How Should We Index Fear?

Because people are aware of being afraid, a simple and valid means of measuring fear is to ask them how they are feeling. It is indexed in the English language by a family of terms that range from worried to terrified. Synonyms that lie near the center of the intensity continuum include scared, afraid, and frightened (Ortony, Clore, & Collins, 1988). For example, using a response scale where 0 = None of this feeling and 4 = A great deal of this feeling, how are frightened are you about Covid-19? The average, or mean value across persons provides an estimate of how the public at large is feeling (assuming that the sample of respondents is representative).

Interpreting the mean alone can be misleading because it represents only one aspect of the distribution of scores. Imagine that we survey 100 people and find that 20 of them give an answer of 0 = None of this feeling, 20 give an answer of 2, 20 of 2, 20 of 3, and 20 of 4 = A lot of this feeling. Some people are very frightened, others not at all, and most are in the middle. Averaging these scores gives a mean of 2. Now imagine another scenario in which we survey 100 people and equal numbers of them say that their fear is represented by the value of 1, 2, or 3. The mean is 2 again, but there is no one who is very frightened and no one who is not at all scared. Instead, people are reporting a pretty uniform reaction to the perceived threat.

The effect size index d is a means of combining information about the mean and the variation around it. In this application, the formula is simple: M/SD (Ellis, 2010). To the extent that the threatening event produces a more uniform effect on respondents, the SD is smaller and the corresponding d value is larger. The reverse is also true: Less uniformity yields a larger SD and a smaller d. We have made statistical adjustments to d to correct for the effects of measurement error. The resulting coefficient is known as Δ (i.e., delta). All of the coefficients displayed in the figure are Δ values.