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Bivariate Analysis: Test<strong>in</strong>g Relations 599<br />

TABLE 20.3<br />

Percentage of Teenage Births <strong>in</strong> the 50 U.S. States<br />

Northeast Midwest South West<br />

x 1 x 1<br />

2<br />

x 2 x 2<br />

2<br />

x 3 x 3<br />

2<br />

x 4 x 4<br />

2<br />

NY 9.2 84.64 KS 13.1 171.61 FL 13.4 179.56 NM 17.9 320.41<br />

VT 8.9 79.21 SD 11.5 132.25 AR 19.8 392.04 OR 13.2 174.24<br />

NJ 7.7 59.29 WI 10.6 112.36 KY 17.0 289.00 ID 13.5 182.25<br />

PA 10.6 112.35 IA 11.0 121.00 LA 18.9 357.21 HI 10.3 106.09<br />

MA 7.3 53.29 IN 14.5 210.25 MD 10.3 106.09 NV 13.3 176.89<br />

NH 7.4 54.76 OH 13.3 176.89 MS 21.3 453.69 CO 11.9 141.61<br />

ME 9.7 94.09 ND 9.6 92.16 AL 18.3 334.89 UT 10.6 112.36<br />

CT 8.2 67.24 MI 12.2 148.84 DE 13.7 187.69 CA 12.0 144.00<br />

RI 10.3 106.09 MN 8.5 72.25 GA 15.9 252.81 WY 14.4 207.36<br />

MO 14.4 207.36 OK 17.2 295.84 WA 11.3 127.69<br />

NE 10.6 112.36 VA 11.0 121.00 AZ 15.0 225.00<br />

IL 12.7 161.29 NC 15.0 225.00 AK 11.2 125.44<br />

WV 16.8 282.24 MT 12.5 156.25<br />

TN 16.8 282.24<br />

SC 16.8 282.24<br />

TX 16.2 262.44<br />

x 1 79.3 x 2 142.0 x 3 258.4 x 4 167.1<br />

x 12 710.97 x 22 1,718.62 x 32 4,303.98 x 42 2,199.59<br />

n 9 n 12 n 16 n 13<br />

x 1 8.811 x 2 11.833 x 3 16.150 x 4 12.854<br />

s 12 1.531 s 22 3.481 s 32 8.721 s 42 4.309<br />

SOURCE: Statistical Abstracts of the United States, 1998, Table 103.<br />

At the bottom of table 20.3, I’ve calculated the four separate, or with<strong>in</strong>-group,<br />

variances, us<strong>in</strong>g formula 20.3 above. Apply<strong>in</strong>g formula 20.4, the total sums of<br />

squares for the data <strong>in</strong> table 20.3 is:<br />

710.971,718.624,303.982,199.59 (79.3142258.5167)2<br />

50<br />

8,993.16 418,350.24 8,933.16 8,367.005 556.16<br />

50<br />

The formula for calculat<strong>in</strong>g the sum of the squares between groups is:

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