80% Power for Pearson's r .01 to .98 According to R Package pwr

Statistical power and power analysis have been topics of discussion in psychological research since the 1960s (see Cohen, 1992 for a brief overview). Statistical power was defined by Cohen as "the long-term probability, given the population ES [e.g. r,  d ], alpha [e.g. .05, .01], and N [sample size], of rejecting the H0 [the null hypothesis]" (1992, p. 156). The bits in square brackets that ruin that quotation are mine. Sorry.

The idea of statistical power makes most (perfect) sense from the classic NHST statistical framework, where the researcher is thought of as drawing random samples from some larger population. Power analysis provides an answer to the following question: if (a) a population effect size of some magnitude exists, (b) I have a significance criterion of x for my statistical tests, and (c) I draw samples from a population, what sample size do I need if, in the long term, I am to correctly reject the null hypothesis with a certain probability?

The theoretically required sample size depends on the effect size anticipated, the significance criterion employed, and the desired long-term probability of rejecting the null hypothesis. In practice, the smaller the effect size anticipated, the smaller the significance criterion employed, and the greater the desired long term probability of rejecting the null hypothesis, the larger the sample size the researcher will require. Statistical power thus depends on the nature of your phenomena (strong versus weak), the nature of your statistical tests (conservative versus liberal), and your approach to uncertainty in the long term (risk-averse versus risk-taking).

According to Cohen (1992, p. 156) power depends on one other thing too: whether you are doing a one-sided or two-sided test. In the context of a Pearson's r correlation a two-sided test is when you don't have an a priori hypothesis as to the sign (+ versus -) of the correlation. A one-sided test is when you do. I have a feeling that in social and personality psychology most tests of correlations will be one-sided (e.g. that self-esteem is positively associated with life satisfaction, but negatively associated with depression). So if you use R keep in mind that the pwr package computes power for a two-sided test as default and the values in the table of Cohen (1992) are also for two-sided tests. Sample sizes for .10 should be used for one-side tests (p. 156). In my Masters I planned a sample size for a research project involving only one-side tests without knowing that. The practical implications of ignoring the one-side/two sided distinction will depend on effect size: at the low end of the effect size spectrum you might need a few hundred more participants for a two-sided test; as soon as your correlation reaches medium effect size territory, however, we're only looking at a dozen more.

To help get a feel for the theoretically required sample size for 80% power for cross-sectional work with Pearson's rs and to concretely describe power analysis, I have made the table below. It contains the sample size required for all whole number Pearson's rs from .01 through .98, for two-sided and one-sided tests provided by the R package pwr (which is based on Cohen, 1988). It also presents one-sided N as a proportion of two-sided N, as well as the difference in N  between the two. The sample sizes required are exactly the same for negative correlations.

For one-sided tests the following code is required:

pwr.r.test(n = , r = .10 , sig.level = .05, power = .80, alternative = "greater")

For two-sided tests the following code is required:

pwr.r.test(n = , r = .005 , sig.level = .05, power = .80)

