Types of Data & Measurement Scales: Nominal, Ordinal, Interval and Ratio

http://www.mymarketresearchmethods.com/types-of-data-nominal-ordinal-interval-ratio/ 19/9/15

There are four measurement scales (or types of data): nominal, ordinal, interval and ratio. These are simply ways to categorize different types of variables. This topic is usually discussed in the context of academic teaching and less often in the real world. If you are brushing up on this concept for a statistics test, thank a psychologist researcher namedStanley Stevensfor coming up with these terms. These four measurement scales (nominal, ordinal, interval, and ratio) are best understood with example, as youll see below.

NominalLets start with the easiest one to understand. Nominal scales are used for labeling variables, without anyquantitativevalue. Nominal scales could simply be called labels. Here are some examples, below. Notice that all of these scales are mutually exclusive (no overlap) and none of them have any numerical significance. A good way to remember all of this is that nominal sounds a lot like name and nominal scales are kind of like names or labels.

Examples of Nominal Scales

Note: a sub-type of nominal scale with only two categories (e.g. male/female) is called dichotomous. If you are a student, you can use that to impress your teacher.

Continue reading about types of data and measurement scales: nominal, ordinal, interval, and ratio

OrdinalWith ordinal scales, it is the order of the values is whats important and significant, but the differences between each one is not really known. Take a look at the example below. In each case, we know that a #4 is better than a #3 or #2, but we dont knowand cannot quantifyhowmuchbetter it is. For example, is the difference between OK and Unhappy the same as the difference between Very Happy and Happy? We cant say.

Ordinal scales are typically measures of non-numeric concepts like satisfaction, happiness, discomfort, etc.

Ordinal is easy to remember because is sounds like order and thats the key to remember with ordinal scalesit is theorderthat matters, but thats all you really get from these.

Advanced note: The best way to determinecentral tendencyon a set of ordinal data is to use the mode or median; the mean cannot be defined from an ordinal set.

Example of Ordinal Scales

IntervalInterval scales are numeric scales in which we know not only the order, but also the exact differences between the values. The classic example of an interval scale isCelsiustemperature because the difference between each value is the same. For example, the difference between 60 and 50 degrees is a measurable 10 degrees, as is the difference between 80 and 70 degrees. Time is another good example of an interval scale in which theincrementsare known, consistent, and measurable.

Interval scales are nice because the realm of statistical analysis on these data sets opens up. For example,central tendencycan be measured by mode, median, or mean; standard deviation can also be calculated.

Like the others, you can remember the key points of an interval scale pretty easily. Interval itself means space in between, which is the important thing to rememberinterval scales not only tell us about order, but also about the value between each item.

Heres the problem with interval scales: they dont have a true zero. For example, there is no such thing as no temperature. Without a true zero, it is impossible to compute ratios. With interval data, we can add and subtract, but cannot multiply or divide. Confused? Ok, consider this: 10 degrees + 10 degrees = 20 degrees. No problem there. 20 degrees is not twice as hot as 10 degrees, however, because there is no such thing as no temperature when it comes to the Celsius scale. I hope that makes sense. Bottom line, interval scales are great, but we cannot calculate ratios, which brings us to our last measurement scale

Example of Interval Scale

RatioRatio scales are the ultimatenirvanawhen it comes to measurement scales because they tell us about the order, they tell us the exact value between units, AND they also have an absolute zerowhich allows for a wide range of bothdescriptive and inferential statisticsto be applied. At the risk of repeating myself, everything above about interval data applies to ratio scales + ratio scales have a clear definition of zero. Good examples of ratio variables include height and weight.

Ratio scales provide a wealth of possibilities when it comes to statistical analysis. These variables can be meaningfully added, subtracted, multiplied, divided (ratios). Central tendencycan be measured by mode, median, or mean; measures of dispersion, such as standard deviation and coefficient of variation can also be calculated from ratio scales.

This Device Provides Two Examples of Ratio Scales (height and weight)

SummaryIn summary,nominalvariables are used to name, or label a series of values. Ordinalscales provide good information about theorderof choices, such as in a customer satisfaction survey. Intervalscales give us the order of values + the ability to quantifythe difference between each one. Finally,Ratioscales give us the ultimateorder, interval values, plus theability to calculate ratiossince a true zero can be defined.

summary of data types and scale measures

Thats it! I hope this explanation is clear and that you know understand the four types of data measurement scales: nominal, ordinal, interval, and ratio!

Levels of measurementhttp://psychology.ucdavis.edu/faculty_sites/sommerb/sommerdemo/scaling/levels.htm 19/9/15What a scale actually means and what we can do with it depends on what its numbers represent. Numbers can be grouped into 4 types or levels: nominal, ordinal, interval, and ratio. Nominal is the most simple, and ratio the most sophisticated. Each level possesses the characteristics of the preceding level, plus an additional quality.

