Tuesday, February 02, 2021
Bayesian statistics: A tutorial taught at Experimental Methods for Language Acquisition research (EMLAR XVII 2021)
Saturday, January 16, 2021
Applications are open for the fifth summer school in statistical methods for linguistics and psychology (SMLP)
Instructors: Doug Bates, Reinhold Kliegl, Phillip Alday, Bruno Nicenboim, Daniel Schad, Anna Laurinavichyute, Paula Lisson, Audrey Buerki, Shravan Vasishth.
There will be four streams running in parallel: introductory and advances courses on frequentist and Bayesian statistics. Details, including how to apply, are here.
Saturday, January 02, 2021
Should statistical data analysis in psychology be like defecating?
There was an interesting thread on twitter about linear mixed models (LMMs) that someone made me aware of recently. (I stopped following twitter because of its general inanity, but this thread is worth commenting on.) The gist of the complaints (trying to recreate this list from memory) were. My list is an amalgamation of comments from different people; I think that the thread started here:
Inspired by @IrisVanRooij, I want to express some concerns that may be controversial and even outrageous to some but I feel we at least should have a discussion. I'm wondering if statistics in psycholinguistics could use a rethink. It feels like the tail now wags the dog.
— Fernanda Ferreira (@fernandaedi) December 20, 2020
To summarize the complaints:
- LMMs take too long to fit (cf. repeated measures ANOVA). This slows down student output.
- Too much time is spent on thinking about what the right analysis is.
- The interpretation of LMMs can change dramatically depending on which model you fit.
- Reviewers will always object to whatever analysis one does and demand a different one. Often which analysis one does doesn't matter as regards interpretation.
- The lme4 package exhibits all kinds of weird and unstable behavior. Should we trust its output?
- The focus has shifted away from substantive theoretical issues within psych* to statistical methods, but psych* people cannot be statisticians and can never know enough. This led to the colorful comment that doing statistics should be like taking a crap---it shouldn't become the center of your entire existence.
Indeed, a mathematical psychologist I know, someone who knows what they're doing, once told me that if you cannot answer your question with a paired t-test, you are asking the wrong question. In fact, if I go back to my existing data-sets that I have published between 2002 and 2020, almost all of them can be reasonably analyzed using a series of paired t-tests.
There is a presupposition that lies behind the above complaints: the purpose of data analysis is to find out whether an effect is significant or not. Once one understands that that's not the primary purpose of a statistical analysis, things start to make more sense. The problem is that it's just very hard to comprehend this point; this is because the idea of null hypothesis significance testing is very deeply entrenched in our minds. Walking away from it feels impossible.
Here are some thoughts about the above objections.
1. If you want the simplicity of paired t-tests and repeated measures ANOVA, absolutely go for it. But release your data and code, and be open to others analyzing your data differently. I think it's perfectly fine to spend your entire life doing just paired t-tests and publishing the resulting t and p-values. Of course, you are still fitting linear mixed models, but heavily simplified ones. Sometimes it won't matter whether you fit a complicated model or a simple one, but sometimes it will. It has happened to me that a paired t-test was exactly the wrong thing to do, and I spent a lot of time trying to model the data differently. Should one care about these edge cases? I think this is a subjective decision that each one of us has to make individually. Here is another example of a simple two-condition study where a complicated model that took forever to fit gave new insight into the underlying process generating the data. The problem here comes down to the goal of a statistical analysis. If we accept the premise that statistical significance is the goal, then we should just go ahead and fit that paired t-test. If, instead, the goal is to model the generative process, then you will start losing time. What position you take really depends on what you want to achieve.
2. There is no one right analysis, and reviewers will always object to whatever analysis you present. The reason that reviewers propose alternative analyses has nothing to do with the inherent flexibility of statistical methods. It has to do with academics being contrarians. I notice this in my own behavior: if my student does X, I want them to do Y!=X. If they do Y, I want them to do X!=Y. I suspect that academics are a self-selected lot, and one thing they are good at is objecting to whatever someone else says or does. So, the fact that reviewers keep asking for different analyses is just the price one has to pay for dealing with academics, it's not an inherent problem with statistics per se. Notice that reviewers also object to the logic of a paper, and to the writing. We are so used to dealing with those things that we don't realize it's the same type of reaction we are seeing to the statistical analyses.