r	Two-Sided	One-Sided	One-Sided as % of Two-Sided N	Two-Sided – One-Sided
.01	78485.47	61823.42	78.77%	-16662.05
.02	19619.02	15454.24	78.77%	-4164.78
.03	8717.822	6867.354	78.77%	-1850.468
.04	4902.403	3861.944	78.78%	-1040.459
.05	3136.41	2470.869	78.78%	-665.541
.06	2177.105	1715.223	78.78%	-461.882
.07	1598.674	1259.593	78.79%	-339.081
.08	1223.25	963.8714	78.80%	-259.3786
.09	965.8606	761.1258	78.80%	-204.7348
.10	781.7516	616.1032	78.81%	-165.6484
.11	645.5317	508.8029	78.82%	-136.7288
.12	541.9252	427.1924	78.83%	-114.7328
.13	461.2951	363.6803	78.84%	-97.6148
.14	397.3175	313.2856	78.85%	-84.0319
.15	345.7037	272.6297	78.86%	-73.074
.16	303.4615	239.356	78.88%	-64.1055
.17	268.4522	211.7797	78.89%	-56.6725
.18	239.1141	188.6706	78.90%	-50.4435
.19	214.2852	169.1135	78.92%	-45.1717
.20	193.0867	152.416	78.94%	-40.6707
.21	174.8439	138.0468	78.95%	-36.7971
.22	159.0316	125.5922	78.97%	-33.4394
.23	145.2367	114.7266	78.99%	-30.5101
.24	133.1299	105.1909	79.01%	-27.939
.25	122.4466	96.77644	79.04%	-25.67016
.26	112.9721	89.31424	79.06%	-23.65786
.27	104.5307	82.66581	79.08%	-21.86489
.28	96.97745	76.71702	79.11%	-20.26043
.29	90.19199	71.37305	79.13%	-18.81894
.30	84.07364	66.55463	79.16%	-17.51901
.31	78.53776	62.19504	79.19%	-16.34272
.32	73.51267	58.23783	79.22%	-15.27484
.33	68.93741	54.63501	79.25%	-14.3024
.34	64.75983	51.34549	79.29%	-13.41434
.35	60.93514	48.33393	79.32%	-12.60121
.36	57.42466	45.56996	79.36%	-11.8547
.37	54.19491	43.02712	79.39%	-11.16779
.38	51.21669	40.68248	79.43%	-10.53421
.39	48.46455	38.51594	79.47%	-9.94861
.40	45.91614	36.50995	79.51%	-9.40619
.41	43.55186	34.64901	79.56%	-8.90285
.42	41.35434	32.91948	79.60%	-8.43486
.43	39.30827	31.30931	79.65%	-7.99896
.44	37.40001	29.80769	79.70%	-7.59232
.45	35.61745	28.40513	79.75%	-7.21232
.46	33.94976	27.09311	79.80%	-6.85665
.47	32.38727	25.86401	79.86%	-6.52326
.48	30.92127	24.71096	79.92%	-6.21031
.49	29.54402	23.6278	79.97%	-5.91622
.50	28.24841	22.60907	80.04%	-5.63934
.51	27.0281	21.64969	80.10%	-5.37841
.52	25.87738	20.74515	80.17%	-5.13223
.53	24.79101	19.89129	80.24%	-4.89972
.54	23.76423	19.08448	80.31%	-4.67975
.55	22.79277	18.32132	80.38%	-4.47145
.56	21.87264	17.59861	80.46%	-4.27403
.57	21.00035	16.91359	80.54%	-4.08676
.58	20.17253	16.26368	80.62%	-3.90885
.59	19.3862	15.64652	80.71%	-3.73968
.60	18.63858	15.05985	80.80%	-3.57873
.61	17.92718	14.50177	80.89%	-3.42541
.62	17.24958	13.97038	80.99%	-3.2792
.63	16.60367	13.46401	81.09%	-3.13966
.64	15.98746	12.98108	81.20%	-3.00638
.65	15.3991	12.52014	81.30%	-2.87896
.66	14.83688	12.07985	81.42%	-2.75703
.67	14.29923	11.65895	81.54%	-2.64028
.68	13.78464	11.25629	81.66%	-2.52835
.69	13.29182	10.87079	81.79%	-2.42103
.70	12.81943	10.50145	81.92%	-2.31798
.71	12.36629	10.14733	82.06%	-2.21896
.72	11.93129	9.807556	82.20%	-2.123734
.73	11.51337	9.481297	82.35%	-2.032073
.74	11.11156	9.167802	82.51%	-1.943758
.75	10.72496	8.866322	82.67%	-1.858638
.76	10.35266	8.576185	82.84%	-1.776475
.77	9.993879	8.296739	83.02%	-1.69714
.78	9.647812	8.027358	83.20%	-1.620454
.79	9.313733	7.76751	83.40%	-1.546223
.80	8.990898	7.516578	83.60%	-1.47432
.81	8.678654	7.274044	83.82%	-1.40461
.82	8.376314	7.039387	84.04%	-1.336927
.83	8.083248	6.812124	84.27%	-1.271124
.84	7.798814	6.591688	84.52%	-1.207126
.85	7.522376	6.377668	84.78%	-1.144708
.86	7.253296	6.16953	85.06%	-1.083766
.87	6.99092	5.966757	85.35%	-1.024163
.88	6.734556	5.768836	85.66%	-0.96572
.89	6.483499	5.575197	85.99%	-0.908302
.90	6.236905	5.385215	86.34%	-0.85169
.91	5.993871	5.198218	86.73%	-0.795653
.92	5.753285	5.013335	87.14%	-0.73995
.93	5.513883	4.829639	87.59%	-0.684244
.94	5.27376	4.645742	88.09%	-0.628018
.95	5.030555	4.459864	88.66%	-0.570691
.96	4.780486	4.269295	89.31%	-0.511191
.97	4.51724	4.069485	90.09%	-0.447755
.98	4.228144

Refs

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum. 

Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155-159.