I thought I should update the blog even though these days I don’t do a lot of blogging-worthy stuff.
i. A blog I recently discovered: Empirical Zeal. There’s some interesting posts there, for example I liked this one on the state of Indian rural education (though the findings reported are not exactly worthy of celebration).
ii. The acquisition of language by children. From the introduction:
“Imagine that you are faced with the following challenge. You must discover the internal structure of a system that contains tens of thousands of units, all generated from a small set of materials. These units, in turn, can be assembled into an infinite number of combinations. Although only a subset of those combinations is correct, the subset itself is for all practical purposes infinite. Somehow you must converge on the structure of this system to use it to communicate. And you are a very young child.
This system is human language. The units are words, the materials are the small set of sounds from which they are constructed, and the combinations are the sentences into which they can be assembled. Given the complexity of this system, it seems improbable that mere children could discover its underlying structure and use it to communicate. Yet most do so with eagerness and ease, all within the first few years of life.”
It’s actually pretty wild, once you start thinking about it.
iii. The Null Ritual – What You Always Wanted to Know About Significance Testing but Were Afraid to Ask (via Gwern? I no longer remember how I found this.). An excerpt from the article:
“Question 1: What Does a Significant Result Mean?
What a simple question! Who would not know the answer? After all, psychology students spend months sitting through statistics courses, learning about null hypothesis tests (significance tests) and their featured product, the p-value. Just to be sure, consider the following problem (Haller & Krauss, 2002; Oakes, 1986):
Suppose you have a treatment that you suspect may alter performance on a certain task. You compare the means of your control and experimental groups (say, 20 subjects in each sample). Furthermore, suppose you use a simple independent means t-test and your result is signifi cant (t = 2.7, df = 18, p = .01). Please mark each of the statements below as “true” or “false.” False means that the statement does not follow logically from the above premises. Also note that several or none of the statements may be correct.
(1) You have absolutely disproved the null hypothesis (i.e., there is no difference between the population means). ® True False ®
(2) You have found the probability of the null hypothesis being true. ® True False ®
(3) You have absolutely proved your experimental hypothesis (that there is a difference between the population means). ® True False ®
(4) You can deduce the probability of the experimental hypothesis being true. ® True False ®
(5) You know, if you decide to reject the null hypothesis, the probability that you are making the wrong decision. ® True False ®
(6) You have a reliable experimental finding in the sense that if, hypothetically, the experiment were repeated a great number of
times, you would obtain a significant result on 99% of occasions. ® True False ®
Which statements are true? If you want to avoid the I-knew-it-all-along feeling, please answer the six questions yourself before continuing to read. When you are done, consider what a p-value actually is: A p-value is the probability of the observed data (or of more extreme data points), given that the null hypothesis H0 is true, defined in symbols as p(D |H0).Th is defi nition can be rephrased in a more technical form by introducing the statistical model underlying the analysis (Gigerenzer et al., 1989, chap. 3). Let us now see which of the six answers are correct:
Statements 1 and 3: Statement 1 is easily detected as being false. A significance test can never disprove the null hypothesis. Significance tests provide probabilities, not definite proofs. For the same reason, Statement 3, which implies that a significant result could prove the experimental hypothesis, is false. Statements 1 and 3 are instances of the illusion of certainty (Gigerenzer, 2002).
Statements 2 and 4: Recall that a p-value is a probability of data, not of a hypothesis. Despite wishful thinking, p(D |H0) is not the same as p(H0 |D), and a significance test does not and cannot provide a probability for a hypothesis. One cannot conclude from a p-value that a hypothesis has a probability of 1 (Statements 1 and 3) or that it has any other probability (Statements 2 and 4). Therefore, Statements 2 and 4 are false. The statistical toolbox, of course, contains tools that allow estimating probabilities of hypotheses, such as Bayesian statistics (see below). However, null hypothesis testing does not.
Statement 5: The “probability that you are making the wrong decision” is again a probability of a hypothesis. This is because if one rejects the null hypothesis, the only possibility of making a wrong decision is if the null hypothesis is true. In other words, a closer look at Statement 5 reveals that it is about the probability that you will make the wrong decision, that is, that H0 is true. Thus, it makes essentially the same claim as Statement 2 does, and both are incorrect.
Statement 6: Statement 6 amounts to the replication fallacy. Recall that a p-value is the probability of the observed data (or of more extreme data points), given that the null hypothesis is true. Statement 6, however, is about the probability of “significant” data per se, not about the probability of data if the null hypothesis were true. The error in Statement 6 is that p = 1% is taken to imply that such significant data would reappear in 99% of the repetitions. Statement 6 could be made only if one knew that the null hypothesis was true. In formal terms, p(D |H0) is confused with 1 – p(D). The replication fallacy is shared by many, including the editors of top journals. […] To sum up, all six statements are incorrect. Note that all six err in the same direction of wishful thinking: They overestimate what one can conclude from a p-value. […]
We posed the question with the six multiple-choice answers to 44 students of psychology, 39 lecturers and professors of psychology, and 30 statistics teachers […] How many students and teachers noticed that all of the statements were wrong? As Figure 1 shows, none of the students did. […] Ninety percent of the professors and lecturers also had illusions, a proportion almost as high as among their students. Most surprisingly, 80% of the statistics teachers shared illusions with their students.”