Nominal

Nominal is hardly measurement. It refers to quality more than quantity. A nominal level of measurement is simply a matter of distinguishing by name, e.g., 1 = male, 2 = female. Even though we are using the numbers 1 and 2, they do not denote quantity. The binary category of 0 and 1 used for computers is a nominal level of measurement. They are categories or classifications. Nominal measurement is like using categorical levels of variables, described in theDoing Scientific Researchsection of the Introduction module.

Examples:

MEAL PREFERENCE: Breakfast, Lunch, Dinner

RELIGIOUS PREFERENCE: 1 = Buddhist, 2 = Muslim, 3 = Christian, 4 = Jewish, 5 = Other

POLITICAL ORIENTATION: Republican, Democratic, Libertarian, Green

Nominal time of day- categories; no additional informationOrdinal

Ordinal refers to order in measurement. An ordinal scale indicates direction, in addition to providing nominal information. Low/Medium/High; or Faster/Slower are examples of ordinal levels of measurement. Ranking an experience as a "nine" on a scale of 1 to 10 tells us that it was higher than an experience ranked as a "six." Many psychological scales or inventories are at the ordinal level of measurement.

Examples:

RANK: 1st place, 2nd place, ... last place

LEVEL OF AGREEMENT: No, Maybe, Yes

POLITICAL ORIENTATION: Left, Center, Right

Ordinaltime of day- indicates direction or order of occurrence; spacing between is unevenInterval

Interval scales provide information about order, and also possess equal intervals. From the previous example, if we knew that the distance between 1 and 2 was the same as that between 7 and 8 on our 10-point rating scale, then we would have an interval scale. An example of an interval scale is temperature, either measured on a Fahrenheit or Celsius scale. A degree represents the same underlying amount of heat, regardless of where it occurs on the scale. Measured in Fahrenheit units, the difference between a temperature of 46 and 42 is the same as the difference between 72 and 68. Equal-interval scales of measurement can be devised for opinions and attitudes. Constructing them involves an understanding of mathematical and statistical principles beyond those covered in this course. But it is important to understand the different levels of measurement when using and interpreting scales.

Examples:

TIME OF DAY on a 12-hour clock

POLITICAL ORIENTATION: Score on standardized scale of political orientation

OTHER scales constructed so as to possess equal intervals

Interval time of day- equal intervals; analog (12-hr.) clock, difference between 1 and 2 pm is same as difference between 11 and 12 amRatio

In addition to possessing the qualities of nominal, ordinal, and interval scales, a ratio scale has an absolute zero (a point where none of the quality being measured exists). Using a ratio scale permits comparisons such as being twice as high, or one-half as much. Reaction time (how long it takes to respond to a signal of some sort) uses a ratio scale of measurement -- time. Although an individual's reaction time is always greater than zero, we conceptualize a zero point in time, and can state that a response of 24 milliseconds is twice as fast as a response time of 48 milliseconds.

Examples:

RULER: inches or centimetersYEARS of work experience

INCOME: money earned last yearNUMBER of children

GPA: grade point average

Ratio- 24-hr. time has an absolute 0 (midnight); 14 o'clock is twice as long from midnight as 7 o'clockApplications

The level of measurement for a particular variable is defined by the highest category that it achieves. For example, categorizing someone as extroverted (outgoing) or introverted (shy) is nominal. If we categorize people 1 = shy, 2 = neither shy nor outgoing, 3 = outgoing, then we have an ordinal level of measurement. If we use a standardized measure of shyness (and there are such inventories), we would probably assume the shyness variable meets the standards of an interval level of measurement. As to whether or not we might have a ratio scale of shyness, although we might be able to measure zero shyness, it would be difficult to devise a scale where we would be comfortable talking about someone's being 3 times as shy as someone else.

Measurement at theintervalorratiolevel is desirable because we can use the more powerful statistical procedures available for Means and Standard Deviations. To have this advantage, oftenordinaldata are treated as though they were interval; for example, subjective ratings scales (1 = terrible, 2= poor, 3 = fair, 4 = good, 5 = excellent). The scale probably does not meet the requirement of equal intervals -- we don't know that the difference between 2 (poor) and 3 (fair) is the same as the difference between 4 (good) and 5 (excellent). In order to take advantage of more powerful statistical techniques, researchers often assume that the intervals are equal.Self-test #2

HYPERLINK "http://psychology.ucdavis.edu/faculty_sites/sommerb/sommerdemo/scaling/quiz/q2_level_rec.htm" \t "_self" Self-test #3Enrichment #1(not required):Statistical procedures for each level of measurementOn toconsumer ratings