Examples of Measures

There are only a handful of different types of measures -- Categorical and interval (you may sometimes see categorical variables referred to as factor variables and interval variables referred to as continuous variables). Within categorical, you will find dichotomous (two categories) or polychotomous (three or more categories) and they may be nominal or ordinal in nature.

Categorical Variables (emphasis on categories of responses)

Dichotomous -- e.g., Passed a class

0 - Failed

1 - Passed

Polychotomous (3+ categories) -- nominal and ordinal

Nominal -- e.g., Religious Affiliation (order does not represent numeric value; the assigned numbers merely represent the categories)

0 - Jewish

1 - Hinduism

2 - Muslim

3 - Christian

4 - Buddhist

5 - Other (specified)

Ordinal -- e.g., Self-Rated Health (order/number does convey a meaningful order in the categories, but the "distance" between categories is not necessarily uniform)

0 - Poor

1 - Fair

2 - Good

3 - Very Good

4 - Excellent

Interval or Continuous Variables -- e.g., GPA (many finite values in a range; quantitative uniformity between/across values)

"Gray Area" Variables -- There are some variables where things are a little gray...

1. Likert Scales (e.g., strongly disagree to strongly agree on a 5-pt scale; or very liberal to very conservative on a 10 pt scale (with only the values of 1 and 10 having labels). Are these ordinal variables or interval? Technically, they are ordinal variables, particularly in the first example. As such, you are always justified treating them as categorical/ordinal variables. That said, it is a matter of ongoing debate whether it is acceptable, at least in some instances, to treat these variables as quasi-interval in nature. My own position is that it depends on a few factors:

Is it a primary variable of interest, or merely a control variable? If the former, then you'll likely treat it as ordinal. If the latter, then you may consider treating it as interval, depending on other factors.
Consider your analysis. If you are conducting a bivariate analysis, it may be best to treat such a variable as ordinal if there are 5 or fewer categories. If there are more than 5 categories (e.g,. 7 or 10), then you may be more justified in treating it as interval. This is particularly true if value labels are only provided for the ends of the scale (0 is "low" and 10 is "high"). Alternatively, you may opt to collapse categories and treat it as ordinal. If the latter, consider the distribution of your cases and the consequences of losing some of your variation.
Your sample size. The larger the sample size, the better able you are to retain variables as ordinal, as each subgroup is likely to be adequately represented within the sample. If a frequency distribution shows an empty or lowly “enrolled” category, though, you may consider collapsing categories first, as your results for that category are unlikely to offer much in the way of precision (in your finding). Again, consider the consequences of losing nuance and variation.
The more categories there are in a variable (and assuming a standard set of labels), the more you are justified in treating a variable as interval in nature.

In short, you are ALWAYS justified in treating such variables as ordinal (especially when each value has a label associated with it). The case for treating such a variable as interval depends on a variety of factors. Remember -- the consideration to treat an ordinal variable as interval pertains to scales that are more uniform (e.g., strongly agree to strongly disagree). This is in contrast to other types of ordinal variables (e.g., self-rated health, as shown above), which should be treated as categorical.

2. Categorized Interval/Continuous Variables — Sometimes you will run across variables that are categorized versions of interval variables. A classic example is income. In some cases, researchers may only provide respondents with set categories of income, rather than asking about income directly. In other cases, you may have an interval variable and opt to categorize responses (perhaps meaningful age categories in lieu of actual ages -- where life stage is more important than years of life). In these instances, it is appropriate to treat as categorical. It is sometimes possible to treat as interval, based on the same considerations listed above.

3. Composite Variables — In some cases, you may construct a composite variable from a number of ordinal (categorical) variables. The resulting composite variable (often based on the mean of (standardized) responses), will take on more of the qualities of an interval variable (more nuance in values; less definable categories). In such cases, researchers will treat composite variables as interval variables.

Note: Nominal variables should NEVER be treated as interval.