Understanding Psychology (10th Ed)

Mother’s IQ
Daughter’s IQ
135 
122
128 
130
125
110
120 
132
114 
100
110 
116
102 
108
96
89
90
84
86
92
IQ Scores of Mothers and Daughters
highest score on the fi rst variable would be associated with the lowest score on the 
second variable, the second highest score would be associated with the second low-
est score, and so forth.
Correlation coeffi cients at or only slightly greater or slightly less than zero indi-
cate that there is no relationship between the two variables. In such cases, there is 
no tendency for high values on one variable to be associated with either high or low 
values on the second variable. 
Correlation coeffi cients that range between zero and 
1
/
2
1.00 refl ect varying 
degrees of relationship between the two variables. For instance, a value of 
1
.20 or 
2
.20 would indicate that there was a slight relationship between the two variables; 
a value of around 
1
.50 or –.50 would indicate a moderate relationship; a value of 
1
.80 or 
2
.80 would indicate a relatively strong relationship. As an example, if we 
were to calculate the correlation of the two sets of variables in Figure 2 (most 
advanced calculators do the necessary calculations automatically), we would fi nd a 
correlation that is quite strong: The coeffi cient is 
1
.86. 
It is important to note that fi nding a strong correlation between two variables 
does
not 
in any way indicate that changes in one variable
cause changes in 
another—only that the variables are associated with one another. Although it may 
seem plausible to us that it is the mother’s intelligence that causes higher intel-
ligence in a daughter, for example, it is just as possible that a daughter’s intelli-
gence affects how the mother performs on an IQ test (Perhaps the daughter’s 
behavior affects the general home environment, infl uencing the mother’s perfor-
mance on IQ tests.) It is even plausible that some unmeasured—and previously 
unconsidered—third variable is causing both mother’s and daughter’s IQs to 
increase or decrease simultaneously. In a clear example of this possibility, even if 
we found that ice cream sales and rates of violent crime are positively correlated 
with one another (as they happen to be), we would not presume that they are 
causally related. In this case, it is likely that both are infl uenced by a third factor—
the weather. 
The crucial point is that even if we fi nd a perfect correlation between two sets 
of variables, we will not be able to say that the two variables are linked causally—
only that they are strongly related to one another.
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