Statistics リファレンス
リファレンス 用 descriptive および inferential statistics: mean, median, variance, hypothesis testing.
Descriptive Statistics
Mean (average) is sensitive to outliers; median is robust. Mode is the most frequent value. Variance and standard deviation measure spread. Quartiles and IQR (Q3-Q1) are robust spread measures. Skewness measures asymmetry; kurtosis measures tail weight. The five-number summary (min, Q1, median, Q3, max) summarizes distribution. Box plots visualize it. Correlation (Pearson r) measures linear relationship; Spearman rho measures monotonic. Covariance Cov(X,Y) = E[XY] - E[X]E[Y]. Choose statistics based on data type and distribution shape.
- mean/median
- Average vs middle
- std dev
- Spread measure
- correlation
- Linear relation
robustness differssqrt(variance)Pearson rInferential Statistics
Hypothesis testing: null (H0) vs alternative (H1). p-value: probability of data given H0. Significance level α (typically 0.05) controls Type I error. Power (1-β) controls Type II error. Confidence intervals estimate parameter ranges. t-test compares means (small samples, unknown variance). Chi-square test compares categorical distributions. ANOVA compares multiple groups. Regression models relationships. The p-value controversy: significance does not imply practical importance. Bayesian inference provides an alternative framework with prior and posterior distributions.
- p-value
- P(data | H0)
- confidence
- Parameter range
- t-test
- Compare means
significance95% CIsmall samples