Here is a discussion that I recently had with my colleague John. He approached me with the following request:
“I sent a manuscript to Nature and it is going quite well. Actually the reviewers are rather positive, but one of them asks us to justify better why we used a one-tailed t test to find the main result. What should I write in the methods section?
— It depends. Why did you use a one-tailed t test?
— Well, we first tried the standard t test, but it was borderline significant. My student realized that if we used the one-tailed t test, the result was significant so we settled for this variant. We specified this clearly in the text, and I am now surprised that I have to justify it. Isn’t it just an accepted variant of the t test?
— To be honest, I understand your confusion. The guidelines are rather ill-defined. Actually, Nature journals make it worse by requesting this information for every test, even for those that are only one-tailed like the chi-square.
— OK, but what should I do now? For instance, how do you justify using a one-tailed t...
You went to high school and you learned genetics. You heard about a certain Gregor Mendel who crossed peas and came up with the idea that there is a dominant and a recessive allele. You did not particularly like the guy because there would always be a question about peas with recessive and dominant alleles at the exam. But you grew up, became wiser and just as you started to like him, you heard from someone that he faked his data. You felt disoriented for a while, why annoy you with this stuff at school if it is wrong? But then you came to the conclusion that he just got lucky and that he was right for the wrong reasons. After all, he was just a monk on gardening duties, why would you expect him to understand anything about real science?
Gregor Mendel was a monk, but he was also a trained scientist. He studied assiduously for twelve years (including about seven years on physics and mathematics), to then become a teacher of physics and natural sciences at the gymnasium of Brno. He prepared his most famous experiment for two years, meticulously checking and choosing his...
The first thing you learn in statistics is that “correlation does not imply causation”. As obvious as it sounds, most human mistakes fall in this category, and not only in statistics. The major difficulty with this question is that it is fairly easy to define correlation, but it is much harder to define causation, let alone quantify it. No surprise many statisticians just avoid talking about causation to stay out of the danger zone.
I see no greater impediment to scientific progress than the prevailing practice of focusing all our mathematical resources on probabilistic and statistical inferences while leaving causal considerations to the mercy of intuition and good judgment.
This book lays the foundation of the now popular Bayesian networks. The key idea is that you can distinguish correlation from causation if you can observe several independent causes. For instance, suppose that patients suffering from a certain type of cancer are often immunodeficient. You wonder whether immunodeficiency is a cause or a consequence of this cancer type.
Say that variable A is whether patients have...
A colleague of mine (let’s call him John) recently put me in a difficult situation. John is a very good immunologist who, as nearly everybody in the field, had to embrace the “omics” revolution. Spirited and curious, he has taken the time to look more closely into statistics and he now has an understanding of most popular parametric and nonparametric tests. One day, he came to me with the following situation.
“I have this gene expression data, you see... I know that a gene is up-regulated, but it is just not significant...