Essay on Statistics: Spearman ' s Rank Correlation Coefficient and Mario F . Triola

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Formulas and Tables by Mario F. Triola
Copyright 2011 Pearson Education, Inc.

TABLE A-5
Critical Values of the Pearson Correlation Coefficient r n 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 60 70 80 90 100 a 0.05 .950 .878 .811 .754 .707 .666 .632 .602 .576 .553 .532 .514 .497 .482 .468 .456 .444 .396 .361 .335 .312 .294 .279 .254 .236 .220 .207 .196 a 0.01 .990 .959 .917 .875 .834 .798 .765 .735 .708 .684 .661 .641 .623 .606 .590 .575 .561 .505 .463 .430 .402 .378 .361 .330 .305 .286 .269 .256

TABLE A-6
Critical Values of Spearman’s Rank Correlation Coefficient rs n 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
NOTES: 1. For n 7 30, use rs = ;z> 1n - 1 where z corresponds to the level of significance. For example, if a 0.05, then z 1.96. 2. If the absolute value of the test statistic rs exceeds the positive critical value, then reject H0: rs 0 and conclude that there is a correlation. Based on data from “Biostatistical Analysis, 4th edition,” © 1999, by Jerrold Zar, Prentice Hall, Inc., Upper Saddle River, New Jersey, and “Distribution of Sums of Squares of Rank Differences to Small Numbers with Individuals,” The Annals of Mathematical Statistics, Vol. 9, No. 2, with permission of the Institute of Mathematical Statistics.

a

0.05 — .886 .786 .738 .700 .648 .618 .587 .560 .538 .521 .503 .485 .472 .460 .447 .435 .425 .415 .406 .398 .390 .382 .375 .368 .362

a

0.01 — — .929 .881 .833 .794 .755 .727 .703 .679 .654 .635 .615 .600 .584 .570 .556 .544 .532 .521 .511 .501 .491 .483 .475 .467

NOTE: To test H0: r 0 against H1: r 0, reject H0 if the absolute value of r is greater than the critical value in the table.

General considerations • Context of the data • Source of the data • Sampling method • Measures of center • Measures of variation • Nature of distribution • Outliers • Changes over time • Conclusions • Practical implications

FINDING P-VALUES

HYPOTHESIS TEST: WORDING OF FINAL CONCLUSION

Inferences about M: choosing between t and normal distributions t distribution: or Normal distribution: or s not known and normally distributed population s not known and n 30 s known and normally distributed population s known and n 30 30

Nonparametric method or bootstrapping: Population not normally distributed and n

TABLE A-3

t Distribution: Critical t Values
0.005 0.01 Area in One Tail 0.025 Area in Two Tails 0.05 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.040 2.037 2.035 2.032 2.030 2.028 2.026 2.024 2.023 2.021 2.014 2.009 2.000 1.994 1.990 1.987 1.984 1.972 1.968 1.966 1.965 1.962 1.961 1.960 0.05 0.10

Degrees of…