PEARSON’S CORRELATION COEFFICIENT r (Critical Values)
Level of Significance for a One-Tailed Test
.05
.025
.01
.005
.0005
.05
.025
.01
.005
.0005
Level of Significance for a Two-Tailed Test
df=(N-2)
.10
.05
.02
.01
.001
df=(N-2)
.10
.05
.02
.01
.001
1
0.988
0.997
0.9995
0.9999
0.99999
21
0.352
0.413
0.482
0.526
0.640
2
0.900
0.950
0.980
0.990
0.999
22
0.344
0.404
0.472
0.515
0.629
3
0.805
0.878
0.934
0.959
0.991
23
0.337
0.396
0.462
0.505
0.618
4
0.729
0.811
0.882
0.971
0.974
24
0.330
0.388
0.453
0.496
0.607
5
0.669
0.755
0.833
0.875
0.951
25
0.323
0.381
0.445
0.487
0.597
6
0.621
0.707
0.789
0.834
0.928
26
0.317
0.374
0.437
0.479
0.588
7
0.582
0.666
0.750
0.798
0.898
27
0.311
0.367
0.430
0.471
0.579
8
0.549
0.632
0.715
0.765
0.872
28
0.306
0.361
0.423
0.463
0.570
9
0.521
0.602
0.685
0.735
0.847
29
0.301
0.355
0.416
0.456
0.562
10
0.497
0.576
0.658
0.708
0.823
30
0.296
0.349
0.409
0.449
0.554
11
0.476
0.553
0.634
0.684
0.801
40
0.257
0.304
0.358
0.393
0.490
12
0.457
0.532
0.612
0.661
0.780
60
0.211
0.250
0.295
0.325
0.408
13
0.441
0.514
0.592
0.641
0.760
120
0.150
0.178
0.210
0.232
0.294
14
0.426
0.497
0.574
0.623
0.742
∞
0.073
0.087
0.103
0.114
0.146
15
0.412
0.482
0.558
0.606
0.725
16
0.400
0.468
0.542
0.590
0.708
17
0.389
0.456
0.529
0.575
0.693
18
0.378
0.444
0.515
0.561
0.679
19
0.369
0.433
0.503
0.549
0.665
20
0.360
0.423
0.492
0.537
0.652
1) Decide if you should use a One-Tailed or Two-Tailed Test: (MSLS: 38.2)
a. One-Tail: if you have an a priori: hypothesis as to the sign (- or +) of the correlation.
b. Two-Tail: if you have no a priori: hypothesis as to the sign of the correlation.
2) Calculate df (degrees of freedom) = N (sample size) - 2). (MSLS: 31)
3) Locate this df in the table.
4) Use this row of threshold values.
5) Read across this row from left to right until you find a value greater than your calculated r
statistic.
6) The P–value for your observation is the P–value at the top of the first column to the left of your
value.
e.g. if r for df = 15 is 0.523, then P < 0.025 for a One-Tailed Test; if r is 0.599, then P < 0.01.
7) A P < 0.05 (or smaller) value indicates that you can reject the null hypothesis that the two
variables are not correlated. In other words, you have evidence the variables are significantly
related. If your r statistic value lies to the left of the 0.05 column, then your results are not
significant (n.s. P > 0.05). You cannot reject the null hypothesis that the variables are unrelated.