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.”
经过一番研究，我发现可以使用t检验或方差分析（ANOVA）检验。t检验使用单一变量来研究两组之间的差异，而自变量必须只有两组。方差分析测试两组或更多组数据之间差异的显著性。自变量必须有两个或更多类别。方差分析只能确定组与组之间存在差异，但不能说明哪组不同。奇怪的是，如果对两个自变量进行方差分析，得出的结果与使用t检验得出的结果是一样的。下面是我的数据快照：
After using the JMP software and turning on the ‘Means/ANOVA/Pooled t’, my data now looks like this:
根据 JMP 支持页面、 "概率 > F 值衡量的是，在除截距外所有参数都为零的情况下，获得与观测值一样大的 F 比值的概率。概率 > F 值越小，表明观察到的 F 比值越小。这样的值被认为是模型中至少存在一个显著效应的证据"。这个数据符合描述，因此我使用了辅助检验，即 Tukey-Kramer 检验来验证我的结果。选择该测试后，数据图像会略微变为这样：
当我第一次使用这个测试时，我并不完全明白这些圆圈代表什么。以下是我找到的最全面的图表。
由于圆圈完全没有重叠，因此结果大相径庭。
当您选择 Tukey-Kramer 分析时，还会弹出一个最小显著性差异或 LSD 阈值矩阵。显示如下：
阅读矩阵的方法是，当您比较 A 和 B 时，有一个正数表示这对平均数有显著差异。
From time to time I will be sprinkling in posts that are different from my standard program of fluxers, preheaters, etc. to discuss other topics or experiments that I have conducted here at the Indium Corporation. Please feel free to reach out and contact me with any questions, concerns, or fun facts. (I love fun facts!!!) I am always open to new ideas and concepts.
