【正文】 ernal Use Only 63 Example: Comparing Two Means Of Two Samples 例 : T值的計算 (比較二個樣本均值 ) A plant has two PET lines with identical equipment, except for the carbonators. It is believed that the carbonators behave the same on The average. The hypothesis was tested . 一工廠的二條 PET 生產線除碳酸化器外其它設備完全相同．工廠認為二個不同碳酸化器性能沒有差異，并對此假設作了檢驗， 獲表中所列數據 (Step 1)． Is there evidence to indicate the two carbonators are not giving the same performance? Stated another way: 有證據表明二個不同碳酸化器性能有差異嗎 ? x1x2?Classified Internal Use Only 64 Example: Comparing Two Means Of Two Samples 例 : T值的計算 (比較二個樣本均值 ) Step 2 計算 3個過程數 : n1 = n2 = 5 = = S1 = S2 = x1Step 3 計算組合方差 : Sp = x2? ?? ? ? ?? ?2551515 222???????? ???????? ??sp 007 2 ?sp 0077 ?s pClassified Internal Use Only 65 Example: Comparing Two Means Of Two Samples 例 : T值的計算 (比較二個樣本均值 ) Step 4 計算 T 統(tǒng)計值 : t = ? ? ???????????????5151tStep 5 計算自由度 : n1 + n2 – 2 = 5 + 5 – 2 = 8 degrees of freedom Classified Internal Use Only 66 Example: Comparing Two Means Of Two Samples 例 : T值的計算 (比較二個樣本均值 ) Step 7 查表確定 T 臨界值 T 臨界值 = ?Step 8評價結果 : The T statistic is greater than T critical: The two processes are not averaging the same. 沒有證據表明二過程是以同一均值運行的． Step 6 確定恰當的 值 : = ??Classified Internal Use Only 67 STEP 1 Randomly sample from the two processes under investigation. 由受檢二過程隨機采樣 . SUMMARY STEP 2 Calculate 3 pieces of information for each process. 計算出二過程的三個數據： 樣品數： n1 = n2 = 5 過程 均值： 1 = 2 = 樣本標準偏差 ： S1 = S2 = STEP 3 計算組合方差參數 Sp = Step 5 計算自由度 n1 + n2 – 2 = 5 + 5 – 2 = 8 STEP 7 T 臨界值 = STEP 6 = STEP 8 T 統(tǒng)計值 T 臨界值 ? 原 假設 (無差異假設 ) 檢驗的結論是否定的 The two processes are not averaging the same. 沒有證據表明二過程以同一均值運行 xxSTEP 4 計算 T 統(tǒng)計值 t = Classified Internal Use Only 68 Performing TTest (paired difference) 用 T檢驗 (配對比照檢驗 ) ? Step 1 由受檢過程隨機采樣． Randomly sample from the process under investigation. ? Step 2 Split each homogeneous sample into two identical halves. 將每批樣品均分為二份． ? Step 3 Randomly assign each half to the labs or the instruments. 隨機分配樣品． ? Step 4 Test the material for each half by each lab or instrument. 測試樣品 ? Step 5 Calculate d 計算 d. ? Step 6 Calculate dbar 計算 d 均值． ? Step 7 Calculate Sd 計算 Sd ( d 值標準偏差 ). ? Step 8 計算 T值 . Calculate T statistical. ? Step 9 計算自由度． Calculate the appropriate degrees of freedom. ? Step 10 確定恰當的 值． Decide on an appropriate false alarm rate. ? Step 11 查表確定 T臨界值 . Determine the critical value of T from the table. ? Step 12 評價結果 Evaluate the results. ?Classified Internal Use Only 69 Example: Compare Process Averages Using Paired Difference 例： T 檢驗 (配對比照 ) A lab of the bottling plant wants to make sure if its spectrophotometer performs the same for the same sample as the spectrophotometer of a validated lab. 21 batches of syrup are split into halves and assigned one each half to its own lab and the validated lab for testing according to the procedures Step 1 4. 裝瓶廠 QC 為了證實其實驗室分光光度計與認可實驗室的測試結果在樣品包含的時間段內是否存在顯著差異，將 21 批產品按配對比照方法 Step 14 隨機分成各二份 , 分別測試，用 T 檢驗分析數據． Classified Internal Use Only 70 Split And Assign Samples 由過程采集的樣品 隨機樣 1 隨機樣 2 隨機樣 3 隨機樣 4 比照儀器 2 比照儀器 1 Classified Internal Use Only 71 Example: Compare Process Average Using Paired Difference 例： T 檢驗 (配對比照 ) Step 5 Calculate d d = The difference between the paired halves. Step 6 Calculate = ndd ??Step 7 Calculate = ? ?12?? ?? nddsdsddClassified Internal Use Only 72 Example: Compare Process Average Using Paired Difference 例： T 檢驗 (配對比照 ) Step 8 Calculate T statistic 21438 ???????????????ndts dT statistic = Step 9 Calculate degrees of freedom degrees of freedom = 21 – 1 = 20 Step 10 Decide appropriate level false alarm rate = ?Classified Internal Use Only 73 Example: Compare Process Average Using Paired Difference 例： T 檢驗 (配對比照 ) Step 11 Determine critical value of T from the table T critical = Step 12 Evaluate the result T statistic is smaller than T critical : We conclude that there is no enough evidence to indicate that the two pieces of testing equipment are performing differently over time. 沒有充分證據表明該廠實驗室的測試結果與認可 實驗室的測試結果在樣品包含的時間段內存在顯著差異 Classified Internal Use Only 74 謝謝！ 謝謝觀看 /歡迎下載 BY FAITH I MEAN A VISION OF GOOD ONE CHERISHES AND THE ENTHUSIASM THAT PUSHES ONE TO SEEK ITS FULFILLMENT REGARDLESS OF OBSTACLES. BY FAITH I BY FAITH