【文章內容簡介】 isplays “between” and “within” variation 圖上顯示了各分組的平均值 , 再將平均值連起來 The chart displays the means at each subgroup, then connects the means 產量 種類 田 按田按種類苜蓿產量多變量圖 14 質量工具總結 Quality Tools Summary 目視圖表有助于找出根本原因 Visual graphs aid your team in determining possible root causes 有助于支持比較分析 , 即什么缺陷為“是” , 什么缺陷為“不是” Helps in backing up your parative analysis, .. what the defect is and what the defect is not 盡量使用所有工具 , 某個特別圖表或許會讓你有些新發(fā)現 Use all the tools possible….something might jump out at you with a particular graph 圖表可以做得很快 , 盡情使用吧 Graphs can be constructed very quickly, so use them! 15 假設性試驗 Hypothesis Testing Y=f(x1, x2, x3,…) 確定的 X X’s identified X是必然的還是偶然的 ? Is the X significant or is it just chance?? 16 為何使用假設性試驗 Why Hypothesis Testing? 有時 , 圖表顯示不出平均值、變異等的差異 Sometimes it is not graphically obvious that there is a difference in means, variation, etc. 此時 , 決策就會主觀化 In these cases, decisions are subjective 進行假設性試驗 , 客觀地決定是否有差異 Perform a hypothesis test to decide objectively whether there is a difference 所有人都可依數據做出同樣的決定 Everyone makes the same decision based on data 17 假設性試驗 Hypothesis Testing 必須量化及驗證 X和 Y之關系 Need to quantify and verify the relationship between the X’s and Y 虛無假設 Ho State Assumption Null Hypothesis – Ho 對立假設 Ha State Alternative Alternative Hypothesis – Ha 進行試驗 Run Test 解釋結果 Interpret Results 18 P值 P Value 一般工業(yè)標準 ( ) General Industry Standard (.05 or .01) ?P值小于 , 存在差異 Pvalue .05, conclude there is a difference ?出錯機會小于 5% Have 5% chance of being wrong P值是固定的嗎 ?? Is the PValue fixed?? 注意 : 統計上看差異是必然的 , 但它并不一定是重要的或有意義的 NOTE: Just because a difference is statistically significant does not mean that it is important or interesting. 19 假設性試驗的形式 Types of Hypothesis Tests 數據類型 Data World 試驗 Test 作用 Function 連續(xù)性 Continuous 單樣本 T檢驗 1Sample tTest 將平均值與目標值相比較 Compares the mean to a target 雙樣本 T檢驗 2Sample tTest 比較兩個平均值 Compares 2 means 變異數分析 ANOVA 比較兩個或更多平均值 Compares 2 or more means 方差齊性測試 Test for Equal Variances 褶皺檢驗 FTest 比較兩個或更多變異 Compares 2 or more variances 離散性 – 缺陷次數及不良品數據 Discrete (Defect Defective Data) 卡方檢驗 ChiSquare Test 比較同組或同類里的物品數量 Compares the number of items in groups or categories 非參數 Non Parametric 無母 數檢定 KruskalWallis Test 將兩個或更多平均值與未知分布相比較 Compares 2 or more means with unknown distributions 20 假設性試驗總結 Hypothesis Testing Summary 假設性試驗令決策不是靠猜測 , 每人都可以得出相同的結果 Hypothesis testing takes the guess work out of making a decision…everyone will end up with the same answer 用于確定是偶然 , 還是樣品真的有差異 Used to determine if it was just chance or if there really is a difference in samples 記住 : 數據類型決定了測試方法 Remember what data world you are in to determine what kind of test to use 21 線性回歸 Linear Regression 用于描述 2個變量之間的關系 Useful for describing the relationship between 2 variables 當 2個變量有關系時 Used when 2 variables are related 從另一個變量預測這個變量 , 其準確性比偶然性更高 Used to predict one variable from the second variable with better than chance accuracy Ho: 斜度 =0 Slope = 0 Ha: 斜度 ?0 Slope ? 0 22 線性模型 Linear Model DY DX bo = 相交點 intercept b1 = slope = DY DX 結果 Oute : Y = b1x + bo 23 回歸舉例 Regression Example 對年齡與平均車速的關系進行研究 A study was initiated looking at the average car speed of individuals versus the age of the individual. 負相關 Negative Correlation 不相關 No Correlation 斜度 =0 Slope = 0 Y = b1x + b Y = b, 因此 therefore Y = `Y (Y的平均值 ) (mean of Y) 如果不相關會怎么樣 ? What if no correlation? 司機年齡 司機年齡 平均車速 平均車速 24 結果解釋 Interpretation of Results 該差異在統計上有必然較小的比例 Statistically significant Small % of variation explained “不重要 ” “Generally not important” 該差異在統計上并沒有必然較小的比例 Not statistically significant Small % of variation explained “別處看看 ” “Look elsewhere” 該差異在統計上有必然較大的比例 Statistically significant Large % of variation explained “瞧 !” “BINGO!” 該差異在統計上并沒有必然較大的比例 Not statistically significant Large % of variation explained “收集多點數據” “Get more data” R2Adjusted Large R2調整 大 R2Adjusted Small R2調整 小