October 20th, 2010

[Note: Most of the information for this article comes from “The Six Sigma Handbook”[i]]

Why do we measure things? To see how things are, or if change has occurred or to understand something. Measurement is just looking at something and describing it in numbers. The rules (mapping functions) that we use to describe the “thing” in numbers provide us with a model of reality. If this model is correct (valid) we can learn about the real world by studying the model and the numbers that it predicts. Without these measurements systems astronomers could not describe the make up of galaxies billions of light-years away from us.

Every questions we have starts in the real world But to understand the question and come up with the answer we use mapping functions (rules) to describe the real world question using numbers. There are times when we map to a non numeric entities in the real world, Like a question about color but we convert these into numbers like the number of red things in a room. These characteristics (elements) are X’s. The “numbers” are Y’s derived using the mapping function as a transfer function of the elements into numbers.

A good example of this we all can relate to is the fuel tank on your car. It would be nice to know how much fuel is in your tank? That would be a measurement of the amount of fuel in your tank.

Real World – Your fuel tank with some amount of fuel in it.

Mapping function – A float with a sensor on a spindle connected to a fuel gage. The gage marked off in numerical intervals. Plus YOU reading the indicator.

Numbers – The gage needle pointing to a numerical value on the gage (like the 1/8 mark just above Empty (0))

Usage – Time to get gas!

Measurement Scales

Not all data (numbers we collect) are created equal. That does not mean some are better than others is just means that some tells us more information than other. You will find that our numbers fall into one of four scales. In teams that I have worked with I always bring up the discussion of measurement scales because not everyone looks at how they would measure something in the same way. Some may look at the fuel tank about as fuel empty or half full, other may talk in gallons of fuel. With that said we need to understand the scale we are going to measure the real world in. The scale of the data to be collected in the measurement process. .So here are the four measurement scales.

  • Nominal Scale – These are numbers that only indicate the presents or absence of an attribute. All we can do here is count items with or without this attribute.
  • Ordinal Scale – This scale gives us a little bit more information. With this scale we can say if an item has more or less of an attribute With this scale we can rank order items.

  • Interval Scale – This scale is use when we are measure the differences between observations. Interval scale numbers that are equally different represent differences of equal magnitude. The zero vale of an interval scale is arbitrary.

  • Ratio Scales – This scale is like Interval Scale except it has a true zero point. In other words you can have nothing less than zero.

Well there you have my thoughts on Measurement and the importance of your scale of measurement. Next time I am going to discuss the different statistical tool use for different scales of measurement. If, you have questions or comments please feel free to contact me by leaving a comment below, emailing me, calling me, or leaving a comment on my website.

Bersbach Consulting
Peter Bersbach
Six Sigma Master Black Belt

[i] Thomas Pyzdek The Six Sigma Handbook, 2003, McGraw Hill

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