2022-01-17 实验设计与分析 周迎春 、王亚平

中国慕课上，上完了周迎春 、王亚平开设的《实验设计与分析 》，课程围绕单因子实验和多因子的析因实验展开。

学习如下

1. F统计量可以检测以上所有实验的显著性。
2. 线性代数很重要，就算只有单一因子的实验，也有多种处理方式、多次重复实验产生的结果向量，如果再考虑不同干扰因素，如材料批次、操作人员等，就会组成矩阵运算。

我未来有多大概率会应用这门课所学呢？实验设计起自1920年的Ronald A. Fisher，至1980年代成熟。经济学少用实验室的数据，上述实验结果检测方法推广到无重复实验、缺乏完整比较对照组的资料框架下，应该用了其他进阶的方法。概率可能偏低。

但我运用这门课复习了t检定量、熟悉了中国的统计学名词翻译，如：

• 方差 (variance) 是各数据偏离平均值 差值的平方和 的平均数

  
  

• 均方误差 (MSE, mean squared error) 是各数据偏离真实值 差值的平方和 的平均数

  
  

上课过程中，我发现3本不错的工具书
简体： 医学统计学笔记与R
繁体： 生医研究之统计方法
英文：JABSTB: Statistical Design and Analysis of Experiments with R

其中尤其有趣的是英文网页这段：

5.1 Our philosophy matters

When I say philosophy I’m thinking in terms of the fundamental ideas. Do you think truth is absolute and attainable, or is it provisional? What is the nature of evidence? What are the merits of inductive and deductive reasoning and how much weight should we give to each? How should you test hypotheses, through affirmation or falsification? Do I lean more Popperian (deduction, falsification) than Carnapian (induction, confirmation)?

Uncertainty is the domain of statistics. By what criteria can we ensure we are minimizing mistakes? By what criteria will we validate an observation? How will we ensure a hypothesis has been well-tested? The answers to this group of questions are found in inferential statistics, which in turn use probability.

One decision you’ll have to make is to choose which of these frameworks to apply for our work: Bayesian statistics or the Fisher/Neyman-Pearson based error statistics, aka “frequentism?”. In the Bayesian framework, which is the older of the two, the rules of probability are used to represent the plausibility of a hypothesis under the observed data. In the Fisher/Neyman-Pearson framework, probability is used to assess the plausibility of the data under a null hypothesis.

(The inferential statistics you will learn are mostly frequentist.)

Equally reasonable people choose either framework. If we search for “Bayesian v frequentism” we run smack dab into what are called the statistics wars. In one or two clicks you are sure to stumble into impassioned arguments on each side. Perhaps one will resonate.

实验的路径多是观察归纳，以判断假说是否成立。
学术研究的路径，未来可期