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Objective Measurement of Subjective Phenomena

6. Problems in Measuring Constructs

Normality of distributions

Skewness: depart from bell-shaped curve by having longer tail at one end of distribution

Kurtosis: depart from bell-shaped curve by having either heavy or light tails (either many or few responses, respectively, at the high and low ends of scale)

Many analytic options (correlation, regression, factor analysis) require the assumption that item scores are (approximately) normally distributed (McDonald, 1999; Nunnally & Bernstein, 1994).

Normal distribution

  • Bell-shaped
  • Mean and Variance describe distribution well
  • Skewness and kurtosis are minimal

Non-normal distribution

Skewed or kurtotic distributions

  • Skewness: depart from bell-shaped curve by having longer tail at one end of distribution
    • Positive skew – long tail at high end of scale
    • Negative skew – long tail at low end of scale

Example 21

Skewness example:

Self-esteem is often negatively skewed because people tend to have positive self evaluations, so few persons use low end of scale.
  • Kurtosis: depart from bell-shaped curve by having either heavy or light tails (either many or few responses, respectively, at the high and low ends of scale)
    • Leptokurtosis – higher, narrower peak of distribution (relative to bell-shaped curve) and therefore “fatter” tails (or more persons scoring in extreme range of values)
    • Platykurtosis – lower, wider peak of distribution (relative to bell-shaped curve) and therefore “thinner” tails (or fewer persons having extreme scores)

Figure 1

Figure of six graphs with varying distributions as discussed in text.

McDonald, R. P. (1999). Test theory: A unified treatment. Mahwah, NJ: Erlbaum.
Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3rd ed.). New York: McGraw-Hill.