Russel-Research-Method-in-Anthropology

Bivariate Analysis: Testing Relations 629
TABLE 20.17
Comparison of the Error Produced by Guessing the Mean TFR in Table 20.14 and the
Error Produced by Applying the Regression Equation for Each Guess
New Error
(y the prediction
TFR Old Error Prediction using the using the regression
Country y (y y) 2 regression equivalent equation) 2
Armenia 1.70 1.999 2.344 .415
Chad 6.07 8.738 6.730 .436
El Salvador 3.17 .003 2.650 .270
Ghana 5.15 4.145 4.384 .587
Iran 2.80 .099 2.803 .000
Latvia 1.25 3.474 1.936 .470
Namibia 4.90 3.190 4.333 .321
Panama 2.63 .234 2.089 .293
Slovenia 1.26 3.437 1.375 .013
Suriname 2.21 .817 2.497 .082
26.136
2.890
This quantity is usually referred to as r-squared (written r 2 ), or the amount
of variance accounted for by the independent variable. It is also called the
coefficient of determination because it tells us how much of the variance in
the dependent variable is predictable from (determined by) the scores of the
independent variable. The Pearson product moment correlation, written as r,
is the square root of this measure, or, in this instance, .943. We calculated r in
table 20.15 by applying formula 20.22.
Calculating r and r 2
I’ve given you this grand tour of regression and correlation because I want
you to see that Pearson’s r is not a direct PRE measure of association; its
square, r 2 , is.
So, what’s better, Pearson’s r or r 2 for describing the relation between interval
variables? Pearson’s r is easy to compute from raw data and it varies from
1 to1, so it has direction and an intuitive interpretation of magnitude.
Mathematically, of course, r has to be at least as big (and almost always bigger)
than r 2 . By contrast, r 2 is a humbling statistic. A correlation of .30 looks
impressive until you square it and see that it explains just 9% of the variance
in what you’re studying.