variables discrete continuous quantitative qualitative

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Kinds of variables

In order to do statistics, we need to be able to recognize the type of data we are dealing with, so if you have data already in a package like SPSS/PASW you need to ask yourself: “What kind of data do we have here.” We need to know have the answer to this question as it will determine the methods we employ for data analysis.

There are two broad types of data: qualitative and quantitative.

Qualitative/Categorical variables

If you have a look at a questionnaire, it is very likely there are questions there that are collecting qualitative data, known also as categorical data.

  • Nominal scale of measurement – measurement where the list of outcomes are categories, and importantly, there are no underlying ordering of the categories. Examples: hair color (black, brown, blonde, red, other).

    The categories are black, brown, blonde, red, other. By no underlying ordering, we mean that we could have listed the outcomes in any other order eg. other, red, brown, blonde, black. Examples of other variables measured on the nominal scale are gender (female/male); smoker (yes/no); ethnicity.

Variables measured on the nominal scale are discrete – discrete meaning that the variable takes on a limited number of outcomes eg. gender which is nominal.

Quantitative variables

  • Interval scale – (1) continuous data where the differences(intervals) between the numbers are comparable, but not the ratios.
    The ratios are not comparable as the values of the thing being measured is not independent of the unit of measurement. (2) There is no "true" zero.

    So what the heck does that mean? A commonly used example of an interval scale is temperature. There is no true zero on the temperature scale as a reading of zero degrees does not mean there is no temperature. Take the readings 10oC = 50F and 20oC=68F. The ratio of the 2 temperatures on the Celsius scale (20 divided by 10 = 2) is not the same as on the Fahrenheit scale (68 divided by 50 = 1.36). However, the difference between 20C and 10C (68F and 50F) is the same as 30C and 20C (86F and 68F).

  • Ratio scale – like the interval scale only there is a true zero,and any 2 values of the thing being measured is independent of the unit of measurement. Example: length. A length of 10cm (about 4 inches) is twice as long as a length of 5cm (about 2 inches). Here, a length of 0cm really does mean there is no length, and the ratio of the 2 values in cm (10 divided by 5) is same as that in inches (4 divided by 2).

Interval and ratio are continuous – continuous meaning variables can take on tiniest fractional values (eg, 0.0001). Example: time for some event to happen.

In between qualitative and quantitative

Ordinal scale - qualitative data where there is a natural ordering of the numbers that represent the categories. However, it is not meaningful to look at differences, ratios, or sums of the numbers. Examples:occupational group (1=unskilled, 2 = skilled manual, 3 = professional) – you see that the degree of skill increases.  Customer satisfaction (1= very satisfied, 2= satisfied, 3 = not satisfied) – level of satisfaction decreases from 1 to 3. Note it is not meaningful to say that 3 = not satisfied is three times more unsatisfied than 1=very satisfied.

Data measured on the ordinal scale are a bit like qualitative data in that the possible outcomes are categories just like for nominal data. But, there is a natural ordering of the categories, just as for interval data. As such don’t be surprised to see in an empirical investigation that ordinal data is sometimes treated as categorical, and sometimes treated as interval.

Ordinal data is discrete