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Chapter 5 z-Scores
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Descriptive statistics
Central tendency Variability Five-number summary Smallest Q1 Median Q3 Largest Inferential statistics
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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
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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
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“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
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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
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Standardized distribution
Shape 與原來分佈形狀相同 The mean µ= 0 The standard deviation σ= 1
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所有的z-score distribution 皆為µ=0，σ=1的分佈
z-score distribution=standardized distribution
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