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Levels of Measurement

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Not all data is created equally. Some is quantitative, and some is qualitative. Some is continuous and some is discrete.

Another way to separate data is to look at what is being measured. To do this there are four levels of measurement: nominal, ordinal, interval and ratio. Different levels of measurement call for different statistical techniques. For example, it makes no sense whatsoever to find the mean, and median of a list of Social Security numbers.

Nominal Level of Measurement

The nominal level of measurement is the lowest of the four ways to characterize data. Nominal means "in name only" and that should help to remember what this level is all about. Nominal data deals with names, categories, or labels.

Data at the nominal level is qualitative. Colors of eyes, yes or no responses to a survey, and favorite breakfast cereal all deal with the nominal level of measurement. Even some things with numbers associated with them, such as a number on the back of a football jersey, are nominal since it is used to "name" an individual player on the field.

Data at this level can't be ordered in a meaningful way, and it makes no sense to calculate things such as means and standard deviations.

Ordinal Level of Measurement

The next level is called the ordinal level of measurement. Data at this level can be ordered, but no differences between the data can be taken that are meaningful.

Here you should think of things like a list of the top ten cities to live. The data, here ten cities, are ranked from one to ten, but differences between the cities don't make much sense. There's no way from looking at just the rankings to know how much better life is in city number 1 than city number 2.

Another example of this are letter grades. You can order things so that A is higher than a B, but without any other information, there is no way of knowing how much better an A is from a B.

As with the nominal level, data at the ordinal level should not be used in calculations.

Interval Level of Measurement

The interval level of measurement deals with data that can be ordered, and in which differences between the data does make sense. Data at this level does not have a starting point.

The Fahrenheit and Celsius scales of temperatures are both examples of data at the interval level of measurement. You can talk about 30 degrees being 60 degrees less than 90 degrees, so differences do make sense. However 0 degrees (in both scales) cold as it may be does not represent the total absence of temperature.

Data at the interval level can be used in calculations. However, data at this level does lack one type of comparison. Even though 3 x 30 = 90, it is not correct to say that 90 degrees Celsius is three times as hot as 30 degrees Celsius.

Ratio Level of Measurement

The fourth and highest level of measurement is the ratio level. Data at the ratio level possess all of the features of the interval level, in addition to a zero value. Due to the presence of a zero, it now makes sense to compare the ratios of measurements. Phrases such as "four times" and "twice" are meaningful at the ratio level.

Distances, in any system of measurement give us data at the ratio level. A measurement such as 0 feet does make sense, as it represents no length. Furthermore 2 feet is twice as long as 1 foot. So ratios can be formed between the data.

At the ratio level of measurement, not only can sums and differences be calculated, but also ratios. One measurement can be divided by any nonzero measurement, and a meaningful number will result.

Think Before You Calculate

Given a list of Social Security numbers, it's possible to do all sorts of calculations with them, but none of these calculations give anything meaningful. What's one Social Security number divided by another one? A complete waste of your time, since Social Security numbers are at the nominal level of measurement.

When you are given some data, think before you calculate. The level of measurement you're working with will determine what it makes sense to do.

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