Some thoughts of statistical tests

1. Common statistical tests are linear models

A post by Jonas Kristoffer Lindeløv points out most of the common statistical tests are actually linear models (at least are special cases or very close). With this idea in mind, teaching and learning those statistical tests becomes easier.

The author summarized all these statistical models into a very nice and clear table, which is shown as follows (to be updated):

2. Bayesian vs. Frequentist

The famous webcomic xkcd has summarized the technical differences between Bayesian and frequentist approaches. (Bayesian vs. Frequentist_by xkcd.png)

Frank Harrell, professor of Biostatistics at Vanderbilt University, talked about his journey from frequentist to Bayesian statistics in his personal webpage. He argues that estimation, which is the focus of Bayesian modeling, is more relevant than traditional questions and hypotheses. We should clear up the common misconception that “absence of evidence is not evidence of absence”. He also points out that many investigators have misunderstanding and misinterpretation when adopting frequentist approach. He ends the post with two nice equations contrasting frequentist and Bayesian approaches:

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Some good resources or tools I would like to recommend to do statistical tests are Laerd Statistics (mainly focus on step-by-step explanation of SPSS), JASP (very user-friendly and for FREE; you can choose either frequentist approach or Bayesian one). Professor Harrell also mentioned the tool Stan, which is based on most popular data analysis langauges, such as R, Python.