Normal distribution

A symmetric, bell-shaped probability distribution that describes how many psychological traits are spread across a population.

The normal distribution (or "bell curve") is a symmetric probability distribution defined by a mean and a standard deviation. In a normal distribution, about 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three.

Many psychological traits — and the assessments that measure them — produce score distributions that approximate normality, which is why standardized scores (Z-scores, T-scores) are designed around it. Not every construct is normally distributed, though: depression and anxiety scales administered to the general population are often skewed because most people fall in the "low" range.

Z-score — A standardized score expressing how many standard deviations a raw score is from the mean.
T-score — A standardized score with a mean of 50 and a standard deviation of 10, commonly used in psychological testing.
Norms — Reference distributions of scores from a defined population, used to interpret an individual's score in context.
Percentile rank — The percentage of scores in a reference group that fall at or below a given score.

Normal distribution

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