So you have come up with a research question and now you must chose a method by which your responses will be obtained. For example, a question like ‘Are you a Trekky?’ leads to a simple yes/no answer. So, are you? No need to fess up. I understand. Don’t know what I am talking about? See the trailer for my favorite of the Star Trek movies: The Wrath of Khan Trailer.
What if you were to ask, ‘How much of a Trekky are you?’. You are no longer able to use a simple two-category response but one that uses a continuous scale.
An important distinction to remember when dealing with responses in research is that in general some will be categorical, such as favorite TV series, race, or marital status, and others continuous variables like blood pressure, cholesterol levels, or how much you enjoy Star Trek shows on a scale of 1 to 10 recorded on a 100 mm line. For those of you who would score high here listen to Santana – You are my kind as a reward.
This brings us to the important concept of the level of measurement. If you are working with named categories – race for example – then you have a nominal variable. Categories that have an order to them – education level for example – are ordinal variables. What if the interval between your responses is fixed and known? Then you have an interval variable – temperature in Celcius or Fahrenheit is a good example. However, is zero degrees Celcius the same as zero degrees Fahrenheit? No. The latter is much colder! Now what if you are working in Kelvin which has a meaningful zero point? Then it is a ratio variable.
Ok, so why the big deal? The important difference is between nominal/ ordinal data and interval/ ratio data. The latter two can be used in what is termed: “parametric statistics” that gives us measures of center (mean) and spread (standard deviation). We have already touched on this in previous posts. See here: Great Expectations. It makes no sense to talk about the average sex of a sample students in your study. These data must be considered as frequencies in separate categories. We previously talked about this a little here: Ogive and this type of data leads to “non-parametric” analysis.
Enough already! I’ll let you get back to streaming Star Trek re-runs…
Next time lets talk a little about parametric statistics and how thy came to be. I’ll leave you with this quote as a teaser from one of the greatest statisticians to ever walk the earth – Ronald Fisher: “The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.”