Understanding Correlations

Correlations measure the relationships between variables in psychometric research. They are the foundation for quantifying how well we are measuring (reliability) and the relevance of what we are measuring (validity). They are based on identifying covariance: i.e. the variation shared between two distributions of scores. The correlation coefficient (r) quantifies the relationship between two variables. The relationship between two variables can be shown as a scattergram.

The correlation coefficient uses a number from -1 to +1 to describe the relationship between two variables. It tells you if more of one variable predicts more of another variable.

  • -1 is a perfect negative relationship
  • +1 is a perfect positive relationship
  • 0 is no relationship

c-1 c1

c0

Weak, Medium and Strong Correlation in Psychometrics

Weak  .1 to .29

cweak

Medium .3  to .59

cmed

Strong greater than .6

cstrong

Real World Correlations

One of the most useful ways to developing an understanding of correlations is to consider some strong correlations for variables we observe every day. From this we can see that even strong correlations are not what we would intuitively call strong predictors.  I don’t think many of us would consider someone’s weight as a strong predictor of their height yet the relationship between height and weight is over large meta studies in the range +.65 to +.75.  Other strong correlations would be education and longevity (r=+.62), education and years in jail –sample of those charged in New York (r= – .72). This last correlation is similar to the correlation between scores on numerical ability test conducted with the same people four weeks apart (r=+.78). All of these are stronger correlations than we get using any particular psychometric tools to assess job performance.

To put psychometric predictions of job performance in context – large scale research such as Hunter & Schmidt suggest the correlations between ability tests and job performance for administrative and professional jobs is a medium positive (r=+.55). This is about the same as current data on structured interviews and job performance in similar roles (r=+.52) and just above the correlations reported for US advertising industry between height and salary (r=+.46). So height is almost as good a predictor of salary as interviews or psychometric tests. In reality the utility of many psychometric correlations is affected by restriction of range. The higher correlations quoted above assume a fully representative population (however in reality we are often selecting between people with similar levels of education). This means we will not get the level of performance discrimination suggested by the above correlations. A more realistic validity for psychometrics or interviews when selecting between educationally matched candidates would be .25 or .3 (weak correlations).

Finally let us look at some weak correlations. Perhaps the correlation between how much student’s socialise in high school and how they perform in exams (r= – .25) does not surprise you.  Where we are surprised is when we have heard over and over that correlations are significant. Perhaps this tells you something about how susceptible we are to the authorative reporting based on large samples. Hirsh (2009) cites correlations between smoking and lung cancer within 25 years as being as low as + .08. He also cites the correlation between Ibuprofane (Nurofen) and pain relief as r = +.14.  Knowing things are weakly or even not correlated can also be useful in psychometrics. Factor analysis is designed to cluster items closely related to each other but relatively independent from other items. The table overleaf shows the extent to which peer ratings on the 5 Factor Model show positive correlations with the corresponding scale  and weak correlations with other scales.  The relationship between the Big 5 and the MBTI overleaf can also be instructive.

Sample Use of Correlation Tables in Psychometric Research


 

 

Self-Report Ratings

 

 

Openness

Conscientiousness

Extraversion

Agreeableness

Emotional Stability

Peer  Ratings

 

Openness

.57

 

Conscientiousness

 

-.08

.43

 

Extraversion

 

.25

.02

.47

 

Agreeableness

 

-.03

.12

-.25

.30

Emotional Stability

-.02

.14

-.02

.11

.42

Costa McCrea; Five Factors in Peer Ratings; Journal of Personality and Social Psychology; 1987, Vol 52, No 1, 81-90

 

 

 

 

Self Report FFM

 

 

Openness

Conscientiousness

Extraversion

Agreeableness

Emotional Stability

Self Report MBTI

 

Introversion

.03

0.08

-.74

-0.3

.16

 

Intuting

 

.72

-0.15

.10

0.04

-0.06

 

Feeling

 

.02

-.10

.19

0.44

0.06

 

Perceiving

 

.30

-.49

.15

-0.06

.11

Costa & McCrea ; Reinterpreting the MBTI; Journal of Personality 57 1, March 1989

 

 

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