Certain statistical tools can only be used for certain types of variables (see below). There are four types of variables:
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Nominal (or Categorial) Variables
A nominal (sometimes called a categorical variable) is one that has two or more categories, but there is no agreed way to order these from highest to lowest. A nominal variable (as in "noun") cannot be counted. For example, gender is a nominal variable having two categories (male and female) and there is no intrinsic ordering to the categories. You can assign a numerical value (e.g "Male" = 1, "Female" = 2) but you cannot rank the data from highest to lowest. Similarly, hair color is also a nominal variable having a number of categories (blonde, brown, brunette, red, etc.). If the variable has a clear way to be ordered/sorted from highest to lowest, then that variable would be an ordinal variable, as described below.
e.g. gender (M/F), color (yellow, red, blue, etc), compass orientation (North, South, East, West), animals (dogs, cats, birds, etc), marital status (married/single/divorced/widow)
Ordinal Variables
Just like a categorical variable, an "ordinal" variable also has two or more categories BUT these categories can be "ordered" from high to low. You can therefore assign a value (e.g: 1 thru 5) to those categories and sort them. HOWEVER, these categories are NOT equally spaced. For example, the difference between "rich" and "middle class" might be greater in $ amount than between "middle-class" and "poor". If the categories are equally spaced, then the variable is an interval variable.
e.g. economic status (rich, middle-class, poor), IQ (high, medium, low), education (college graduate, some college, high school, elementary school), ratings of perception (pleasure, pain, etc), speed (fast / slow), school grades (A thru F), cost of living (expensive, moderate, low), air quality (good, bad)
Interval Variables
Just like an ordinal variable, an interval variable also has two or more categories which can also be ordered from high to low, BUT the intervals between the values of the interval variable are equally spaced. For example, suppose you have a variable such as annual income that is measured in dollars, and we have three people who make $10,000, $15,000 and $20,000. The second person makes $5,000 more than the first person and $5,000 less than the third person, and the size of these intervals is the same. If there were two other people who make $90,000 and $95,000, the size of that interval between these two people is also the same ($5,000). Also, an interval variable does not really have a true zero: a value of "zero" just means "no value": an income of "zero dollars" just means "no income'. A temperature of 0 kelvins means "no temperature measurable". An interval value with a true and attainable value of zero is a ratio variable.
e.g. annual income in $, temperatures, time of day, elevation
Ratio Variables
Just like an interval variable, a ratio variable can be sorted from high to low, and the intervals are equally spaced, BUT ratio variable have a real and attainable value of zero.
e.g. weight, height, speed in km/h, age
Why does the type of variable matter?
Statistical computations and analyses assume that the variables have a specific levels of measurement. For example, it would not make sense to compute an average hair color. An average of a categorical variable does not make much sense because there is no intrinsic ordering of the levels of the categories. Moreover, if you tried to compute the average of educational experience as defined in the ordinal section above, you would also obtain a nonsensical result. Because the spacing between the four levels of educational experience is very uneven, the meaning of this average would be very questionable. In short, an average requires a variable to be interval. Sometimes you have variables that are "in between" ordinal and interval, for example, a five-point likert scale with values "strongly agree", "agree", "neutral", "disagree" and "strongly disagree". If we cannot be sure that the intervals between each of these five values are the same, then we would not be able to say that this is an interval variable, but we would say that it is an ordinal variable. However, in order to be able to use statistics that assume the variable is interval, we will assume that the intervals are equally spaced.
A nominal (sometimes called a categorical variable) is one that has two or more categories, but there is no agreed way to order these from highest to lowest. A nominal variable (as in "noun") cannot be counted. For example, gender is a nominal variable having two categories (male and female) and there is no intrinsic ordering to the categories. You can assign a numerical value (e.g "Male" = 1, "Female" = 2) but you cannot rank the data from highest to lowest. Similarly, hair color is also a nominal variable having a number of categories (blonde, brown, brunette, red, etc.). If the variable has a clear way to be ordered/sorted from highest to lowest, then that variable would be an ordinal variable, as described below.
e.g. gender (M/F), color (yellow, red, blue, etc), compass orientation (North, South, East, West), animals (dogs, cats, birds, etc), marital status (married/single/divorced/widow)
Ordinal Variables
Just like a categorical variable, an "ordinal" variable also has two or more categories BUT these categories can be "ordered" from high to low. You can therefore assign a value (e.g: 1 thru 5) to those categories and sort them. HOWEVER, these categories are NOT equally spaced. For example, the difference between "rich" and "middle class" might be greater in $ amount than between "middle-class" and "poor". If the categories are equally spaced, then the variable is an interval variable.
e.g. economic status (rich, middle-class, poor), IQ (high, medium, low), education (college graduate, some college, high school, elementary school), ratings of perception (pleasure, pain, etc), speed (fast / slow), school grades (A thru F), cost of living (expensive, moderate, low), air quality (good, bad)
Interval Variables
Just like an ordinal variable, an interval variable also has two or more categories which can also be ordered from high to low, BUT the intervals between the values of the interval variable are equally spaced. For example, suppose you have a variable such as annual income that is measured in dollars, and we have three people who make $10,000, $15,000 and $20,000. The second person makes $5,000 more than the first person and $5,000 less than the third person, and the size of these intervals is the same. If there were two other people who make $90,000 and $95,000, the size of that interval between these two people is also the same ($5,000). Also, an interval variable does not really have a true zero: a value of "zero" just means "no value": an income of "zero dollars" just means "no income'. A temperature of 0 kelvins means "no temperature measurable". An interval value with a true and attainable value of zero is a ratio variable.
e.g. annual income in $, temperatures, time of day, elevation
Ratio Variables
Just like an interval variable, a ratio variable can be sorted from high to low, and the intervals are equally spaced, BUT ratio variable have a real and attainable value of zero.
e.g. weight, height, speed in km/h, age
Why does the type of variable matter?
Statistical computations and analyses assume that the variables have a specific levels of measurement. For example, it would not make sense to compute an average hair color. An average of a categorical variable does not make much sense because there is no intrinsic ordering of the levels of the categories. Moreover, if you tried to compute the average of educational experience as defined in the ordinal section above, you would also obtain a nonsensical result. Because the spacing between the four levels of educational experience is very uneven, the meaning of this average would be very questionable. In short, an average requires a variable to be interval. Sometimes you have variables that are "in between" ordinal and interval, for example, a five-point likert scale with values "strongly agree", "agree", "neutral", "disagree" and "strongly disagree". If we cannot be sure that the intervals between each of these five values are the same, then we would not be able to say that this is an interval variable, but we would say that it is an ordinal variable. However, in order to be able to use statistics that assume the variable is interval, we will assume that the intervals are equally spaced.
