Traits

Using Factor Analysis to Describe Personality Differences

Mini Review

  • The lexical hypothesis says the differences between people that matter tend to end up as words in their language.
  • Two researchers reading an English dictionary found about 4,500 words for lasting traits.

How do we scientifically group these 4,500 potential traits into a smaller, manageable number?

Learning Goals

  • Remember:
  • Explain:
    • Explain how factor analysis uses personality scores to reveal underlying traits.
    • Distinguish between a factor and a facet.
    • Compare and contrast the Big Five factors.
  • Apply:
    • Given a list of trait words, decide which Big Five factor each word belongs to and which end of that factor it is on.
    • Given two people with the same score on a Big Five factor, describe how they could still differ.

Grouping Trait Words by the People They Describe

  • In our polls, most of you used words with similar meanings to describe the same person type (parent, teacher, friend, etc.).
  • If two trait words have similar meanings, do they also describe the same people?
    • Is someone described as talkative usually also described as outgoing?
    • Is someone described as organized usually also described as lazy?
  • We can answer this question for any pair of traits by giving people number scores on both, and then calculating the correlation between the two sets of scores.

Correlating Trait Scores

  • Correlation: The degree to which two variables are related, such that when a score on one goes up or down, a score on the other also goes up or down.
  • Positive correlation: When the scores move in the same direction (both go up or down).
    • Ex: As talkative scores go up, outgoing scores also go up.
  • Negative correlation: When the scores move in opposite directions (one goes up and the other goes down).
    • Ex: As talkative scores go up, quiet scores go down.
  • No correlation: When the scores don’t move together at all.
    • Ex: A change in talkative score doesn’t say anything about a change in organized score.

Correlating Trait Scores

This table shows five people’s scores (1 to 5) on four traits.

Person talkative outgoing reserved organized
Jaylon 5 5 1 1
Tara 4 5 2 5
Max 2 1 4 4
Alicia 1 2 5 1
EJ 2 3 5 3
  • Which pairs are correlated and in which direction?

Visualizing Correlations

  • Talkative, outgoing, and reserved are correlated with each other. Organized is not correlated with any of the others, so its three lines are close to flat.
  • Each of those six correlations can be written as a single number.

Summarizing Correlations in a Table

A correlation is always a single number from −1 to +1. The sign tells you the direction (positive or negative) and the size tells you the strength (close to 1 is very strong).

Variable Talkative Outgoing Reserved Organized
Talkative
Outgoing .87
Reserved −.97 −.80
Organized .07 .02 −.05

NOTE: The cells with the dashes would be each variable correlated with itself, so we don’t include those. The empty cells would be the same correlations between the same pairs, so we don’t include those either.

How Big Can Our Table Get?

  • 4 traits make 6 pairs.
  • 10 traits make 45 pairs.
  • 100 traits make 4,950 pairs.
  • The 4,500 trait words from the dictionary study make about 10 million pairs.
  • That’s too big! We need a method that finds patterns across all of those pairs.

Factor Analysis

  • Factor analysis: A statistical method used to find groups of related variables by looking at how strongly they correlate with one another.
  • It takes a massive pile of data and looks for underlying “factors” that explain the patterns.
  • Factor: A broad trait made up of several narrower traits whose scores are correlated across many people.
  • Think of it as an algorithm for sorting items into buckets based on how often they show up at the same time.

A Non-Personality Example

  • Imagine testing 1,000 athletes on 20 different physical challenges: running, jumping, swimming, lifting weights, throwing, etc.
  • If we run a factor analysis on their scores, what clusters might emerge?
    • Factor 1: Sprinting, jumping, agility drills (Factor: Speed)
    • Factor 2: Lifting heavy weights, pushing a sled (Factor: Raw Strength)
    • Factor 3: Long-distance running, swimming (Factor: Endurance)
  • We reduced 20 scores down to 3 core physical factors.
  • Each factor explains the differences in people’s scores on the tasks it includes.

Applying This to Personality

  • Researchers gave huge lists of trait words to thousands of people.
  • They asked participants: “Rate how well this word describes you on a scale from 1 to 5.”
  • They fed all this lexical hypothesis data into computers to run a factor analysis.
  • Regardless of the exact list of words used, the analysis kept spitting out the same five core factors.

The Big Five

  • Big Five: The five broad personality traits that consistently emerge from factor analysis of personality scores.
  • These five traits represent the highest level of organization for personality. Most other traits fall underneath them.

The OCEAN Acronym

To remember the Big Five, just remember the acronym OCEAN:

  • Openness
  • Conscientiousness
  • Extraversion
  • Agreeableness
  • Neuroticism

Here is what factor analysis did with thirty of the real trait words.

