CORRELATION

Correlation is a measure of association or relatedness between two variables.  A positive correlation occurs when high values in one variable "go with" high values in the other variable, and low with low.  A negative correlation occurs when high values in one variable go with low values of the other variable, and low with high.  Here are some data that are positively correlated.

 

Person1         Height    Weight

 Dad                 6'3"      160

 Benjamin         2'2"      28

 Elizabeth          2'5"      28

 Mom               5'4"      115

 

When two variables are correlated, we may say there is "convergence", or that we have "criterion  validity", or that there is "confounding", depending on our purposes.  When one variable is highly correlated with itself at a later time, we say it is "reliable".  In the height/weight example, we could say these two variables converge on a construct of SIZE, or that height is an (externally) valid measure of SIZE (assuming we take weight to be the ultimate criterion of SIZE), or that height and weight are confounded with each other.

 

There are several statistical techniques for making this degree of relatedness explicit.  The most common one is the Pearson correlation coefficient (symbolized as "r"), which ranges from -1.00 (perfect negative relation) through 0.00 (no relationship) to +1.00 (perfect positive relation).  Since perfect relationships are rare, most correlations are decimal fractions.  (Note the height/weight correlation above is not perfect.  Elizabeth should weigh a bit more, or Benjamin a bit less, based on their respective heights, OR, if their weights are equal, their heights should be equal too.  Also notice that correlated variables don't necessarily have the "same numbers".  Finally, notice that it wouldn't matter whether height was in inches, centimeters, finger lengths, etc.  The Pearson r ignores the numbers themselves and looks only at their relationships.)

 

Here are some sample values of r (from Am.Psych.jun84p702modified):

                          "HIGH" CORRELATIONS

IQ test reliability                                   .93

IQ & first grade grades                       .85-.90

traffic fatalities & indices of

     progress in 3rd world countries         -.72

 

                        "MODERATE" CORRELATIONS

IQ in high school & college grades        .50-.55

Physical similarity--spouses                   .40

IQ of fraternal twins                               .54

Aversive maternal and child

     behaviors                                          .55

 

                           "LOW" CORRELATIONS

Reading achievement & TV viewing                  -.05

GRE and grad school grades                              .17

                                   -------------------

1This data is old.  B now weighs 190 and is 6'; E now weighs 122 and is 5' 9".  Is there still a correlation between height and weight in our family?

 

 

Twin Correlations

Interclass correlations (R), sample sizes, and MZA/MZT ratio for monozygotic twins reared apart and together for nine classes of variables, NA = not available. (Science, 250, 1990)

 

 

MZA's           

MZT's             

Relia

RMZA/RMZT
VARIABLES R n R n bility*  
Anthropometric variables
  Fingerprint ridge count 0.97 54 0.96 274 0.99 1.01
  Height 0.86 56 0.93 274 0.98 .925
  Weight 0.73 56 0.83 274 NA .880
Electroencephalographic (brain wave) variables            
  Amount of 8 - 12-Hz (alpha) activity 0.80 35 0.81 42 NA .987
  Mid frequency of alpha activity 0.80 35 0.82 42 NA .975
Psychophysiologic variables            
  Systolic blood pressure 0.64 56 0.70 34 0.70 .914
  Heart rate 0.49 49 0.54 160 0.58 - 0.80 .907
  Electrodermal response (EDR) amplitude            
     Males 0.82 20 0.70 17 NA 1.17
     Females 0.30 23 0.54 19 NA .555
  Trials to habituation EDR 0.43 43 0.42 36 NA 1.02
Information processing ability factors            
  Speed of response 0.56 40 0.73 50 NA .767
  Acquisition speed 0.20 40 NA NA NA NA
  Speed of spatial processing 0.36 40 NA NA NA NA
Mental ability -- general factor            
  WAIS IQ - full scale 0.69 48 0.88 40 0.90 .784
  WAIS IQ - verbal 0.64 48 0.88 40 0.84 727
  WAIS IQ - performance 0.71 48 0.79 40 0.86 .899
  Raven, Mill-Hill composite 0.78 42 0.76 37 NA 1.03
  Special mental abilities 0.78 43 NA NA NA NA
Personality Variables            
  Mean of 11 MPQ Scales 0.50 44 0.49 217 0.88 1.02
  Mean of 18 CPI Scales 0.48 38 0.49 99 0.65 .979
Psychological interests            
  Mean of 23 Strong Campbell Scales 0.39 52 0.48 116 0.82 .813
  Mean of 34 Jackson Vocational scales 0.43 45 NA NA 0.84 NA
  Mean of 17 Minn.  Occupational Interest scales 0.40 40 0.49 376 0.75 .816
Social attitudes            
  Mean of 2 religiosity scales 0.49 31 0.51 458 0.80 .961
  Mean of 14 nonreligious social attitude items 0.34 42 0.28 421 0.48 1.21
   MPQ traditionalism scale 0.53 44 0.50 217 0.49 1.06

*The correlation between two testings of the same individual.  These estimates of the stable component of the observed trait variance also estimate the upper limit for RMZ.