Overview
Major Types of Variables
The two major types of variables are qualitative and quantitative. The type of variables you collect and analyse have a direct bearing on the type of statistical summaries and analyses you can perform.
-
Qualitative - Qualitative variables have different qualities, characteristics or categories, e.g. hair colour (black, brown, blonde,…), disease (cancer, heart disease,…), gender (male, female), country of birth (New Zealand, Japan,…). Qualitative variables are used to categorise quantitative data into groups or to tally frequencies of categories that can be converted to proportions and percentages.
-
Quantitative - Quantitative variables measure a numerical quantity on each unit. Quantitative variables can be either discrete - can only assume a finite or countable number of values, e.g. marks on a test, birthday, number of people in a lecture, or continuous - the value can assume any value corresponding to the points on a number line, e.g. time (seconds), height (cm), weight (kg), age etc.
Levels of Measurement
When you measure a variable, qualitative and quantitative variables can take on different scales or levels of measurement. Levels of measurement have a direct bearing on the quantitative data analysis techniques you will need to use. We need to understand the language used to describe different scales. The following short video by Nicola Petty provides a great overview.
{% youtube hZxnzfnt5v8 %} https://www.youtube.com/watch?v=hZxnzfnt5v8&ab_channel=DrNic%27sMathsandStats
-
Categorical or Nominal (Qualitative). Categorical variables are group variables or categories if you will. There are no meaningful measurement differences such as rankings or intervals between the different categories. Categorical or nominal variables include binary variables (e.g. yes/no, male/female) and multinomial variables (e.g. religious affiliation, hair colour, ethnicity, suburb).
-
Ordinal (Qualitative). Ordinal data has a rank order by which it can be sorted but the differences between the ranks are not relative or measurable. Therefore, ordinal data is not strictly quantitative. For example, consider the 1st, 2nd and 3rd place in a race. We know who was faster or slower, but we have no idea by how much. We need to look at the race times.
-
Interval (Quantitative): An interval variable is similar to an ordinal variable except that the intervals between the values of the interval scale are equally spaced. Interval variables have an arbitrary zero point and therefore no meaningful ratios. An example is our calendar year. 1000 AD is not half of 2000 AD, and 20 degrees Celsius is not twice as “hot” as 10 degrees Celsius. This is because our calendar and Celsius scale have an arbitrary value for zero. Zero AD and zero degrees Celsius do not imply the presence of zero time or zero heat energy.
-
Ratio (Quantitative): A ratio variable is similar to an interval variable; however there is an absolute zero point and ratios are meaningful. An example is time given in seconds, length in centimeters, or heart beats per minute. A value of 0 implies the absence of a variable. We can also make statements like 30 seconds is twice the time of 15 seconds, 10 cm is half the height of 20 cm, and during exercise a person’s resting heart beat almost doubles. Zero heart rate, call 000!