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- Statistical Research Article An elaboration on sample size determination for correlations based on effect sizes and confidence interval width: a guide for researchers
-
Mohamad Adam Bujang
-
Restor Dent Endod 2024;49(2):e21.
DOI: https://doi.org/10.5395/rde.2024.49.e21
Published online: May 2, 2024
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- Correspondence to Mohamad Adam Bujang, PhD. Clinical Research Centre, Sarawak General Hospital, Jalan Tun Ahmad Zaidi Adruce, 93586 Kuching, Sarawak, Malaysia. adam@crc.gov.my
• Received: October 11, 2023 • Accepted: January 4, 2024
Copyright © 2024. The Korean Academy of Conservative Dentistry
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (https://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
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XML DownloadAn elaboration on sample size determination for correlations based on effect sizes and confidence interval width: a guide for researchers
An elaboration on sample size determination for correlations based on effect sizes and confidence interval width: a guide for researchers
Sample size calculation for Pearson’s, Kendall-Tau’s, and Spearman’s rank correlations based on 95% confidence interval (CI) width
| Effect size | Width | Width for both sides | 95% CI | np | nk | ns | diff.* |
|---|---|---|---|---|---|---|---|
| 0.1 | 0.1 | ± 0.05 | 0.050, 0.150 | 1,507 | 662 | 1,515 | 8 |
| 0.2† | ± 0.10† | 0.000, 0.200† | 378† | 168† | 379† | 1† | |
| 0.3† | ± 0.15† | −0.050, 0.250† | 168† | 77† | 169† | 1† | |
| 0.4† | ± 0.20† | −0.100, 0.300† | 95† | 45† | 96† | 1† | |
| 0.5† | ± 0.25† | −0.150, 0.350† | 61† | 30† | 62† | 1† | |
| 0.2 | 0.1 | ± 0.05 | 0.150, 0.250 | 1,417 | 622 | 1,446 | 29 |
| 0.2 | ± 0.10 | 0.100, 0.300 | 355 | 158 | 362 | 7 | |
| 0.3 | ± 0.15 | 0.050, 0.350 | 159 | 72 | 162 | 3 | |
| 0.4† | ± 0.20† | 0.000, 0.400† | 90† | 42† | 91† | 1† | |
| 0.5† | ± 0.25† | −0.050, 0.450† | 58† | 28† | 59† | 1† | |
| 0.3 | 0.1 | ± 0.05 | 0.250, 0.350 | 1,274 | 560 | 1,331 | 57 |
| 0.2 | ± 0.10 | 0.200, 0.400 | 320 | 143 | 334 | 14 | |
| 0.3 | ± 0.15 | 0.150, 0.450 | 143 | 65 | 149 | 6 | |
| 0.4 | ± 0.20 | 0.100, 0.500 | 81 | 38 | 85 | 4 | |
| 0.5 | ± 0.25 | 0.050, 0.550 | 53 | 26 | 55 | 2 | |
| 0.4 | 0.1 | ± 0.05 | 0.350, 0.450 | 1,086 | 478 | 1,173 | 87 |
| 0.2 | ± 0.10 | 0.300, 0.500 | 273 | 122 | 295 | 22 | |
| 0.3 | ± 0.15 | 0.250, 0.550 | 123 | 57 | 132 | 9 | |
| 0.4 | ± 0.20 | 0.200, 0.600 | 70 | 34 | 75 | 5 | |
| 0.5 | ± 0.25 | 0.150, 0.650 | 46 | 23 | 49 | 3 | |
| 0.5 | 0.1 | ± 0.05 | 0.450, 0.550 | 867 | 382 | 975 | 108 |
| 0.2 | ± 0.10 | 0.400, 0.600 | 219 | 99 | 246 | 27 | |
| 0.3 | ± 0.15 | 0.350, 0.650 | 99 | 46 | 111 | 12 | |
| 0.4 | ± 0.20 | 0.300, 0.700 | 57 | 28 | 64 | 7 | |
| 0.5 | ± 0.25 | 0.250, 0.750 | 37 | 19 | 42 | 5 | |
| 0.6 | 0.1 | ± 0.05 | 0.550, 0.650 | 633 | 280 | 746 | 113 |
| 0.2 | ± 0.10 | 0.500, 0.700 | 161 | 73 | 189 | 28 | |
| 0.3 | ± 0.15 | 0.450, 0.750 | 74 | 35 | 86 | 12 | |
| 0.4 | ± 0.20 | 0.400, 0.800 | 43 | 22 | 50 | 7 | |
| 0.5 | ± 0.25 | 0.350, 0.850 | 29 | 16 | 33 | 4 | |
| 0.7 | 0.1 | ± 0.05 | 0.650, 0.750 | 404 | 180 | 503 | 99 |
| 0.2 | ± 0.10 | 0.600, 0.800 | 105 | 49 | 129 | 24 | |
| 0.3 | ± 0.15 | 0.550, 0.850 | 49 | 24 | 60 | 11 | |
| 0.4 | ± 0.20 | 0.500, 0.900 | 30 | 16 | 36 | 6 | |
| 0.5 | ± 0.25 | 0.450, 0.750 | 20 | 12 | 25 | 5 | |
| 0.8 | 0.1 | ± 0.05 | 0.750, 0.850 | 205 | 93 | 269 | 64 |
| 0.2 | ± 0.10 | 0.700, 0.900 | 56 | 27 | 72 | 16 | |
| 0.3 | ± 0.15 | 0.650, 0.950 | 28 | 15 | 35 | 7 | |
| 0.4 | ± 0.20 | 0.600, 1.000 | 18 | 11 | 22 | 4 | |
| 0.5‡ | ± 0.25‡ | 0.550, 1.000‡ | 13‡ | 9‡ | 16‡ | 3‡ | |
| 0.9 | 0.1 | ± 0.05 | 0.850, 0.950 | 62 | 30 | 86 | 24 |
| 0.2 | ± 0.10 | 0.800, 1.000 | 20 | 12 | 27 | 7 | |
| 0.3‡ | ± 0.15‡ | 0.750, 1.000‡ | 12‡ | 8‡ | 16‡ | 4‡ | |
| 0.4‡ | ± 0.20‡ | 0.700, 1.000‡ | 9‡ | 7‡ | 12‡ | 3‡ | |
| 0.5‡ | ± 0.25‡ | 0.650, 1.000‡ | 8‡ | 6‡ | 10‡ | 2‡ |
np, sample size for Pearson’s correlation; nk, sample size for Kendall Tau-b’s correlation; ns, sample size for Spearman’s correlation.
*diff. represents the difference between ns - np; †Lower bound with either zero or negative value; ‡Upper bound with more than 1.000.
Table 1 Sample size calculation for Pearson’s, Kendall-Tau’s, and Spearman’s rank correlations based on 95% confidence interval (CI) width
np, sample size for Pearson’s correlation; nk, sample size for Kendall Tau-b’s correlation; ns, sample size for Spearman’s correlation.
*diff. represents the difference between ns - np; †Lower bound with either zero or negative value; ‡Upper bound with more than 1.000.
