Choice of NHST:  Categorical versus Continuous Variables

    Let me first make a mathematical distinction, the one that was likely made in your statistics class:

Discrete variable - one for which there is a finite number of potential values which the variable can assume between any two points on the scale.
Continuous variable - one which theoretically can assume an infinite number of values between any two points on the scale.

    A categorical variable is a discrete variable. Think of it as a grouping variable. We tend to think of some constructs as being inherently categorical. For example, you are asked to taste a substance and decide whether the dominant taste is sweet, sour, salty, bitter, or umami. It is hard to think of this construct as being continuous. We think of it as qualitative rather than quantitative – that is, we are deciding what type of taste quality dominates, not how much of something it has.

    Now imagine that you are asked to rate how sour this candy tastes, on a nine point scale from 1 (not even a hint of sourness) to 9 (as sour as acetic acid). We may think of the construct as quantitative and continuous. Our measurements may be discrete (we get only integers from 1 to 9, inclusive), but we are comfortable treating them as continuous.

    Whether our variables are categorical or continuous helps determine which NHST is appropriate.  For example, consider the following common NHST procedures, keeping in mind that a normally distributed variable is a continuous variable:

    A variable may be manipulated or measured in a categorical fashion even if we think of the underlying construct as being continuous.  For example, we may think of physical attractiveness as being continuous.  We want to manipulate the physical attractiveness of the defendant in a mock jury trial.   We make three different video tapes of the trial proceedings.  They are identical except with respect to the physical appearance of the defendant.  In one experimental condition the defendant is made up to look unattractive.  For a second condition he is made up to look like an average Joe.  In a second condition he is made up to appear very handsome.  Mock jurors are randomly assigned to these conditions.  We want to determine the relationship between physical attractiveness of the defendant and two dependent variables.  One dependent variable is whether the juror decides the defendant is guilty or not.  The other dependent variable is length of the sentence recommended by the juror (from 0 to 100 years).  The independent variable here would be treated as categorical.  One of the dependent variables would be treated as categorical and the other as continuous (it probably would not be normally distributed, but we shall ignore that for the moment).  Which statistical techniques, from the table above, should be employed to analyze the data?

Sent: Thursday, February 24, 2005 1:37 PM
To: Wuensch, Karl L
Subject: RE: Psyc2210: Methods Section

Professor Wuensch,

    My two constructs are mate selection and how physical attractiveness affects that. When choosing an appropriate bivariate inferential statistic i get confused on just what continuous and cateforical mean, i think that mate selection is continuous and physical attractiveness is categorical, would that be correct?

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Dr. Karl L. Wuensch


 

This page most recently revised on 24. February 2005.