PARTI: Notion of Probablity

Chapter 1. Basic Probability Theory 必要な確率論

  • Slides set 1 (pdf)
    • 1.1 Counting　数える
    1.2 Probability rules
  • Slides set 2 (pdf)
    • 1.3 Conditional Probability, Independence, Bayes theorem　　条件付き確率、独立性、ベイズの定理

    Chapter 2: Random Variables 確率変数

  • Slides set 3 (pdf)
    • 2.1 Discrete Random Variables　離散悪率変数
    2.2 Some important Discrete Random Variables 幾つかの大事な分布
    2.3 Operations on random variables 確率変数への作用
    2.4 Expected value 期待値
    2.5 Variance (discrete case) 分散　（離散の場合）
  • Slides set 4 (pdf)
    • 2.6 Continuous random variable 連続確率変数
    2.7 Some important continuous random variables 大事な連続確率変数の分布
    2.8 Expected value and variance (continuous case)

    Chapter 3: Sampling Distribution and Central Limit Theorem 標本分布中と心極限定理

  • Slides set 5 (pdf)
    • 3.1: Introduction to Sampling
    3.2 Law of Large Numbers (LoLN) and Central Limit Theorem (CLT)大数の法則と中心極限定理
    3.3 Application of the CLT to infer the mean
  • Slides set 6 (pdf)
    • 3.4 More on sample statistics

    PARTII: Statistical Inference

    Chapter 4: Null Hypothesis Significant Test (NHST 帰無仮説検定)

  • Slides set 7 (pdf)
    • 4.1: Concepts and 1st example: z-test
  • Slides set 8 (pdf)
    • 4.2 chi2 and sample variance カイ二乗検定と標本偏差
    4.3 the Student t-test　(small or large sample mean: 小or大標本平均)
    4.4 Two-sample t-test (equal variance) ２標本ｔ検定 (同偏差)
    4.5 Paired difference sampling 対応のあるデータ
    4.6 Comparing two population variances: F-test 二つの母集団の偏差を比較する：F検定
  • Slides set 9 (pdf)
    • 4.7 chi2-test (goodness-of-fit)カイ二乗(簡単な適合度検定)
    4.8 chi2-test of independence独立性のカイニ乗検定
    4.9 chi2-testfor Homogeneity 同質性の検定
    4.10 One-way ANOVA (F-test)一元配置分散分析(F検定)

    Chapter5: Confidence Intervals 信頼区間

  • Slides set 10 (pdf)
    • 5.1 Introduction and CI for normal data (入門、正規母集団のために信頼区間)
    5.2 CI and NHST 信頼区間と帰無仮説検定の関係
    5.3 Non-normal data and polling 正規でない母集団と投票
    5.4 CI for comparing two populations 母集団の二つを比する信頼区間

    Chapter 6: Simple Linear Regression（単）線形回帰

  • Slides set 11 (pdf)
    • 6.1 Introduction　
    6.2 Estimation for simple linear regression
    6.3 Confidence Intervals for a and b
    6.4 Prediction interval
  • Slides set 12 (pdf)
    • 6.5 Relationship with correlation