bulletLevels of Measurementbullet

    The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable.  Though the concept of levels has its problems (see Velleman and Wilkinson, 1993), it is a good way to begin thinking about the data. Traditional texts say that levels of measurement include nominal, ordinal, interval and continuous (or ratio). Traditional definitions of levels fall into two categories of levels:

    bulletCategory 1: Categorical Levels

    Nominal - A set of categories or names that defines groups within a population or a sample. Examples are "liberal and moderate" or "male and female" or "Black, White, Hispanic and Asian." (Nominal = names.)

    Ordinal - Again this is a set of categories, but these categories can be ranked in a meaningful order. An example is "Strongly Disagree, Disagree Somewhat, Agree Somewhat and Strongly Agree." Though ordinal scales can be ranked or ordered, the distance between points varies. We do not know, for instance, what the distance between "Strongly Agree" and "Agree Somewhat" is.  Is it the same distance as between "Strongly Disagree" and "Disagree Somewhat?"
    (Ordinal = ordered)

    With nominal and ordinal measures, the mode can be a helpful measure of central tendency.

    bulletCategory 2: Quantitative Level Variables

    Interval - These are variables that can be rank ordered AND we can measure the distance between values in a meaningful way, such as in years, inches and feet, or quantities.  We find the same distance between each possible value.
    also known as:
    Discrete (interval) - An interval or numeric scale having a small number of possible values. Examples are number of children, age, and test scores. (Discrete = A few)

    Ratio - These variables have a distinct and meaningful zero-point. One example is weight, where zero has a meaningful interpretation and it is meaningful to say A weighs twice as much as B.
    also known as:
    Continuous (ratio) - An interval or numeric scale having a large or indeterminate possible number of possible observations. Examples are temperature or distance measurements. (Continuous = A lot)

    In reality we do not always conform neatly to this two-category-two-type theory of levels.  When we place names and numbers on phenomenon (what we call measurement) we often choose the level of measurement we want to use to define a particular event, feeling or phenomenon. When we measure sex (male or female), for example, we often use a categorical-nominal scale: Male - Female.  In order to take advantage of more powerful statistical methods that can not be used at the categorical-nominal level, however, we assign a numeric value to these categories.  The same phenomenon (sex) may now be called "femaleness," assigning "0" to Male and "1" to Female.

    Statistics is mostly the manipulation of numbers.  Names are not numbers.  We can't do as much statistically with a set of names (i.e., male and female) as we can with a set of numbers (i.e., 0 and 1). The more we can use numbers to define what we are measuring (enumerate), the more we can manipulate the numbers with powerful statistical formulas. So, the idea of "levels of measurement" comes from an understanding in the statistical community of many who have come to see names as a "lower," less powerful level of measurement than numbers.

    The level of measurement helps us decide how to interpret the data from that variable.  Knowing the level of measurement helps us to decide what statistical analysis is appropriate.

    Citations:

    Veleman, Paul F., and Leland Wilkinson.   1993.  "Nominal, Ordinal, Interval, and Ratio Typologies Are Misleading,"  The American Statistician, Vol. 47, No. 1 (February).

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