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Measurement in Statistics

  1. Unit of Measurement vs. Levels of Measurement
  2. Dealing with Errors
  3. Percentages
  4. Index Numbers
Unit of Measurement vs. Levels of Measurement
Two of the most important concepts to understand in statistics is unit of measurement and level of measurement of a variable. A unit of measurement refers to what is being used to measure a variable. Is the variable being measured in terms of time? Miles? A human being? For example, if I am counting chickens, the unit of measurement is a "chicken." If am am counting how long it takes for someone to run around a city block, the unit of measurement becomes "time."

If the unit of measurement can be subdivided, the unit of measurement is continuous. If the unit of measurement can NOT be subdivided, then the variable is discreet. Here are some examples (the text in parentheses are the names of the variable):
  • (hmwktm) How many hours does a student spend working on homework each night
  • (childs) Number of children
  • (wrkdist) How many miles does one commute to work
We used "time" to measure how many hours a student spent on homework so the unit of measurement is time. Since time can be subdivided, the unit of measurement for the variable "hmwktm" is continuous.

The variable "childs" is the tricky variable here. We are measuring this variable in terms of a child, so the unit of measurement is discreet since a human being can not be subdivided. 

Level of Measurement
One of the most important concepts to understand in statistics is the level of measurement of a variable. Variables vary as to their level of measurement and levels of measurement go up in "sophistication." The level of measurement of a variable is very important because it dictates what mathematical calculations can be conducted on a variable. It is vitally important that students are able to quickly identify what level of measurement a variable is.

The most basic level of measurement is nominal while the most sophisticated level of measurement is interval or ratio. Since the level of measurement of a variable dictates what mathematical calculations one can do to a variable, statisticians generally prefer to have the most sophisticated-- interval or ratio. All variables are at least nominal so we usually start there. If we can look at a variable and decide that it can be ranked, then we bump up our level of measurement of our variable to ordinal.
    • Nominal
    • Ordinal
    • Interval
    • Ratio