio data.

1. A ratio scale is used to gather data on age in a Market research survey, uses the scale as follows:

• Younger than 20
• 20-28
• 28-35
• 35-40
• Older than 40

2. A ratio scale is used to figure out how much time people spend on video games.

• Less than 1 hour
• 1 to 2 hours
• 2 to 3 hours
• More than 3 hours

3. What is your weight in kgs?

• Less than 50 kgs
• 51-60 kgs
• 61-70 kgs
• 71-80 kgs
• 81-90 kgs
• Above 90 Kgs

4. What is your height in feet and inches?

• Less than 5 feet
• 5 feet 1 inch – 5 feet 5 inches
• 5 feet 6 inches- 6 feet
• More than 6 feet

5. What is the number of minutes you work out each day?

• 20-30
• 30-45
• 45- 1 hour
• More than 1 hour

Advantages of Ratio Scale

1. A ratio scale of measurement is considered to be the most powerful of the four measurement scales because it has an absolute zero rather than an arbitrary origin. Hence, it encompasses all the properties of the other three measurement scales.
2. Ratio scale data is more informative than ordinal and nominal because the ratio units are directly comparable as they are all of equal value
3. Every statistical technique can be implemented on a ratio scale variable because it has an absolute zero point. For this reason ratio scale is used by businesses to measure sales, costs, market share, and the number of customers on a ratio scale.
4. Calculations done via ratio data are precise as it is measured using a continuous, equidistant scale that shows order, direction, and an accurate difference in the ratio units.
5. Since ratio data have a ‘true zero,’ representing an absence of the variable, it can be used in instances where you cannot have negative values. For example, height, weight, annual salary, sales, and more.
6. Unlike the other three types of data, ratio data can be added, subtracted, multiplied, and divided because it lacks negative values.
7. Ratio scale data can be used to calculate statistical measures such as mode, median, and mean; range, standard deviation, variance, and coefficient of variation.

How to Measure Ratio Scale?

Researchers can perform all statistical analyses on ratio data to identify patterns and trends for informed business decisions. For example, the ratio data of marks obtained by 100 students for an exam can be analyzed by both descriptive and inferential statistics.

1. Descriptive Statistics

Descriptive statistics intend to present a big chunk of data with summary charts, graphs, and tables which makes it easier to understand and visualize raw data. 

For the results of 100 students, you may want to analyze the overall performance of the students and the distribution or spread of the marks. This can easily be done by descriptive statistics.

Data that comes from descriptive statistics include the mode, median, and mean, along with the range, variance, and standard deviation.

Measures of central tendency: It incorporates the ways of describing the central position of a frequency distribution for sample data, which can be described by using a number of statistics, including the mode, median, and mean.

– The mean is equal to the sum of all the values in the data set divided by the number of values in the data set.

– The mode is the most frequent value in the data set.

– The median is the middle value for a data set when arranged in order of magnitude (smallest first).

Measures of spread: It includes the ways of summarizing the data by describing how spread out the values are. To describe the data spread, you can use a number of statistics including the range, variance, and standard deviation.

– The range is the simplest measurement that denotes the difference between the values in a data set. To find the range, simply subtract the lowest value from the greatest value of the data set.

– The variance is the measure of variability that indicates the degree of spread in the data set. The more the spread is, the larger will be the variance in relation to the mean. It is calculated by taking the average of squared deviations from the mean and is expressed as meters squared.

– A standard deviation represents how dispersed the data is in relation to the mean. A low standard deviation means data is clustered around the mean, whereas a high standard deviation indicates data is more spread out.

2. Inferential Statistics

While descriptive statistics are used to present the ratio data in a meaningful way, inferential statistics help study the data even further to draw conclusions and hypotheses about the same information. The main areas involved are:

Estimating parameters: This means taking a statistic from your sample data (such as the sample mean) and using it to draw conclusions about the data sample

Hypothesis tests: This test is used to answer research questions. For example, one might be interested in knowing if a newly launched product feature is effective. Or if a specific product helps customers to perform better in businesses.

The main indexes for inferential statistics are:

• Binomial Theorem
• Hypothesis Testing
• Normal Distributions
• T-Distributions
• Regression Analysis / Linear Regression
• Comparison of means

Difference Between Interval and Ratio Scale

Among all four, interval scale and ratio scale are two of the scales of measurement which describe the attributes in quantitative scales. These two scales are often confusing as ratio data possess all properties of interval data such as – data should have numeric values, the distance between the two points are equal, etc. but zero is arbitrary in internal data whereas, in ratio data, zero is absolute.

Let’s have a look at more differences between these two scales:

1. The variable of the interval scale has a definite order, and the difference between them has meaning but the ratio between them doesn’t have any meaning. For example, increasing the temperature from 15 to 30 degrees Celsius doesn’t mean it’s twice as hot. 

On the other hand, both the difference and the ratio between the variables of the ratio scale have meaning. For example, if you increase weight from 10 kgs to 20 kgs, it’s twice as heavy.

2. Another key difference between an internal scale and a ratio scale is that the ratio scale has a true zero, which means if a value is zero, it doesn’t exist. For example, if you measure height as zero then the height doesn’t exist. 

Whereas the interval scale may have zero but it’s not absolute. For instance, if you measure height as zero, it exists. And even it can be negatives which is just another measurement on the interval scale.

3. Statistical parameters such as multiplication and division have no meaning in interval scale variables, whereas ratio data can be multiplied and divided, and this is one of the notable differences between these measurement scales, which can only be added and subtracted.

For example, in ratio data, the difference between 5 and 6 is the same as the difference between 7 and 8, and 10 is twice as much as 5. This measurement is impossible in interval data.

Leverage the Power of Ratio Scale for Your Next Research

Making use of the right type of measurement scale could certainly help you capture meaningful data and help to make informed business decisions. The ratio scale helps users in collecting intense insights and works best with both inferential and descriptive analysis techniques.

So, are you ready to understand the size of the market, market share, annual sales, revenue, and pricing?

ProProfs Survey Maker can help you create the most engaging scale surveys and questionnaires using ready-made survey templates and survey questions.