My most recent blog topics have had to do with Wave Soldering Machine Components, but statistics is also something that interests me. Have you ever had to compare two or more sets of data to try and understand if they were unrelated or statistically significant? I recently had to solve this problem for myself by comparing variables from two different SMT assembly machines.
This is the first time that I had to use statistics since I took the course in college, so I had to brush up on a few things. The particular test that I needed to perform was unclear to me at the start of the analysis. Let me say that the machines were measuring the exact same variable, the only difference was the machine. I wanted to understand which machine was more accurate. Or, better yet, if there was a statistically significant difference between the two sets of results. Let’s start off with the definition of “statistically significant.” According to Google,the definition of statisticallysignificant is. “the likelihood that a result or relationship is caused by something other than mere random chance.Statisticalhypothesis testing is traditionally employed to determine if a result isstatisticallysignificantor not.”
經過一番研究後，我發現我可以使用t-test 測試或方差分析 (ANOVA) 測試。t-test 使用單一變數來檢視兩個群組之間的差異，而自變數必須只有兩個群組。ANOVA 分析則測試兩組或更多組數據之間差異的顯著性。自變量必須有兩個或兩個以上的類別。方差分析只能判定組別之間有差異，但無法判定哪一組有差異。奇怪的是，如果您對兩個自變數執行方差分析，您會得到與使用t-test 相同的結果。以下是我的資料快照：
After using the JMP software and turning on the ‘Means/ANOVA/Pooled t’, my data now looks like this:
根據 JMP 支援頁面、 "概率 > F 值衡量的是在除截距外所有參數都為零的情況下，獲得與觀察到的一樣大的 F Ratio 的概率。概率 > F 的小值表示觀察到的FRatio不大可能出現。這樣的值被認為是模型中至少有一個顯著效應的證據。"這個資料符合描述，因此我使用了次要測試，Tukey-Kramer 測試來驗證我的結果。當您選擇這個測試時，資料的影像會稍微變成這樣：
當我第一次使用這個測試時，我並不完全了解圓圈所代表的意義。以下是我找到的最全面的圖表。
因為圓圈完全沒有重疊，所以結果有明顯的不同。
當您選擇 Tukey-Kramer 分析時，也會彈出最小顯著差異或 LSD Threshold 矩陣。顯示如下：
閱讀矩陣的方法是，當您比較 A 和 B 時，有一個正數表示這對均值有顯著差異。
我將不時在文章中加入不同於我標準程式的 通量, 預熱器等，討論其他主題或我在 Indium Corporation 進行的實驗。如有任何問題、疑慮或趣事，請隨時與我聯絡。(我喜歡有趣的事實！！）我總是對新的想法和概念持開放態度。
