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Critical Values for the Product-Moment Correlation Coefficient, r

Source:
A Dictionary of Statistics

Critical Values for the Product-Moment Correlation Coefficient, r

It is assumed that X and Y are uncorrelated and have normal distributions.

Critical values for two-tailed tests

The values in the table are the two-tailed 5% and 1% points of the distribution of r and hence are appropriate for upper-tail 2.5% and 0.5% tests.

n

5%

1%

n

5%

1%

n

5%

1%

n

5%

1%

4

.950

.990

13

.553

.684

22

.423

.537

40

.312

.403

5

.878

.959

14

.532

.661

23

.413

.526

50

.279

.361

6

.811

.917

15

.514

.641

24

.404

.515

60

.254

.330

7

.754

.874

16

.497

.623

25

.396

.505

70

.235

.306

8

.707

.834

17

.482

.606

26

.388

.496

80

.220

.286

9

.666

.798

18

.468

.590

27

.381

.487

90

.207

.270

10

.632

.765

19

.456

.575

28

.374

.478

100

.197

.256

11

.602

.735

20

.444

.561

29

.367

.470

110

.187

.245

12

.576

.708

21

.433

.549

30

.361

.463

120

.179

.234

Critical values for one-tailed tests

The values in the table are the upper-tail 5% and 1% points of the distribution of r and hence are appropriate for two-tailed 10% and 2% tests.

n

5%

1%

n

5%

1%

n

5%

1%

n

5%

1%

4

.900

.980

13

.476

.634

22

.360

.492

40

.264

.367

5

.805

.934

14

.458

.612

23

.352

.482

50

.235

.328

6

.729

.882

15

.441

.592

24

.344

.472

60

.214

.300

7

.669

.833

16

.426

.574

25

.337

.462

70

.198

.278

8

.621

.789

17

.412

.558

26

.330

.453

80

.185

.260

9

.582

.750

18

.400

.543

27

.323

.445

90

.174

.245

10

.549

.715

19

.389

.529

28

.317

.437

100

.165

.232

11

.521

.685

20

.378

.516

29

.312

.430

110

.158

.222

12

.497

.658

21

.369

.503

30

.306

.423

120

.151

.212

For values outside the range of the tables, use the fact that, assuming independence, r√(n−2)/(1−r2) is an observation from a tn−2 distribution. Alternatively, use the result that rn−1 is approximately an observation from a N(0, 1) distribution.