3. If you want speed and still want to fit linear mixed models, use the right tools. There are plenty of ways to fit linear mixed models fast. rstanarm, LMMs in Julia, etc. E.g., Doug Bates, Phillip Alday, and Reinhold Kliegl taught a one-week course on fitting LMMs super fast in Julia: see here.
4. The interpretation of linear mixed models depends on model specification. This surprises many people, but the surprise is due to the fact that people have a very incomplete understanding of what they are doing. If you cannot be bothered to study linear mixed modeling theory (understandable, life is short), stick to paired t-tests.
5. lme4's unstable and weird behavior is problematic, but this is not enough reason to abandon linear mixed models. The weirdness of messages, and the inconsistencies of lme4 are really frustrating, one has to admit that. Perhaps this is the price one has to pay for free software (although, having used non-free software like Word, SPSS, Excel, I'm not so sure there is any advantage). But the fact is that LMMs give you the power to incorporate variance components in a sensible way, and lme4 does the job, if you know what you are doing. Like any other instrument one thinks about using as a professional, if you can't be bothered to learn to use it, then just use some simpler method you do know how to use. E.g., I can't use fMRI; I don't have access to the equipment. I'm forced to work with simpler methods, and I have to live with that. If you want more control over your hierarchical models than lme4 provides, learn Stan. E.g., see our chapter on hierarchical models here.
Personally, I think that it is possible to learn enough statistics to be able to use linear mixed models competently; one doesn't need to become a statistician. The curriculum I think one needs in psych and related areas is encapsulated in our summer school on statistical methods, which we run annually at Potsdam. It's a time commitment, but it's worth it. I have seen many people go from zero knowledge to fitting sophisticated hierarchical models, so I know that people can learn all this without it taking over their entire life.
Probably the biggest problem behind all these complaints is the misunderstanding surrounding null hypothesis significance testing. Unfortunately,p-values will rarely tell you anything useful, significant or not, unless you are willing to put in serious time and effort (the very thing people want to avoid doing). So it really not going to matter much whether you compute them using paired t-tests or linear mixed models.
Tuesday, November 10, 2020
Is it possible to write an honest psycholinguistics paper?
I'm teaching a new course this semester: Case Studies in Statistical and Computational Modeling. The idea is to revisit published papers and the associated data and code from the paper, and p-hack the paper creatively to get whatever result you like. Yesterday I demonstrated that we could conclude whatever we liked from a recent paper that we had published; all conclusions (effect present, effect absent) were valid under different assumptions! The broader goal is to demonstrate how researcher degrees of freedom play out in real life.
Then someone asked me this question in the class:
Is it possible to write an honest psycholinguistics paper?
The short answer is: yes, but you have to accept that some editors will reject your paper. If you can live with that, it's possible to be completely honest.
Usually, the only way to get a paper into a major journal is to make totally overblown claims that are completely unsupported or only very weakly supported by the data. If your p-value is 0.06 but you want to claim it is significant, you have several options: mess around with the data till you push it below 0.05. Or claim "marginal significance". Or you can bury that result and keep redoing the experiment till it works. Or run the experiment till you get significance. There are plenty of tricks out there.
If you got super-duper low p-values, you are on a good path to a top publication; in fact, if you have any significant p-values (relevant to the question or not) you are on a good path to publication, because reviewers are impressed with p<0.05 somewhere, anywhere, in a table. That's why you will see huge tables in psychology articles, with tons and tons of p-values; the sheer force of low p-values spread out over a gigantic table can convince the reviewer to accept the paper, even though only a single cell among dozens or hundreds in that table is actually testing the hypothesis. You can rely on the fact that nobody will think to ask whether power was low (the answer is usually yes), and how many comparisons were done.
Here are some examples of successes and failures, i.e., situations where we honestly reported what we found and were either summarily rejected or (perhaps surprisingly) accepted.
For example, in the following paper,
Shravan Vasishth, Daniela Mertzen, Lena A. Jäger, and Andrew Gelman. The statistical significance filter leads to overoptimistic expectations of replicability. Journal of Memory and Language, 103:151-175, 2018.
I wrote the following conclusion:
"In conclusion, in this 100-participant study we don’t see any grounds for claiming an interaction between Load and Distance. The most that we can conclude is that the data are consistent with memory-based accounts such as the Dependency Locality Theory (Gibson, 2000), which predict increased processing difficulty when subject-verb distance is increased. However, this Distance effect yields estimates that are also consistent with our posited null region; so the evidence for the Distance effect cannot be considered convincing."
