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Outline

PERAL Lab Meeting

  • 時間：111 年 7 月 22 日 10:30

  • 地點：Online

  • 出席者：吳坤熹老師、謝萬霖、周以恆、吳騰然、劉怡君、田蕙瑜、洪胤勛、丘世宇、莊才賢、紀見如、劉冠伶、林大智、繆亭霄

  • 會議主題： Statistics - Z-Test & T-Test

  • 主講者: 田蕙瑜

  • 主記: 紀見如

會議內容

  • Image Not Showing Possible Reasons
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    • Hypothesis Testing:驗證是否正確

  • Terminoly: 在統計中，我們想要檢測的母體

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  • Central Limit Therom(CLT，中央極限定理)

    • 整個統計的核心，最常被使用到
    • 不論母體的分布，在進行多次的抽樣時，都會變成 Normal Distribution
    • sample size 愈大時，表現愈明顯

  • Central Limit Throm Example

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    • 舉例: 骰子
    • 結論: 當數值愈大，結果愈接近常態分布

Inferential Statistics(推論統計)

  • Empirial Rule

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    • ± 一個標準差:68%
      ± 兩個標準差:95%
      ± 三個標準差 :99.7%

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  • Z-Distribution

    • also standard Normal Distribution
    • 把常態分布進行標準化的動作，可以對不同資料互相比較離散程度
      • mean mu = 0
      • standard deviation = 0

  • Image Not Showing Possible Reasons
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    • Q1:
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    • Q2: 利用反查表
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    • 利用z-distribution 可以找到相對準確的數值

  • Hypothesis Testing

    • Htpothesis Testing
      • 類似反證法
    • critical value

Hypothrdid testing(提出假說)

  • Image Not Showing Possible Reasons
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    • H0 : 新方法沒有比舊方法好
    • H1 or Ha: 新方法比舊的方法好

  • Hypothesis Testing

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    • 分成三個類別
      • lower-tail: 左邊是希望檢測的H0
      • upper-tail: H0比檢測的母體還要小
      • two-tail: 檢測值同時在左右兩端

  • Steps of Hypothesis Testing

    • Image Not Showing Possible Reasons
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    • alpha : 想要知道有多少準確率
    • approch : 選擇方法來驗證是否為真

  • Z-Test – p-Value Approch

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    • 舉例 : 咖啡罐是否都大於三磅
      • 檢定:找出小於三磅的咖啡來推翻
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      • 需先知道 樣本標準差 0.03
      • 最後可由查表來知道結果
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      • 圖為lower-tail
      • 得出的平均值並沒有都大於三磅
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      • 使用z值當作否決的關鍵
      • alpha = 0.01 約為-2.3跟-2.49之間
      • 可得z值為-2.33
      • 母體平均值比3還要小

總結

  • Image Not Showing Possible Reasons
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建議&問題

  1. P.8 "Expirial" -> "Empirical"? solomon
    Ans: Empirial

  2. P.9 How many students will have grades >= 50? Solomon
    Ans: (100-68)/2 = 16% Jerry

  3. P.11 計算有誤 (62.5-40)/10 solomon
    Ans: 2.25

  4. P.11 查表 Q2 = 1 - 0.9878 solomon
    Ans: 0.0122(1.22% 左右)

  5. p.14 左邊第一章圖 mu跟mu0 是否可以標出來solomon
    Ans: 因為圖已經經過標準化處理，無法標出，可以直接看實際的例子。
    補充: mu0是我們的假設值，這三張圖提供根據實際情況跟目的不同，採用不同的方法

  6. 咖啡罐是否都大於三磅，還是平均值大於等於三磅solomon
    Ans:平均值

  7. p.16 mu是平均值?Eager
    Ans:不應該強調每一罐，而是平均值

  8. p.16 目標:要證明>=三磅? [name=]
    Ans:現在要證明低於三磅

  9. p.18 Why 0.038 < 0.01 ? solomon
    Ans:更正0.0038

  10. p.19 why 得到z值後，可以直接確認結果? jennifer
    Ans:同11

  11. p.15 可以在解釋一次alpha asheley
    Ans:這裡的alpha是一個設定的數值，是目前檢定資料裡面會包含多少%的資料在裡面，看p22，alpha = 1-CL

  12. 如果假設錯誤，會不會影響結果Lawrence
    Ans:會
    補充:可能假說正確，但數據偏差大

  13. p.18 這兩個方法差異在哪?August
    Ans: p使用機率 來確認h0會不會發生，c是利用實際的數值，超過代表h0是錯的

  14. p.3 statisicse 更正August

  15. 中央極限定理至少需要多少樣本 Jerry
    Ans: 30

  16. p.3 敘述統計沒有推翻?Branko
    Ans: 敘述統計沒有推論假說，推論統計包含但不限於假說檢定

  17. p.14 假設有下面三種情況，紅白交界處是設定的a，若算出來落在紅色，則ha，白色則為h0秋分
    Ans: 完全正確

  18. 要假設預期會被推翻的假說?phoebe
    Ans: 可以這麼說

  19. 咖啡的範例phoebe
    Ans: 站在消費者的角度來檢查商家，找到一個小於三磅的咖啡罐 h0就是錯的
    想要驗證的放在ha

  20. =3跟>=3 如何處理phoebe
    Ans:剛剛的alpha是0.01包含整個深色範圍

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  21. p.19 critical value在統計學中的命名由來Toby
    Ans:關鍵性的、臨界值

  22. p.17 alpha是否為0.01 toby
    Ans:是

  23. 之後的報告會圍繞統計嗎Eager
    Ans:是

  24. z-table 是裡面的數值 ，可否提供計算公式 Eager
    Ans:In Excel, Z.TEST(array,x,[sigma])

  25. p.17 why樣本標準差可以這樣計算 Eager
    Ans:其中有省略一些，前提為母體已知且常態分佈才可以套用公式
    帶補充

待追蹤事項

無

臨時動議

無

散會結束時間：12:14

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