Introduction
Parameter | Description | Effect on sample size |
---|---|---|
Alpha (α) | The probability of falsely rejecting the null hypothesis (H0) (i.e., false positive result or type I error)a [5] | The lower α, the higher the sample size |
Beta (β) | The probability of falsely accepting the null hypothesis (H0) (i.e., false negative result or type II error)a [5] | The lower β, the higher the sample size |
Power (1 − β) | The probability of correctly rejecting the null hypothesis (H0)a [5] | The higher 1 − β, the higher the sample size |
Effect size (d or f) | Degree of deviation of an experimental situation compared to an actual situation (i.e., how much does an experiment deviate from reality) [5] | The higher d or f, the lower the sample size |
Variance (σ
2) | Expression of the spreading of data around a mean value [5] | The higher σ
2, the higher the sample size |
Noncentrality parameter (λ) | Degree of deviation from the original distribution [15] |
λ = 0: original distribution λ > 0: increasing noncentrality |
Calculation of the sample size in general cases
Two independent means (Student’s t test)
α
|
β
| Power (1 − β) | Sample size (n)a
|
---|---|---|---|
0.05 | 0.20 | 0.80 | 39 |
0.05 | 0.10 | 0.90 | 52 |
0.05 | 0.05 | 0.95 | 65 |
0.01 | 0.20 | 0.80 | 58 |
0.01 | 0.10 | 0.90 | 74 |
0.01 | 0.05 | 0.95 | 89 |
Multiple means (ANOVA)
α
|
f
|
N (k = 3) |
N (k = 4) |
N (k = 5) |
N (k = 8) |
N (k = 10) |
---|---|---|---|---|---|---|
0.01 | 0.10 | 1395 | 1552 | 1685 | 1992 | 2160 |
0.01 | 0.25 | 228 | 256 | 275 | 328 | 360 |
0.01 | 0.40 | 93 | 104 | 115 | 136 | 150 |
0.05 | 0.10 | 969 | 1096 | 1200 | 1448 | 1580 |
0.05 | 0.25 | 159 | 180 | 200 | 240 | 260 |
0.05 | 0.40 | 66 | 76 | 80 | 104 | 110 |
Statistical power and effect size of postmortem studies
References | Sample size (n) | Number of groups | Effect size |
---|---|---|---|
Rognum et al. [16] | 87 | 4 | 0.36 |
Sato et al. [17] | 18 | 6 | 1.05 |
Singh et al. [18] | 474 | 9 | 0.18 |
Singh et al. [19] | 1026 | 15 | 0.13 |
Wehnet et al. [20] | 128 | 45 | 0.55 |
Mihailovic et al. [21] | 320 | 10 | 0.22 |
Lemaire et al. [22] | 30 | 4 | 0.65 |
Laruelle et al. [23] | 34 | 4 | 0.60 |
Pelander et al. [24] | 50 | 2 | 0.40 |
Vujanić et al. [25] | 540 | 6 | 0.15 |
Krap et al. [26] | 10 | 2 | 1.01 |
Li et al. [27] | 283 | 4 | 0.20 |
Zhu et al. [28] | 405 | 5 | 0.17 |
Koopmanschap et al. [29] | 117 | 3 | 0.29 |
Zhu et al. [30] | 234 | 4 | 0.22 |
Huang et al. [31] | 90 | 10 | 0.43 |
Zheng et al. [32] | 111 | 37 | 0.56 |
Li et al. [33] | 12 | 2 | 0.90 |
Rognum et al. [34] | 32 | 3 | 0.58 |
Maeda et al. [35] | 140 | 4 | 0.28 |
Zhu et al. [36] | 409 | 15 | 0.21 |
Frere et al. [37] | 10 | 2 | 1.01 |
207.3 ± 246.5 | 8.9 ± 11.1 | 0.46 ± 0.30 |
References | Sample size (n) | Number of groups | Achieved power (1 − β) |
---|---|---|---|
Mao et al. [11] | 160 | 2 | 0.99 |
Moriya and Hashimoto [38] | 6 | 2 | 0.14 |
Mao et al. [39] | 48 | 6 | 0.62 |
Querido and Pillay [40] | 36 | 6 | 0.46 |
Laiho and Pentillä [12]a
| 116 | 8 | 0.96 |
73.2 ± 63.0 | 4.80 ± 2.68 | 0.63 ± 0.36 |