Chapter 5 z-Scores
Descriptive statistics Central tendency Variability Five-number summary Smallest Q1 Median Q3 Largest Inferential statistics
Example 5.1 你的統計考76分,將如何判斷你考的好不好? 若全班分數的mean=70 若全班分數的σ=3 若全班分數的 σ=12
z-Score=standard score 每一觀察值(x)都可以轉換成z分數 得知z分數可以 In a single distribution:了解每個觀察值在整體資料分佈的相對位置 (relative location) in comparing two distributions: z 分數可形成”標準化分佈”,標準化分佈可以進行比較
“標準化”的概念 標準化 standardization 為何要將原使分數標準化? raw scores z-scores or
z-score: Sing: +/-符號告訴你關察值比mean大(+)或小(-) Magnitude: 數值告訴你該關察值距離mean有多遠 若將每一關察值轉換成z-score,則整體分佈(distribution)則轉換成”標準分佈”(standardized distribution) Standardized distribution is to make dissimilar distribution comparable
Standardized distribution Shape 與原來分佈形狀相同 The mean µ= 0 The standard deviation σ= 1
所有的z-score distribution 皆為µ=0,σ=1的分佈 z-score distribution=standardized distribution