Normally, such a tentative statement would lead to a rejection. E.g., here is a statement in another paper that led to a desk rejection (same editor) in the same journal where the above paper was published:
"In sum, taken together, Experiment 1 and 2 furnish some weak evidence for an interference effect, and only at the embedded auxiliary verb."
We published the above (rejected) paper in Cognitive Science instead.
Lena A. Jäger, Daniela Mertzen, Julie A. Van Dyke, and Shravan Vasishth. Interference patterns in subject-verb agreement and reflexives revisited: A large-sample study. Journal of Memory and Language, 111, 2020.
In the above paper, we were pretty clear about the fact that we didn't manage to achieve high enough power even in our large-sample study: Table A1 shows that for the critical effect we were studying, we probably had power between 25 and 69 percent, which is not dramatically high.
There are many other such examples from my lab, of papers accepted despite tentative claims, and papers rejected because of tentative claims. In spite of the rejections, my plan is to continue telling the story like it is, with a limitations section. My hope is that editors will eventually understand the following point:
Almost no paper in psycholinguistics is going to give you a decisive result (it doesn't matter what the p-values are). So, rejecting a paper on the grounds that it isn't reporting a conclusive result is based on a misunderstanding about what we learnt from that paper. We almost never have conclusive results, even when we claim we do. Once people realize that, they will become more comfortable accepting more realistic conclusions from data.
Monday, September 07, 2020
Registration open for two statistics-related webinars: SMLP Wed 9 Sept, and Fri 11 Sept 2020
As part of the summer school in Statistical Methods for Linguistics and Psychology, we have organized two webinars that anyone can attend. However, registration is required. Details below
Keynote speakers
- Wed 9 Sept, 5-6PM:Christina Bergmann (Title: The "new" science: transparent, cumulative, and collaborative)
Register for webinar: here
Abstract: Transparency, cumulative thinking, and a collaborative mindset are key ingredients for a more robust foundation for experimental studies and theorizing. Empirical sciences have long faced criticism for some of the statistical tools they use and the overall approach to experimentation; a debate that has in the last decade gained momentum in the context of the "replicability crisis." Culprits were quickly identified: False incentives led to "questionable research practices" such as HARKing and p-hacking and single, "exciting" results are over-emphasized. Many solutions are gaining importance, from open data, code, and materials - rewarded with badges - over preregistration to a shift away from focusing on p values. There are a host of options to choose from; but how can we pick the right existing and emerging tools and techniques to improve transparency, aggregate evidence, and work together? I will discuss answers fitting my own work spanning empirical (including large-scale), computational, and meta-scientific studies, with a focus on strategies to see each study for what it is: A single brushstroke of a larger picture. - Fri 11 Sept, 5-6PM: Jeff Rouder Title: Robust cognitive modeling
Register for webinar: here
Abstract: In the past decade, there has been increased emphasis on the replicability and robustness of effects in psychological science. And more recently, the emphasis has been extended to cognitive process modeling of behavioral data under the rubric of “robust models." Making analyses open and replicable is fairly straightforward; more difficult is understanding what robust models are and how to specify and analyze them. Of particular concern is whether subjectivity is part of robust modeling, and if so, what can be done to guard against undue influence of subjective elements. Indeed, it seems the concept of "researchers' degrees of freedom" plays writ large in modeling. I take the challenge of subjectivity in robust modeling head on. I discuss what modeling does in science, how to specify models that capture theoretical positions, how to add value in analysis, and how to understand the role of subjective specification in drawing substantive inferences. I will extend the notion of robustness to mixed designs and hierarchical models as these are common in real-world experimental settings.
Sunday, September 06, 2020
Some thoughts on teaching statistics courses online
Someone asked to write down how I teach online. Because of corona, I have moved all my courses at the university online, and as a consequence I had to clean up my act and get things in order.
The first thing I did was record all my lectures in advance. This was a hugely time-consuming enterprise. I bought a licence for screencast-o-matic, which is something like 15 Euros a year, and a Blue Yeti microphone (144 Euros, including express shipping). I already have a Logitech HD 1080p camera. I also bought a Windows (Dell) tablet computer through the university, so I could write freehand with an electronic pen. Somehow, writing freehand during a lecture solidifies understanding in the student's mind in a way that a mere slide presentation does not. I don't know why this is the case but I firmly believe one should show derivations in real time.
