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# PEARSON'S r

Pearson’s r measures how much changes in one variable correspond with equivalent changes in the other variables. It can also be used as a measure of association between an interval and an ordinal variable, or between an interval and a dummy variable. (Dummy variables are nominal variables coded as 1 or 0, present or absent. See chapter 19 on text analysis.) The square of Pearson’s r is a PRE measure of association for linear relations between interval variables. R-squared tells us how much better we could predict the scores of a dependent variable, if we knew the scores of some independent variable.

Table 21.14 shows data for two interval variables for a random sample of 10 of the 50 countries in table 20.8: (1) infant mortality and (2) life expectancy for women.

To give you an idea of where we're going with this example, the correlation between INFMORT and TFR across the 50 countries in table 20.8 is around 0.91, and this is reflected in the sample of 10 countries for which the correlation is r = 0.81.

Now, suppose you had to predict the TFR for each of the 10 countries in table 21.14 without knowing anything about the infant mortality rate for those countries. Your best guess—your lowest prediction error—would be the mean, 2.63 children per woman. You

Table 21.13 Computing Spearman's Rank Order Correlation Coefficient for the Data in Table 21.12

 Hunter Rank for meat Rank for fish Difference in the ranks d2 Alejandro 1 10 -9 81 Jaime 2 9 -7 49 Leonardo 3 15 -12 144 Humberto 4 6 -2 4 Daniel 5 7 -2 4 Joel 6 12 -6 36 Jorge 7 14 -7 49 Timoteo 8 16 -8 64 Tomas 9 5 4 16 Lucas 10 8 2 4 Guillermo 11 2 9 81 Victor 12 11 1 1 Manuel 13 13 0 0 Benjamin 14 4 10 100 Jonatan 15 3 12 144 Lorenzo 16 1 15 225 total d2 1,002 r“ = - wa-i) = - 6012/4080 = -474

Table 21.14 Infant Mortality by TFR for 10 Countries from Table 20.8

 Country INFMORT x TFR y Armenia 22.2 1.79 Chad 129.9 5.78 El Salvador 17.5 2.22 Ghana 67.0 4.00 Iran 24.2 1.74 Latvia 8.3 1.48 Namibia 27.2 3.07 Panama 15.7 2.41 Slovenia 3.6 1.47 Suriname 20.5 2.29 Mean of x = 25.49 Mean of y = 2.63

FIGURE 21.4.

A plot of the data in table 21.14. The dotted lineisthemeanofTFR. Thesolidlineis drawn from the regression equation y = 1.018 +

.051 x.

can see this in figure 21.4 where I’ve plotted the distribution of TFR and INFMORT for the 10 countries in table 21.14.

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