# Bell-Shaped Distribution of Personality Traits

**DOI:**https://doi.org/10.1007/978-3-319-28099-8_1047-1

## Synonyms

## Definition

A symmetrical, unimodal distribution of individual differences along a personality trait dimension.

## Introduction

The distribution of most normal personality traits tends to have a more or less symmetrical, bell-shaped form. Such a distribution has a single mode, its mean is very close to its median, the majority of individuals congregate in the vicinity of the mean and median, and relatively few individuals fall in the two tails. Bell-shaped distributions are sometimes incorrectly equated to the normal (Gaussian) distribution, but that distribution is only one form that bell-shaped distributions can take. For instance, non-Gaussian bell-shaped distributions include the logistic and Student’s *t* distributions, and they may differ from the normal curve in being narrower with heavier tails (leptokurtic) or flatter with fewer extreme outliers (platykurtic).

The processes that give rise to bell-shaped distributions are consistent with what is known about the origins and underpinnings of personality traits. Bell-shaped distributions tend to result from the summation of many independent influences of small effect, just as traits represent the combination of numerous small genetic and environmental influences. Thus, the fact that most personality traits are distributed in a bell-shaped fashion accords with the causal structure of these traits.

Not all personality trait measures do yield bell-shaped distributions, however, and these variations may be valid or spurious (Micceri 1989). Two variations are especially important: skewed (asymmetrical) distributions and bimodal distributions. Skewness is not uncommon in measures of personality traits and especially those traits that are pathological in nature. Measures of personality disorders, for example, are often positively skewed (i.e., having a relatively long tail of high-scoring individuals), consistent with the distribution of mental disorder symptoms. This form of skewness reflects the fact that most individuals outside clinical settings have few pathological attributes, but people with some pathological features vary widely in how many they display. Skewed distributions in measures of personality traits may therefore validly reflect the underlying nature of the traits in question. However, it is also possible for skewness to reflect a measurement artifact. For example, a trait scale composed of correlated true/false items that consistently have a low-frequency high-scoring response will yield a positively scored distribution, even if the underlying trait is normally distributed.

Bimodal distributions are another departure from the typical bell-shaped distribution of personality traits. Although such double-peaked distributions are sometimes taken as evidence that two underlying latent classes – such as personality types – are admixed in the same sample, they are much more likely to be the outcome of a measurement artifact (Meehl 1992). To generate a valid bimodal distribution, the two underlying component distributions must barely overlap, a rarity in psychological measurement. Indeed, two admixed but overlapping distributions may generate a bell-shaped distribution when combined, as occurs in the distribution of human height, which represents the sum of diverging component distributions of male and female height. Thus, when bell-shaped distributions are observed, they may conceal two (or more) latent personality classes, but when bimodal distributions are found, they are unlikely to do so.

## Conclusions

The fact that personality traits tend to have a bell-shaped distribution is convenient for researchers because parametric statistics such as Pearson correlations and *t*-tests rest on assumptions that variables are distributed normally. Generally personality trait measures oblige. It is also true that most parametric statistics are relatively robust to departures from normality. However, in cases where, for whatever reason, personality trait measures are distributed in markedly non-normal (or non-bell-shaped) ways, researchers should be mindful that the assumptions of default parametric statistics are violated. In this eventuality, researchers may be advised to employ nonparametric (i.e., rank-based) statistics or to transform their measures so that distributions become more normal (e.g., log transforms to reduce positive skew).

## Cross-References

## References

- Meehl, P. E. (1992). Factors and taxa, traits and types, differences of degree and differences in kind.
*Journal of Personality, 60*, 117–174.CrossRefGoogle Scholar - Micceri, M. (1989). The unicorn, the normal curve, and other improbable creatures.
*Psychological Bulletin, 105*, 156–166.CrossRefGoogle Scholar