Is the level of measurement where data are classified into categories and the order of those categories is not important?

A classification that relates the values that are assigned to variables with each other

Inhaltsverzeichnis Show

• What is Level of Measurement?
• Four Measurement Levels
• More Resources
• What level of measurement that is used to classify or categorize data?
• What is the level of measurement for categorical data?
• What is nominal level of measurement?
• What is ordinal level of measurement?

What is Level of Measurement?

In statistics, level of measurement is a classification that relates the values that are assigned to variables with each other. In other words, level of measurement is used to describe information within the values. Psychologist Stanley Smith is known for developing four levels of measurement: nominal, ordinal, interval, and ratio.

Four Measurement Levels

The four measurement levels, in order, from the lowest level of information to the highest level of information are as follows:

1. Nominal scales

Nominal scales contain the least amount of information. In nominal scales, the numbers assigned to each variable or observation are only used to classify the variable or observation. For example, a fund manager may choose to assign the number 1 to small-cap stocks, the number 2 to corporate bonds, the number 3 to derivatives, and so on.

2. Ordinal scales

Ordinal scales present more information than nominal scales and are, therefore, a higher level of measurement. In ordinal scales, there is an ordered relationship between the variable’s observations. For example, a list of 500 managers of mutual funds may be ranked by assigning the number 1 to the best-performing manager, the number 2 to the second best-performing manager, and so on.

With this type of measurement, one can conclude that the number 1-ranked mutual fund manager performed better than the number 2-ranked mutual fund manager.

3. Interval scales

Interval scales present more information than ordinal scales in that they provide assurance that the differences between values are equal. In other words, interval scales are ordinal scales but with equivalent scale values from low to high intervals.

For example, temperature measurement is an example of an interval scale: 60°C is colder than 65°C, and the temperature difference is the same as the difference between 50°C and 55°C. In other words, the difference of 5°C in both intervals shares the same interpretation and meaning.

Consider why the ordinal scale example is not an interval scale: A fund manager ranked 1 probably did not outperform the fund manager ranked 2 by the exact same amount that a fund manager ranked 6 outperformed a fund manager ranked 7. Ordinal scales provide a relative ranking, but there is no assurance that the differences between the scale values are the same.

A drawback in interval scales is that they do not have a true zero point. Zero does not represent an absence of something in an interval scale. Consider that the temperature -0°C does not represent the absence of temperature. For this reason, interval-scale-based ratios fail to provide some insights – for example, 50°C is not twice as hot as 25°C.

4. Ratio scales

Ratio scales are the most informative scales. Ratio scales provide rankings, assure equal differences between scale values, and have a true zero point. In essence, a ratio scale can be thought of as nominal, ordinal, and interval scales combined as one.

For example, the measurement of money is an example of a ratio scale. An individual with $0 has an absence of money. With a true zero point, it would be correct to say that someone with $100 has twice as much money as someone with $50.

More Resources

Thank you for reading CFI’s guide on Level of Measurement. To keep learning and developing your knowledge of business intelligence, we highly recommend the additional CFI resources below:

• Basic Statistics Concepts for Finance
• Central Tendency
• Geometric Mean
• Standard Deviation

Levels of Measurement

In 1946, Harvard University psychologist Stanley Smith Stevens developed the theory of the four levels of measurement when he published an article in Science entitled, "On the Theory of Scales of Measurement." In this famous article, Stevens argued that all measurement is conducted using four measurement levels. The four levels of measure, in order of complexity, are:

Nominal

Ordinal

Interval

Ratio

Here is a simple trick for remembering the four levels of measurement: Think "NOIR." Noir is the French word for black. "N" is for nominal. "O" is for Ordinal. "I" is for Interval. And, "R" is for ratio.

Categorical and Quantitative Measures:

The nominal and ordinal levels are considered categorical measures while the interval and ratio levels are viewed as quantitative measures.

Knowing the level of measurement of your data is critically important as the techniques used to display, summarize, and analyze the data depend on their level of measurement.

Let us turn to each of the four levels of measurement.

A. The Nominal Level

The nominal level of measurement is the simplest level. "Nominal" means "existing in name only." With the nominal level of measurement all we can do is to name or label things. Even when we use numbers, these numbers are only names. We cannot perform any arithmetic with nominal level data. All we can do is count the frequencies with which the things occur.

With nominal level of measurement, no meaningful order is implied. This means we can re-order our list of variables without affecting how we look at the relationship among these variables.