The article has much more.
“More than 25% of the U.S. population aged [>65] years has diabetes (1), and the aging of the overall population is a significant driver of the diabetes epidemic. […] The incidence of diabetes increases with age until about age 65 years, after which both incidence and prevalence seem to level off”. I should have known the first number was in that neighbourhood, but somehow I had failed to realize that it was that high; most often prevalence estimates are calculated/reported using the entire population in the denominator, but of course such estimates can be deceiving if you do not think about how they are calculated and I clearly hadn’t. At least 1 in 4 in the above-65 age bracket. That’s a lot of people. The article doesn’t have a lot of data, it’s a ‘consensus report’ handling mostly various treatment guideline suggestions and similar stuff.
v. What is the most uncomfortable situation have you ever been put in- by a guy? Any kind of unwanted flirtation- or something of that nature (Reddit). Lots of really horrible stuff; reading stuff like this makes what might be perceived of as some females’ ‘somewhat overcautious’ behaviour towards members of the opposite sex easier to understand. An example from the link:
“The last stranger-danger moment I will share tonight was at an end-of-midterms party sponsored by the student union at a local bar. I was there with my best friend, and she’s very pretty and very friendly, so we’d very quickly attracted a group of four or five men who were hanging around with us for most of the night. I hadn’t seen any of them before, so I assumed they were students from a different department, and we end up getting a table together and talking for a while. Once my friend mentions that she has a boyfriend, most of them shift their attention to me, though there’s one who still seems interested in her. As I’m talking to them, I find that they’re not students at our university, but that they’re a group of friends visiting from the a couple towns over. Nothing too creepy, so far.
My friend finishes her drink, so the guy she’s talking to goes to buy her another. She’s a little suspicious, so she starts drinking it VERY slowly. Meanwhile, I’m getting distracted talking to one of the guys who works in the same field I’ll be entering soon, and we end up talking for a while about that. He keeps telling me that I’m very beautiful, which I keep brushing off because I knew he was interested in my friend initially, and I was interested in someone else at the time, anyway. Somewhere in the middle of all this, my friend has stopped drinking the drink that was bought for her, and someone asks if she’s going to finish it. She says no.
Eventually, the guy I’m talking to apologizes for his “bad” English, saying that he hasn’t really had to use it since he was in school, which was OVER TEN YEARS AGO. At about the same time, my friend is telling the guy she’s talking to that it’s funny that they decided to visit our city on that particular weekend, because this is a student end-of-midterm party, and he answers, “I know. That’s kind of why we came here.” Someone else asks my friend if she’s going to finish her drink, and she says no, but he can have it if he wants. The drink ‘accidentally’ gets spilled in the process, and she’s signalling me to get the fuck out of there, so I take the opportunity to drag her to the bathroom. I start to notice that she’s acting really fucked up – she can usually drink a ton more than I can, and she’d only had one drink of her own and maybe a third (probably less than that, actually) of the one that guy bought for her. She says she thinks the drink they gave her was drugged, and then she gets sick. I ended up staying the night at her place to keep an eye on her, but I didn’t think to take her to the hospital or anything, so I guess we’ll never know what exactly happened…”
Of course if you’re like me you don’t engage in risky behaviours like drinking with strangers and in that case it doesn’t really matter much if you’re male or female, but then again I’m not like normal people. Most males probably significantly underestimate how risky some of their behaviours – behaviours they would not ever even think of as ‘particularly risky’ – are when a female engages in them. Note that even males that fall into the “I can’t imagine you raising your voice”-category (a female friend said this about me in a conversation I had with her earlier today) are likely to be affected by the behaviours of the (type of) males described in the link; once a female has been through situations like the ones described at the link, she’s less likely to give males the benefit of the doubt and more likely to misinterpret behaviour and the motivations driving behaviour. Reading this stuff has made me believe that the behaviour of ‘overcautious’ females may be better justified and less ‘irrational’ than males tend to think it is.
vi. I haven’t commented on the new DSM-5 – let’s just say I’ve had better things to do. Here’s one take on it (“It’s arcane, contradictory and talks about invisible entities which no-one can really prove. Yes folks, the new psychiatric bible has been finalised.”). The most ‘relevant’ change to me is the fact that they’ll remove the Asperger Syndrome diagnosis, and instead merge it with other autism spectrum disorders. If you’re asking me what I think about that, the answer is that I don’t really care.
vii. Cheetahs on the Edge (via Ed Yong). A must-see:
“Using a Phantom camera filming at 1200 frames per second while zooming beside a sprinting cheetah, the team captured every nuance of the cat’s movement as it reached top speeds of 60+ miles per hour.
The extraordinary footage that follows is a compilation of multiple runs by five cheetahs during three days of filming.”
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