Measurement NOIR

This is the fourth and final posts discussing the common measurement types used within social sciences. An easy acronym to help you remember the 4 measurement types is:

NOIR (No-are)

• Nominal
• Ordinal
• Interval
• Ratio

Today’s post will discuss ratio measurements, what they are, how and when to use them. Identifying your data’s measurement type is an important step when deciding what type of statistical analyses can be done.

Speaking of NOIR, check out this Jazz Noir playlist on Spotify.

Ratio Measurements

Ratio measurements are the crème de la crème of measurement types. They maintain all the properties of the previous measurement types: categories, orders, known spacing and add a true zero point. The addition of true zero point is important because it allows statements such as “twice as much” or “complete absence of” to be meaningful. The best example of a ratio measurement is something we all want more of: Money.

It might seem weird why such a stink is made about the presence of a true zero, and in most practical instances you can ignore it, but scientific language needs to be precise in the language it uses. Looking back at the example used in the interval measurement post, whether the average highs were twice as hot as the average lows depended completely on which scale was used, Fahrenheit or Celsius. If temperature was measured on a ratio scale, Kelvins, instead of an interval scale then these claims could be made. Imagine walking around saying it’s 292 Kelvins outside, that would be weird.

When we talk about money (a ratio measurement), dependence on which scale is used doesn’t lead to this confusion. Imagine you are deciding between two computers, one costs $500 American dollars and the other costs $1000 American dollars. It’s valid to say one computer is twice as expensive as the other. Now suppose you live in Canada and the exchange rate is $1.25 Canadian dollars per $1.00 American dollar. Those same computers now cost $625 and $1250 Canadian dollars. The ratio between the cost, whether in American or Canadian dollars, remains the same.

As a final note, the claim of having $0.00 dollars means you have no money. The previous statement means something very specific, namely a lack of any money. This does not mean, however, values less than zero are not allowed, this depends on the measurement. Having -$300 is a valid ratio measurement when talking about money. It doesn’t make sense to talk about -4 students when considering people in a class (another ratio measurement). The zero value anchors the measurement to a tangible concept but does not dictate allowable values.

Analysis

Addition, subtraction, multiplication and division are all valid mathematical operations for ratio measurements. Due to this, all types of analysis can be done with ratio measurements.

A precaution that is necessary when dealing with ratio measurements is to not accidentally convert it into an interval measurement. This is achieved by moving the true zero point to some other location. Consider the relationship between the Celsius and Kelvin temperature scales.

^oC = K - 273.15

The Kelvin temperature scale is a ratio measurement since zero represents the absence of temperature. The Celsius scale is an interval measurement since the zero point only represents the freezing point, not a lack of temperature. The only difference between the two temperature scales is a relative shift, specifically 273.15. Conversion from ratio to interval measurements can occur when adding or subtracting but not when multiplying or dividing.

Review

Properties of ratio measurements include:

1. Defined Order
   • Measurements can be classified as bigger/smaller, better/worse, later/earlier, etc. than other measurements and ordered accordingly.

2. Known Spacing

   • The spacing between the orders is defined and known.

3. True Zero

4. A true zero point exists which indicates the absence or lack of the measurement.

5. Yes - Multiplication/Division ; Yes - Addition/Subtraction

   • Addition and subtraction can be used freely as well as multiplication and division. When using addition / subtraction make sure the zero point doesn’t get shifted, doing so converts a ratio measurement into an interval measurement (c.f. Kelvin vs Celsius)

6. Central Tendencies

   • As all operations are allowed, the use of any central tendency measurement is allowed: mean, geometric mean, harmonic mean, median or mode.

GoFactr

Make sure to use GoFactr.com for all your research statistical needs. The online statistics program that computes descriptive statistics, ANOVAs, T-Tests, Linear and Logistic regression and Factor Analysis. No software to download means it runs conveniently from your tablet, chromebook, smartphone, laptop or desktop.

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Acknowledgements

Photo by Nattanan Kanchanaprat