Monthly Archives: April 2019

Personality and Gender

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The so-called “Big Five” personality traits are often misunderstood. They all have catchy names, expressed by the acronym CANOE (or OCEAN), but in fact all they are is a summary of answers to certain kinds of personality questions:

  • Conscientiousness: I pay attention to details; I follow a schedule; …
  • Agreeableness: I am interested in people; I feel the emotions of others; …
  • Neuroticism: I get upset easily; I worry about things; …
  • Openness to experience: I am full of ideas; I am interested in abstractions; …
  • Extraversion: I am the life of the party; I start conversations; … (this last one is also measured by the MBTI test)

These tests work in multiple cultures. In this article, I am using data from the Dutch version of the test, the “Vijf PersoonlijkheidsFactoren Test” developed by Elshout and Akkerman. Specifically, I am using data from 8,954 psychology freshmen at the University of Amsterdam during 1982–2007 (Smits, I.A.M., Dolan, C.V., Vorst, H.C., Wicherts, J.M. and Timmerman, M.E., 2013. Data from ‘Cohort Differences in Big Five Personality Factors Over a Period of 25 Years’. Journal of Open Psychology Data, 1(1), p.e2). In my analysis, I have compensated for missing data and for the fact that the sample was 69% female.

The Dutch test consists of 70 items, in 5 groups of 14. The following tree diagram (click to zoom) is the result of UPGMA hierarchical clustering on pairwise correlations between all 70 items. It can be seen that they naturally cluster into 5 groups corresponding almost perfectly to the “Big Five” personality traits – the exception being item A11, which fits extraversion slightly better (r = 0.420) than its own cluster of agreeableness (r = 0.406). This lends support to the idea that the test is measuring five independent things, and that these five things are real.

On tests like this, women consistently score, on average, a little higher than men in conscientiousness, agreeableness, neuroticism, and extraversion (and in this dataset, on average, a little lower in openness to experience). Mean values for conscientiousness in this dataset (on a scale of 14 to 98) were 60.3 for women and 56.1 for men (a difference of 4.2). For agreeableness, they were 70.6 for women and 67.6 for men (a difference of 3.0). There are also small age effects for conscientiousness, agreeableness, and openness to experience (over the 18–25 age range), which I have ignored.

The chart below (click to zoom) shows distributions of conscientiousness and agreeableness among men and women, and the relative frequency of different score ranges (compensating for the fact that the sample was 69% female). Thus, based on this data, a random sample of people with both scores in the range 81 to 90 would be 74% female. With both scores in the range 41 to 50, the sample would be 72% male. This reflects a simple mathematical truth – small differences in group means can produce substantial differences at the tails of the distribution.

Revising the Metric System

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Relationship between the new SI units (image produced using the igraph package of R)

On May 20, a major redefinition of SI (metric) units comes into force. In particular, the second, metre, ampere, mole, kilogram, kelvin, and candela will be defined as follows:

The second (unit of time)

As it is now, the second will be defined using ultra-precise caesium clocks. Specific microwave radiation from caesium atoms is defined to have a frequency of exactly 9.192 631 770 GHz. That is, counting 9,192,631,770 waves will take exactly one second.

The metre (unit of length)

As it is now, the metre will be defined using the speed of light, which is defined to be exactly 299,792,458 metres per second. That is, the metre is the distance travelled by light in one 299,792,458th of a second (where the second is defined as above).

The ampere (unit of electric current)

The definition of the ampere (amp) has been greatly simplified, taking account of the connection between electricity and electrons. The ampere is a coulomb of electric charge flowing past a given point per second, and the charge on a single electron is now defined to be 1.602 176 634 × 10−19 coulombs. Thus an ampere is about 6,241,509,074 billion electrons flowing past a given point in a second.

As a consequence of this new definition, two important natural constants which used to have defined values (the permeability of free space and the permittivity of free space) now have experimentally determined ones. This will require rewriting pretty much every physics and electrical engineering textbook.

The mole (unit of amount of substance)

The mole represents Avogadro’s number of atoms, molecules, or other particles. Previously, Avogadro’s number was defined to be the number of carbon atoms in 12 grams of pure carbon-12. It is now defined to be exactly 6.022 140 76 × 1023.

The kilogram (unit of mass)

Until 2019, the kilogram was defined by the mass of a specific metal cylinder held in Paris. This has been felt to be unsatisfactory for many years. The current definition uses the fact that the energy of a light photon (in joules) is its frequency times Planck’s constant h, which is defined to be exactly 6.626 070 15 × 10−34.

In practice, a Kibble balance will be used to measure weights by balancing them against an electrically produced force. Units derived from the kilogram include:

  • The newton (unit of force): the force needed to accelerate 1 kilogram at a rate of 1 metre per second squared
  • The pascal (unit of pressure): 1 newton of force per square metre
  • The joule (unit of energy): the energy used in applying a force of 1 newton over a distance of 1 metre
  • The watt (unit of power): 1 joule of energy per second
  • The volt (unit of electric potential): the amount of electric potential across a resistance producing 1 watt of heat per ampere of current
  • The ohm (unit of electrical resistance): the resistance which produces 1 ampere of current when 1 volt of electric potential is applied

See also what NIST has to say about the kilogram.

The kelvin (unit of temperature)

Temperature in degrees Celsius was originally measured on a scale with 0 °C being the freezing point of water and 100 °C the boiling point (at standard pressure). The lowest possible temperature turned out to be absolute zero, −273.15 °C. In 1954, the two fixed points on the scale were changed to −273.15 °C (0 kelvins) and the triple point of water, 0.01 °C (273.16 kelvins).

This definition proved unhelpful for calibrating thermometers intended for very high temperatures, and the current definition uses the fact that the average translational kinetic energy (in joules) of a moving atom of a monoatomic ideal gas is (3/2) k T, where T is the temperature of the gas in kelvins, and the Boltzmann constant k is defined to be exactly 1.380 649 × 10−23.

The candela (unit of luminous intensity in a given direction)

The definition of the candela remains what it has been, except that it is influenced by the change in definition of the kilogram (and hence the watt). A light source that emits monochromatic yellowish-green light at a frequency of 540 THz (roughly 555 nm wavelength) is taken to emit 683 lumens per watt, and a light source that uniformly radiates 1 candela in all directions has a total luminous flux of 4π lumens (the constant 683 reflects the human ability to perceive light). The lux is a lumen per square metre.

The dream

When the metric system was first introduced, the metre was defined in terms of the world (1/10,000,000 of the distance between the Equator and the North Pole, measured via Paris). Today, the metric system carries that philosophy to its ultimate conclusion, with all units except the candela defined in terms of the universe. Five of the units are defined in terms of fundamental physical constants: the speed of light (first measured by Rømer in 1676), the charge on the electron (first measured directly by Robert A. Millikan in 1909), the Avogadro constant (measured several ways by Jean Perrin around 1910), and the Planck and Boltzmann constants (first defined by Max Planck around 1900).

The redefined metric system is a little difficult to grasp without understanding modern physics, but fortunately most of us will just keep on using exactly the same measurement instruments as we have done for years.