Nominal, ordinal, interval and ratio data: How to Remember the differences

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Quantitative researchers measure variables to answer their research question.
The level of measurement that is used to measure a variable has a significant impact on the type of tests researchers can do with their data and therefore the conclusions they can come to. The higher the level of measurement the more statistical tests that can be run with the data. That is why it is best to use the highest level of measurement possible when collecting information.
In this video nominal, ordinal, interval and ratio levels of data will be described in order from the lowest level to the highest level of measurement. By the end of this video you should be able to identify the level of measurement being used in a study. You will also be familiar with types of tests that can be done with each level.
To remember these levels of measurement in order use the acronym NOIR or noir.
The nominal level of measurement is the lowest level. Variables in a study are placed into mutually exclusive categories. Each category has a criteria that a variable either has or does not have. There is no natural order to these categories.
The categories may be assigned numbers but the numbers have no meaning because they are simply labels. For example, if we categorize people by hair color people with brown hair do not have more or less of this characteristic than those with blonde hair.
Nominal sounds like name so it is easy to remember that at a nominal level you are simply naming categories.
Sometimes researchers refer to nominal data as categorical or qualitative because it is not numerical.

Ordinal data is also considered categorical. The difference between nominal and ordinal data is that the categories have a natural order to them. You can remember that because ordinal sounds like order.
While there is an order, it is also unknown how much distance is between each category.
Values in an ordinal scale simply express an order.
All nominal level tests can be run on ordinal data.
Since there is an order to the categories the numbers assigned to each category can be compared in limited ways beyond nominal level tests. It is possible to say that members of one category have more of something than the members of a lower ranked category. However, you do not know how much more of that thing they have because the difference cannot be measured.
To determine central tendency the categories can be placed in order and a median can now be calculated in addition to the mode.
Since the distance between each category cannot be measured the types of statistical tests that can be used on this data are still quite limited. For example, the mean or average of ordinal data cannot be calculated because the difference between values on the scale is not known.

Interval level data is ordered like ordinal data but the intervals between each value are known and equal. The zero point is arbitrary. Zero simply represents an additional point of measurement.
For example, tests in school are interval level measurements of student knowledge. If you scored a zero on a math test it does not mean you have no knowledge. Yet, the difference between a 79 and 80 on the test is measurable and equal to the difference between an 80 and an 81.
If you know that the word interval means space in between it makes remembering what makes this level of measurement different easy.

Ratio measurement is the highest level possible for data. Like interval data, Ratio data is ordered, with known and measurable intervals between each value. What differentiates it from interval level data is that the zero is absolute. The zero occurs naturally and signifies the absence of the characteristic being measured. Remember that Ratio ends in an o therefore there is a zero.
Typically this level of measurement is only possible with physical measurements like height, weight and length.
Any statistical tests can be used with ratio level data as long as it fits with the study question and design.