検出力分析を使用して研究に必要なサンプルサイズを計算します。t検定、分散分析、相関、カイ二乗、比率検定に対応しています。
Sample size calculation (also called power analysis) determines the minimum number of participants needed for a study to detect a meaningful effect. It is a critical step in research planning — too few participants and you risk missing a real effect (Type II error); too many and you waste time and resources. Most IRBs (Institutional Review Boards) and grant agencies require a formal power analysis as part of the research proposal.
Every power analysis involves four interconnected parameters. If you know any three, you can solve for the fourth. In practice, researchers most commonly fix alpha, power, and effect size to solve for sample size (N).
1. Effect Size (d, f, r, or w)
The expected magnitude of the effect you want to detect. Larger effects require fewer participants. Use Cohen's d for t-tests, Cohen's f for ANOVA, r for correlation, and Cohen's w for chi-square tests. If you don't know the expected effect size, use conventions: small, medium, or large.
2. Significance Level (α)
The probability of a Type I error — rejecting the null hypothesis when it is actually true (a false positive). The conventional level is α = .05, meaning a 5% chance of incorrectly declaring significance.
3. Statistical Power (1 - β)
The probability of correctly detecting a real effect — avoiding a Type II error (a false negative). The conventional minimum is .80 (80%), meaning an 80% chance of finding the effect if it truly exists. Some fields recommend .90 or higher.
4. Sample Size (N)
The total number of participants required. This is typically the unknown you solve for. More participants increase power but also increase cost and time.
Jacob Cohen (1988) established widely-used conventions for small, medium, and large effect sizes. Use these when you lack pilot data or prior research to estimate the expected effect.
| Test | Measure | Small | Medium | Large |
|---|---|---|---|---|
| T-tests | Cohen's d | 0.20 | 0.50 | 0.80 |
| ANOVA | Cohen's f | 0.10 | 0.25 | 0.40 |
| Correlation | r | 0.10 | 0.30 | 0.50 |
| Chi-square | Cohen's w | 0.10 | 0.30 | 0.50 |
| Proportions | Cohen's h | 0.20 | 0.50 | 0.80 |
A researcher plans to compare exam scores between two teaching methods. Based on prior literature, they expect a medium effect size (Cohen's d = 0.50). They set α = .05 and power = .80.
Parameters
Result
Required sample size: N = 128 (64 per group)
A power analysis for an independent-samples t-test was conducted using an effect size of d = 0.50, α = .05, and power = .80. The required sample size is N = 128 (64 per group).
Include the power analysis in the Participants or Method section of your paper. State the test type, effect size, alpha level, desired power, and resulting sample size.
T-Test Example
An a priori power analysis for an independent-samples t-test was conducted using StatMate (Cohen's d = 0.50, α = .05, power = .80). The required minimum sample size was determined to be N = 128 (64 per group).
ANOVA Example
A power analysis for a one-way ANOVA with 4 groups was conducted using Cohen's f = 0.25 (medium effect), α = .05, and power = .80. The minimum required sample size wasN = 180 (45 per group).
StatMate's sample size calculations use the standard normal approximation method with exact z-scores from the jStat library. For t-tests, the formula is n = (zα/2 + zβ)2 × 2 / d2. Achieved power is computed by back-solving using the calculated sample size. Results have been validated against G*Power and R's pwr package.
t検定
2群の平均値を比較
分散分析
3群以上の平均値を比較
カイ二乗検定
カテゴリ変数の関連を検定
相関分析
関係の強さを測定
記述統計
データを要約
1標本t検定
既知の値との比較
マン・ホイットニーU
ノンパラメトリック群間比較
ウィルコクソン検定
ノンパラメトリック対応検定
回帰分析
X-Yの関係をモデル化
重回帰分析
複数の予測変数
クロンバックのα
尺度の信頼性
ロジスティック回帰
二値アウトカムの予測
因子分析
潜在因子構造の探索
クラスカル・ウォリス
ノンパラメトリック3群以上比較
反復測定
被験者内分散分析
二元配置分散分析
要因計画の分析
フリードマン検定
ノンパラメトリック反復測定
フィッシャーの正確検定
2×2表の正確検定
マクネマー検定
対応のある名義データの検定
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