Thirty Trait Words Before Factor Analysis

creativeimaginativeintellectualunintellectualuncreativedeepsloppyorganizeddisorganizedefficientpracticalcarelessboldquiettalkativeenergeticwithdrawnshykindwarmsympatheticcooperativecoldrudemoodytemperamentaltouchyjealousunenviousrelaxed

The Same Thirty Words Grouped by Their Correlations

creativeimaginativeintellectualunintellectualuncreativedeepsloppyorganizeddisorganizedefficientpracticalcarelessboldquiettalkativeenergeticwithdrawnshykindwarmsympatheticcooperativecoldrudemoodytemperamentaltouchyjealousunenviousrelaxed

Each Group of Correlated Words Is One Factor

creativeimaginativeintellectualunintellectualuncreativedeepsloppyorganizeddisorganizedefficientpracticalcarelessboldquiettalkativeenergeticwithdrawnshykindwarmsympatheticcooperativecoldrudemoodytemperamentaltouchyjealousunenviousrelaxed

Researchers Named These Five Factors

Openness
Conscientiousness
Extraversion
Agreeableness
Neuroticism
creativeimaginativeintellectualunintellectualuncreativedeepsloppyorganizeddisorganizedefficientpracticalcarelessboldquiettalkativeenergeticwithdrawnshykindwarmsympatheticcooperativecoldrudemoodytemperamentaltouchyjealousunenviousrelaxed

Words inside one circle are correlated with each other, including words with opposite meanings. The thirty words come from the Mini-Markers study (1994), the English adjectives that correlated most strongly with each factor.

Openness

  • Openness to experience: A Big Five trait reflecting a person’s tendency to seek out new ideas, experiences, and imaginative pursuits.
  • High scorers: Creative, curious, artistic, prefer variety over routine.
  • Low scorers: Practical, conventional, prefer familiar routines, focused on the concrete.

Conscientiousness

  • Conscientiousness: A Big Five trait reflecting a person’s tendency to be organized, responsible, and hard-working.
  • High scorers: Reliable, disciplined, rule-following, plan ahead.
  • Low scorers: Disorganized, spontaneous, careless, easily distracted.

Extraversion

  • Extraversion: A Big Five trait reflecting a person’s tendency to be outgoing, energetic, and socially engaged.
  • High scorers: Talkative, assertive, seek out excitement and social interaction.
  • Low scorers (Introverts): Quiet, reserved, prefer solitary activities or small groups.

Agreeableness

  • Agreeableness: A Big Five trait reflecting a person’s tendency to be cooperative, compassionate, and trusting of others.
  • High scorers: Empathetic, kind, helpful, eager to avoid conflict.
  • Low scorers: Competitive, critical, skeptical, willing to argue.

Neuroticism (sometimes called Emotional Stability)

  • Neuroticism: A Big Five trait reflecting a person’s tendency to experience negative emotions and psychological stress.
  • High scorers: Anxious, easily upset, sensitive to stress, moody.
  • Low scorers: Emotionally stable, calm, resilient under pressure.

The Two Ends of a Personality Factor

  • Words at the same end of a factor are positively correlated with each other. Words at opposite ends are negatively correlated with each other.

bold, talkative, energeticquiet, shy, withdrawn

  • Those six words are one circle, extraversion. A person low on one end is high on the other, since the two ends are one spectrum.
  • Some of the words you used to describe your teacher show the same thing.

Our Polls: The Two Ends of a Personality Factor

  • Most of you described your teacher using a word that means kind or caring.
  • Most of you who did NOT instead used a word at the other end of that spectrum: mean, strict, and firm.
  • Scores on mean and scores on kind tend to be strongly negatively correlated, so those words are the two ends of one factor, agreeableness.
  • All five factors have two ends like this.

The Big Five Describes Degrees, Not Types

  • The high end and the low end of a factor are not two kinds of people, so nobody is simply an “extravert” or an “introvert.”
  • Each of the Big Five is a continuous spectrum, which is this course’s Degrees, NOT Types theme.
  • Most people score near the middle on any of the five, and only a small percentage are at either extreme.
  • A score on one of the five places a person on a line, and it drops a lot of detail about them.

What a Personality Factor Leaves Out

  • A factor keeps what a group of trait scores has in common and drops the differences inside the group.
    • Ex: Two people get the same score on extraversion. One is cheerful and funny but shy with strangers. The other talks to anyone but rarely jokes.
  • Fewer factors make a simpler map of a person. More factors keep finer detail.
  • Researchers keep some of the finer detail by splitting each factor into smaller groups of traits.

Personality Facets

  • Facet: A narrower group of related traits inside a broad factor.
  • A factor summarizes what its facets have in common. A facet holds detail the factor dropped.
    • Ex: Sociability and assertiveness are two facets inside extraversion, and a person can be high on one but low on the other.
  • What comes out of a factor analysis depends on the words and the people that go in.

Is the Big Five Universal?

  • Researchers have collected trait words in dozens of languages and run the same kind of factor analysis on scores from those languages.
  • Big Five in 56 nations (2007): Researchers gave the same Big Five questionnaire to people in 56 countries across every world region.
    • Finding: The same five factors appeared in every region, with small differences from country to country.
  • The results differ a little from study to study because researchers choose which words go in, who gets scored, and what to name each factor.

Every score in this deck was made up. How do we get real scores from real people?…