Related link :
Sample Size Introduction and Explanation Page
Sample Size for Mean of Paired Difference Program Page
Paired Difference Explained Page
Tables of Sample Size for Paired Difference
References
Abbreviations
α = alpha, p, Probability of Type I Error
Power = 1-β, 1-Probability of Type II Error
es = Effect Size = Mean of paired difference to be detected / Expected Standard Deviation of the paired difference
Value in cells = sample size = number of pairs
bold : commonly used sample sizes for small, moderate, and large effect size
Power | 0.8 | 0.9 | 0.95 |
α | 0.1 | 0.05 | 0.01 | 0.001 | 0.1 | 0.05 | 0.01 | 0.001 | 0.1 | 0.05 | 0.01 | 0.001 |
es | 1 tail | 2 tail | 1 tail | 2 tail | 1 tail | 2 tail | 1 tail | 2 tail | 1 tail | 2 tail | 1 tail | 2 tail | 1 tail | 2 tail | 1 tail | 2 tail | 1 tail | 2 tail | 1 tail | 2 tail | 1 tail | 2 tail | 1 tail | 2 tail |
0.05 | 1804 | 2475 | 2475 | 3142 | 4018 | 4675 | 6189 | 6836 | 2629 | 3427 | 3427 | 4205 | 5210 | 5955 | 7650 | 8367 | 3427 | 4331 | 4331 | 5200 | 6311 | 7129 | 8974 | 9749 |
0.1 | 452 | 620 | 620 | 787 | 1007 | 1172 | 1551 | 1713 | 658 | 858 | 858 | 1053 | 1305 | 1492 | 1917 | 2096 | 858 | 1084 | 1084 | 1302 | 1580 | 1785 | 2247 | 2442 |
0.15 | 202 | 277 | 277 | 351 | 449 | 523 | 692 | 765 | 293 | 382 | 382 | 469 | 582 | 665 | 855 | 935 | 382 | 483 | 483 | 580 | 704 | 796 | 1002 | 1088 |
0.2 | 114 | 156 | 156 | 199 | 254 | 296 | 392 | 433 | 166 | 216 | 216 | 265 | 329 | 376 | 483 | 529 | 215 | 272 | 272 | 327 | 397 | 449 | 566 | 615 |
0.25 | 73 | 101 | 101 | 128 | 164 | 191 | 253 | 279 | 106 | 139 | 139 | 171 | 211 | 242 | 311 | 340 | 138 | 175 | 175 | 210 | 256 | 289 | 364 | 396 |
0.3 | 51 | 71 | 71 | 90 | 115 | 134 | 177 | 196 | 74 | 97 | 97 | 119 | 148 | 169 | 218 | 238 | 96 | 122 | 122 | 147 | 178 | 202 | 254 | 277 |
0.35 | 38 | 52 | 52 | 66 | 85 | 99 | 131 | 145 | 55 | 72 | 72 | 88 | 109 | 125 | 161 | 177 | 71 | 90 | 90 | 108 | 132 | 149 | 188 | 205 |
0.4 | 29 | 40 | 40 | 51 | 66 | 77 | 102 | 113 | 42 | 55 | 55 | 68 | 85 | 97 | 125 | 137 | 55 | 69 | 69 | 84 | 102 | 115 | 145 | 158 |
0.45 | 24 | 32 | 32 | 41 | 53 | 61 | 82 | 90 | 34 | 44 | 44 | 54 | 67 | 77 | 100 | 109 | 44 | 55 | 55 | 67 | 81 | 92 | 116 | 126 |
0.5 | 19 | 27 | 27 | 34 | 43 | 51 | 67 | 74 | 28 | 36 | 36 | 44 | 55 | 63 | 82 | 90 | 36 | 45 | 45 | 54 | 66 | 75 | 95 | 103 |
0.55 | 16 | 22 | 22 | 28 | 36 | 42 | 56 | 62 | 23 | 30 | 30 | 37 | 46 | 53 | 68 | 75 | 30 | 38 | 38 | 45 | 55 | 63 | 79 | 86 |
0.6 | 14 | 19 | 19 | 24 | 31 | 36 | 48 | 53 | 20 | 26 | 26 | 32 | 39 | 45 | 58 | 64 | 25 | 32 | 32 | 39 | 47 | 53 | 68 | 74 |
0.65 | 12 | 16 | 16 | 21 | 27 | 31 | 42 | 46 | 17 | 22 | 22 | 27 | 34 | 39 | 51 | 55 | 22 | 27 | 27 | 33 | 41 | 46 | 58 | 64 |
0.7 | 11 | 14 | 14 | 18 | 24 | 28 | 37 | 41 | 15 | 19 | 19 | 24 | 30 | 34 | 44 | 49 | 19 | 24 | 24 | 29 | 35 | 40 | 51 | 56 |
0.75 | 9 | 13 | 13 | 16 | 21 | 25 | 33 | 36 | 13 | 17 | 17 | 21 | 26 | 30 | 39 | 43 | 17 | 21 | 21 | 26 | 31 | 35 | 45 | 49 |
