Levels of Measurement |
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Levels of Measurement
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Levels of measurement, also called scales of measurement, tell you how precisely variables are recorded. In scientific research, a variable is anything that can take on different values across your data set (e.g., height or test scores). There are 4 levels of measurement: Nominal: the data can only be categorized Ordinal: the data can be categorized and ranked Interval: the data can be categorized, ranked, and evenly spaced Ratio: the data can be categorized, ranked, evenly spaced, and has a natural zero.Depending on the level of measurement of the variable, what you can do to analyze your data may be limited. There is a hierarchy in the complexity and precision of the level of measurement, from low (nominal) to high (ratio). Table of contentsNominal, ordinal, interval, and ratio dataWhy are levels of measurement important?Which descriptive statistics can I apply on my data?Quiz: Nominal, ordinal, interval, or ratio?Frequently asked questions about levels of measurement Nominal, ordinal, interval, and ratio dataGoing from lowest to highest, the 4 levels of measurement are cumulative. This means that they each take on the properties of lower levels and add new properties. Nominal level Examples of nominal scales You can categorize your data by labelling them in mutually exclusive groups, but there is no order between the categories. City of birth Gender Ethnicity Car brands Marital status Ordinal level Examples of ordinal scales You can categorize and rank your data in an order, but you cannot say anything about the intervals between the rankings.Although you can rank the top 5 Olympic medallists, this scale does not tell you how close or far apart they are in number of wins. Top 5 Olympic medallists Language ability (e.g., beginner, intermediate, fluent) Likert-type questions (e.g., very dissatisfied to very satisfied) Interval level Examples of interval scales You can categorize, rank, and infer equal intervals between neighboring data points, but there is no true zero point.The difference between any two adjacent temperatures is the same: one degree. But zero degrees is defined differently depending on the scale – it doesn’t mean an absolute absence of temperature. The same is true for test scores and personality inventories. A zero on a test is arbitrary; it does not mean that the test-taker has an absolute lack of the trait being measured. Test scores (e.g., IQ or exams) Personality inventories Temperature in Fahrenheit or Celsius Ratio level Examples of ratio scales You can categorize, rank, and infer equal intervals between neighboring data points, and there is a true zero point.A true zero means there is an absence of the variable of interest. In ratio scales, zero does mean an absolute lack of the variable. For example, in the Kelvin temperature scale, there are no negative degrees of temperature – zero means an absolute lack of thermal energy. Height Age Weight Temperature in Kelvin Why are levels of measurement important?The level at which you measure a variable determines how you can analyze your data. The different levels limit which descriptive statistics you can use to get an overall summary of your data, and which type of inferential statistics you can perform on your data to support or refute your hypothesis. In many cases, your variables can be measured at different levels, so you have to choose the level of measurement you will use before data collection begins. Example of a variable at 2 levels of measurementYou can measure the variable of income at an ordinal or ratio level. Ordinal level: You create brackets of income ranges: $0–$19,999, $20,000–$39,999, and $40,000–$59,999. You ask participants to select the bracket that represents their annual income. The brackets are coded with numbers from 1–3. Ratio level: You collect data on the exact annual incomes of your participants. Participant Income (ordinal level) Income (ratio level) A Bracket 1 $12,550 B Bracket 2 $39,700 C Bracket 3 $40,300At a ratio level, you can see that the difference between A and B’s incomes is far greater than the difference between B and C’s incomes. At an ordinal level, however, you only know the income bracket for each participant, not their exact income. Since you cannot say exactly how much each income differs from the others in your data set, you can only order the income levels and group the participants. What can proofreading do for your paper?Scribbr editors not only correct grammar and spelling mistakes, but also strengthen your writing by making sure your paper is free of vague language, redundant words, and awkward phrasing. 
See editing example Which descriptive statistics can I apply on my data?Descriptive statistics help you get an idea of the “middle” and “spread” of your data through measures of central tendency and variability. When measuring the central tendency or variability of your data set, your level of measurement decides which methods you can use based on the mathematical operations that are appropriate for each level. The methods you can apply are cumulative; at higher levels, you can apply all mathematical operations and measures used at lower levels. Data type Mathematical operations Measures of central tendency Measures of variability Nominal Equality (=, ≠) Mode None Ordinal Equality (=, ≠) Comparison (>, , , |
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