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    Chapter 2: Multiple Choice Questions

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    Chapter 2: Multiple Choice Questions

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    Level of Measurement

    In statistics, level of measurement is a classification that relates the values that are assigned to variables with each other.

    Level of Measurement

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

    Written by CFI Team

    Updated April 23, 2022

    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

    स्रोत : corporatefinanceinstitute.com

    Nominal, Ordinal, Interval, Ratio Scales with Examples

    Nominal, Ordinal, Interval and Ratio are the four fundamental levels of measurement scales used to capture data using surveys and questionnaires.

    Nominal, Ordinal, Interval, Ratio Scales with Examples

    Levels of Measurement in Statistics

    To perform statistical analysis of data, it is important to first understand variables and what should be measured using these variables. There are different levels of measurement in statistics and data measured using them can be broadly classified into qualitative and quantitative data.

    First,  let’s understand what a variable is.  A quantity whose value changes across the population and can be measured is called variable. For instance, consider a sample of employed individuals. The variables for this set of the population can be industry, location, gender, age, skills, job-type, paid time off, etc The value of the variables will differ with each employee spotlight.

    For example, it is practically impossible to calculate the average hourly rate of a worker in the US. So, a sample audience is randomly selected such it represents the larger population appropriately. Then the average hourly rate of this sample audience is calculated. Using statistical tests, you can conclude the average hourly rate of a larger population.

    The level of measurement of a variable decides the statistical test type to be used. The mathematical nature of a variable or in other words, how a variable is measured is considered as the level of measurement.

    What are Nominal, Ordinal, Interval and Ratio Scales?

    Nominal, Ordinal, Interval, and Ratio are defined as the four fundamental levels of measurement scales that are used to capture data in the form of surveys and questionnaires, each being a multiple choice question.

    Each scale is an incremental level of measurement, meaning, each scale fulfills the function of the previous scale, and all survey question scales such as Likert, Semantic Differential, Dichotomous, etc, are the derivation of this these 4 fundamental levels of variable measurement. Before we discuss all four levels of measurement scales in details, with examples, let’s have a quick brief look at what these scales represent.

    Nominal scale is a naming scale, where variables are simply “named” or labeled, with no specific order. Ordinal scale has all its variables in a specific order, beyond just naming them. Interval scale offers labels, order, as well as, a specific interval between each of its variable options.  Ratio scale bears all the characteristics of an interval scale, in addition to that, it can also accommodate the value of “zero” on any of its variables.

    Here’s more of the four levels of measurement in research and statistics: Nominal, Ordinal, Interval, Ratio.

    Nominal Scale: 1st Level of Measurement

    Nominal Scale, also called the categorical variable scale, is defined as a scale used for labeling variables into distinct classifications and doesn’t involve a quantitative value or order. This scale is the simplest of the four variable measurement scales. Calculations done on these variables will be futile as there is no numerical value of the options.

    There are cases where this scale is used for the purpose of classification – the numbers associated with variables of this scale are only tags for categorization or division. Calculations done on these numbers will be futile as they have no quantitative significance.

    For a question such as:

    Where do you live? 1- Suburbs 2- City 3- Town

    Nominal scale is often used in research surveys and questionnaires where only variable labels hold significance.

    For instance, a customer survey asking “Which brand of smartphones do you prefer?” Options : “Apple”- 1 , “Samsung”-2, “OnePlus”-3.

    In this survey question, only the names of the brands are significant for the researcher conducting consumer research or netnography. There is no need for any specific order for these brands. However, while capturing nominal data, researchers conduct analysis based on the associated labels.

    In the above example, when a survey respondent selects Apple as their preferred brand, the data entered and associated will be “1”. This helped in quantifying and answering the final question – How many respondents selected Apple, how many selected Samsung, and how many went for OnePlus – and which one is the highest.

    This is the fundamental of quantitative research, and nominal scale is the most fundamental research scale.

    Nominal Scale Data and Analysis

    There are two primary ways in which nominal scale data can be collected:

    By asking an open-ended question, the answers of which can be coded to a respective number of label decided by the researcher.

    The other alternative to collect nominal data is to include a multiple choice question in which the answers will be labeled.

    In both cases, the analysis of gathered data will happen using percentages or mode,i.e., the most common answer received for the question. It is possible for a single question to have more than one mode as it is possible for two common favorites can exist in a target population.

    Nominal Scale Examples


    Political preferences

    Place of residence

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