0.8 | 8 | 12 | 12 | 15 | 19 | 22 | 29 | 33 | 12 | 15 | 15 | 19 | 24 | 27 | 35 | 39 | 15 | 19 | 19 | 23 | 28 | 32 | 40 | 44 |
0.85 | 8 | 10 | 10 | 13 | 17 | 20 | 27 | 30 | 10 | 14 | 14 | 17 | 21 | 24 | 32 | 35 | 13 | 17 | 17 | 20 | 25 | 28 | 36 | 40 |
0.9 | 7 | 9 | 9 | 12 | 16 | 18 | 24 | 27 | 9 | 12 | 12 | 15 | 19 | 22 | 29 | 32 | 12 | 15 | 15 | 18 | 23 | 26 | 33 | 36 |
0.95 | 6 | 9 | 9 | 11 | 14 | 17 | 22 | 25 | 9 | 11 | 11 | 14 | 18 | 20 | 26 | 29 | 11 | 14 | 14 | 17 | 21 | 24 | 30 | 33 |
1 | 6 | 8 | 8 | 10 | 13 | 15 | 21 | 23 | 8 | 10 | 10 | 13 | 16 | 19 | 24 | 27 | 10 | 13 | 13 | 15 | 19 | 22 | 28 | 30 |
1.05 | 5 | 7 | 7 | 10 | 12 | 14 | 19 | 21 | 7 | 10 | 10 | 12 | 15 | 17 | 23 | 25 | 9 | 12 | 12 | 14 | 18 | 20 | 26 | 28 |
1.1 | 5 | 7 | 7 | 9 | 12 | 13 | 18 | 20 | 7 | 9 | 9 | 11 | 14 | 16 | 21 | 23 | 8 | 11 | 11 | 13 | 16 | 19 | 24 | 26 |
1.15 | 5 | 7 | 7 | 8 | 11 | 13 | 17 | 19 | 6 | 8 | 8 | 10 | 13 | 15 | 20 | 22 | 8 | 10 | 10 | 12 | 15 | 17 | 22 | 24 |
1.2 | | 6 | 6 | 8 | 10 | 12 | 16 | 18 | 6 | 8 | 8 | 10 | 12 | 14 | 19 | 20 | 7 | 9 | 9 | 11 | 14 | 16 | 21 | 23 |
1.25 | | 6 | 6 | 7 | 10 | 11 | 15 | 17 | 6 | 7 | 7 | 9 | 12 | 13 | 18 | 19 | 7 | 9 | 9 | 11 | 13 | 15 | 20 | 22 |
1.3 | | 6 | 6 | 7 | 9 | 11 | 14 | 16 | 5 | 7 | 7 | 9 | 11 | 13 | 17 | 18 | 6 | 8 | 8 | 10 | 13 | 14 | 19 | 20 |
1.35 | | 5 | 5 | 7 | 9 | 10 | 14 | 15 | 5 | 7 | 7 | 8 | 10 | 12 | 16 | 17 | 6 | 8 | 8 | 10 | 12 | 14 | 18 | 19 |
1.4 | | 5 | 5 | 6 | 8 | 10 | 13 | 15 | 5 | 6 | 6 | 8 | 10 | 11 | 15 | 17 | 6 | 7 | 7 | 9 | 11 | 13 | 17 | 18 |
1.45 | | 5 | 5 | 6 | 8 | 9 | 13 | 14 | | 6 | 6 | 7 | 9 | 11 | 14 | 16 | 5 | 7 | 7 | 9 | 11 | 12 | 16 | 17 |
1.5 | | 5 | 5 | 6 | 8 | 9 | 12 | 14 | | 6 | 6 | 7 | 9 | 10 | 14 | 15 | 5 | 7 | 7 | 8 | 10 | 12 | 15 | 17 |
1.55 | | | | 6 | 7 | 9 | 12 | 13 | | 5 | 5 | 7 | 9 | 10 | 13 | 15 | 5 | 6 | 6 | 8 | 10 | 11 | 15 | 16 |
1.6 | | | | 5 | 7 | 8 | 11 | 13 | | 5 | 5 | 7 | 8 | 10 | 13 | 14 | 5 | 6 | 6 | 7 | 9 | 11 | 14 | 15 |
1.65 | | | | 5 | 7 | 8 | 11 | 12 | | 5 | 5 | 6 | 8 | 9 | 12 | 14 | | 6 | 6 | 7 | 9 | 10 | 14 | 15 |
1.7 | | | | 5 | 7 | 8 | 11 | 12 | | 5 | 5 | 6 | 8 | 9 | 12 | 13 | | 6 | 6 | 7 | 9 | 10 | 13 | 14 |
1.75 | | | | 5 | 6 | 8 | 10 | 11 | | 5 | 5 | 6 | 7 | 9 | 12 | 13 | | 5 | 5 | 7 | 8 | 10 | 13 | 14 |
1.8 | | | | 5 | 6 | 7 | 10 | 11 | | | | 6 | 7 | 8 | 11 | 12 | | 5 | 5 | 6 | 8 | 9 | 12 | 13 |
1.85 | | | | 5 | 6 | 7 | 10 | 11 | | | | 5 | 7 | 8 | 11 | 12 | | 5 | 5 | 6 | 8 | 9 | 12 | 13 |
1.9 | | | | 5 | 6 | 7 | 10 | 11 | | | | 5 | 7 | 8 | 11 | 12 | | 5 | 5 | 6 | 8 | 9 | 11 | 13 |
1.95 | | | | | 6 | 7 | 9 | 10 | | | | 5 | 7 | 8 | 10 | 11 | | 5 | 5 | 6 | 7 | 9 | 11 | 12 |
2 | | | | | 6 | 7 | 9 | 10 | | | | 5 | 6 | 8 | 10 | 11 | | 5 | 5 | 6 | 7 | 8 | 11 | 12 |
Machin D, Campbell M, Fayers, P, Pinol A (1997) Sample Size Tables for Clinical
Studies. Second Ed. Blackwell Science IBSN 0-86542-870-0 p. 73-74
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