Here are some examples of nominal level data:

1. The number on an athlete's uniform
2. Your social security number
3. Your Visa card number
4. Your political party affiliation
5. The city where you were born
6. Your religion
7. Your social security number
8. The color of your eyes
9. The color of your hair
10. The color of the candies in a bag of M&Ms

With the nominal level of measurement, we are limited in the types of analyses we can perform. We can count the frequencies of items of interest, but we cannot sort the data in a way that changes the relationship among the variables under investigation. We can calculate the mode of the frequently occurring value or values. And, we can also perform a variety of non-parametric hypotheses tests. Non-parametric tests make no assumptions regarding the population from which the data are drawn. But, we cannot calculate common statistical measures like the mean, median, variance, or standard deviation.

B. The Ordinal Level

The ordinal level of measurement is a more sophisticated scale than the nominal level. This scale enables us to order the items of interest using ordinal numbers. Ordinal numbers denote an item's position or rank in a sequence: First, second, third, and so on. But, we lack a measurement of the distance, or intervals, between ranks. For example, let's say we observed a horse race. The order of finish is Rosebud #1, Sea Biscuit #2, and Kappa Gamma #3. We lack information about the difference in time or distance that separated the horses as they crossed the finish line.

Here are some examples of ordinal level data:

1. Order of finish in a race or a contest
2. Letter grades: A, B, C, D, or F
3. Ranking of chili peppers on a scale of hot, hotter, hottest
4. A student's year of study in high school or college: Freshman, Sophomore, Junior, and Senior
5. Stage of cancer: Stage I, II, III, or IV
6. Level of agreement: Strongly Disagree, Disagree, Neutral, Agree, Strongly Agree

With the ordinal level of measurement, we can count the frequencies of items of interest and sort them in a meaningful rank order. And, as we said, we cannot, however, measure the distance between ranks. In terms of statistical analyses, we can count the frequency of an occurrence of an event, calculate the median, percentile, decile, and quartiles. We can also perform a variety of non-parametric hypotheses tests. But, we cannot calculate common statistical measures like the mean, median, variance, or standard deviation. And, we cannot perform parametric hypothesis tests using z values, t values, and F values.

C. The Interval Level

With the interval level of measurement we have quantitative data. Like the ordinal level, the interval level has an inherent order. But, unlike the ordinal level, we do have the distance between intervals on the scale. The interval level, however, lacks a real, non-arbitrary zero.

To repeat, here are three characteristics of the interval level:

1. The values have a meaningful order
2. The distances between the ranks are measureable
3. There is no "true" or natural zero

The classic example of the interval scale is temperature measured on the Fahrenheit or Celsius scales. Let's suppose today's high temperature is 60º F and thirty days ago the high temperature was only 30º F. We can say that the difference between the high temperatures on these two days is 30 degrees. But, because our measurement scale lacks a real, non-arbitrary zero, we cannot say the temperature today is twice as warm as the temperature thirty days ago.

In addition to temperature on the Fahrenheit or Celsius scales, examples of interval scale measures include:

1. Scores on the College Board's Scholastic Aptitude Test, which measures a student's scores on reading, writing, and math on a scale of 200 to 800
2. Intelligence Quotient scores
3. Dates on a calendar
4. The heights of waves in the ocean
5. Longitudes on a globe or map
6. Shoe size

With the interval level of measurement, we can perform most arithmetic operations. We can calculate common statistical measures like the mean, median, variance, or standard deviation. But, because we lack a non-arbitrary zero, we cannot calculate proportions, ratios, percentages, and fractions. We can also perform all manner of hypotheses tests as well as basic correlation and regression analyses.

D. The Ratio Level

The last and most sophisticated level of measurement is the ratio level. As with the ordinal and interval levels, the data have an inherent order. And, like the interval level, we can measure the intervals between the ranks with a measurable scale of values. But, unlike the interval level, we now have meaningful zero. The addition of a non-arbitrary zero allows use to calculate the numerical relationship between values using ratios: fractions, proportions, and percentages.

An example of the ratio level of measurement is weight. A person who weights 150 pounds, weights twice as much as a person who weighs only 75 pounds and half as much as a person who weighs 300 pounds. We can calculate ratios like these because the scale for weight in pounds starts at zero pounds.

n addition to weight, examples of ratio scale measures include:

1. Height
2. Income
3. Distance travelled
4. Time elapsed or time remaining
5. Money in your bank account, wallet, or pocket

With the ratio level of measurement, we can perform all arithmetic operations including proportions, ratios, percentages, and fractions. In terms of statistical analyses, we can calculate the mean, geometric mean, harmonic mean, median, mode, variance, and standard deviation. We can also perform all manner of hypotheses tests as well as correlation and regression analyses.

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What level of measurement that is used to classify or categorize data?

What is the level of measurement for categorical data?

What is nominal level of measurement?

What is ordinal level of measurement?