The way I do my recordings is that I start screencast-o-matic (the new Mac OS X makes this incredibly hard, you have to repeatedly open the settings and give the software permission to record--thanks, Apple). Then, I record the lecture in one shot, no editing at all. If I make a mistake during the lecture, I just live with it (and sometimes the mistakes are horrendous). Sometimes my cat Molly video-bombs my lectures, I just let it all happen. All this makes my video recordings less than professional looking, but I think it's good enough. Nobody has complained about this so far. I use Google Chrome's Remote Desktop feature to link my Macbook Pro with the Windows machine, and switch between RStudio on the Mac and the Windows tablet for writing. On Windows, I use the infinite writing space provided by OneNote. For writing on pdfs, I use the PDF reader by Xodo.
Here are my videos from my frequentist course:
https://vasishth.github.io/IntroductionStatistics/
The way students are expected to work is to watch the videos, and then do exercises that I give out. My lecture notes provide a written record of the material, plus the exercises:
https://vasishth.github.io/Freq_CogSci/
The solutions are given out after the submission deadline. In my courses, I stipulate that you can only take the class if you commit to doing at least 80% of the homework. I force people to quit the class if they don't do the HW; many people try to audit the classes without doing the HW. In my experience, they don't get anything out of the class, so I don't allow audits without doing the HW. This is a very effective strategy, because it forces the students to engage. One rule I have is that if you submit the HW and make an honest attempt to solve the problems you will get 100% on the HW no matter what. This decouples learning from grades and reduces student stress considerably, and allows them to actually learn the material. Some students complain that the HW is hard; but it's supposed to make them think, and there is no shame in not being able to do it. Some students are unable to adjust to the fact that not everything will be easy to do.
Two other components of the class are (a) weekly meetings over zoom, where students can ask me anything, and (b) an online discussion forum where people can post questions. Students used these options really intelligently, and although I had to spend a lot of time answering questions on the forum, I think on balance it was worth the effort. I think the students got a lot out of my courses, judging from the teaching evaluations (here and here).
The main takeaway for me was that the online component of these stats courses that I teach is crucial for student learning, and in future editions of my courses, there will always be an online component. One day we will have face to face classes, and I think those are very valuable for establishing human contact. But the online component really adds value, especially the pre-recorded lectures and the discussion forum.
Wednesday, August 19, 2020
Two keynote lectures at the Fourth Summer School on Statistical Methods for Linguistics and Psychology, 7-11 September 2020
We have two interesting zoom talks at the SMLP summer school, which is being held fully online this year. In my next post, I will be posting all the lecture materials for two of the four streams: Frequentist Foundations, and Introduction to Bayesian Data Analysis.
Two keynote lectures may be of general interest to the public (zoom link will be provided in this post closer to the date):
Wednesday 9 Sept, 5PM CEST (Berlin time):
Christina Bergmann (Title: The "new" science: transparent, cumulative, and collaborative)
Abstract: Transparency, cumulative thinking, and a collaborative mindset are key ingredients for a more robust foundation for experimental studies and theorizing. Empirical sciences have long faced criticism for some of the statistical tools they use and the overall approach to experimentation; a debate that has in the last decade gained momentum in the context of the "replicability crisis." Culprits were quickly identified: False incentives led to "questionable research practices" such as HARKing and p-hacking and single, "exciting" results are over-emphasized. Many solutions are gaining importance, from open data, code, and materials - rewarded with badges - over preregistration to a shift away from focusing on p values. There are a host of options to choose from; but how can we pick the right existing and emerging tools and techniques to improve transparency, aggregate evidence, and work together? I will discuss answers fitting my own work spanning empirical (including large-scale), computational, and meta-scientific studies, with a focus on strategies to see each study for what it is: A single brushstroke of a larger picture.
Friday 11 Sept, 5PM CEST (Berlin time):
Saturday, April 04, 2020
Developing the right mindset for learning statistics: Some suggestions
Developing the right mindset for learning statistics: Some suggestions
Shravan Vasishth
4/3/2020
Introduction
Over the last few decades, statistics has become a central part of the linguist’s toolkit. In psychology, there is a long tradition of using statistical methods for data analysis, but linguists and other cognitive scientists are relative newcomers to this area, and the formal statistics coursework provided in graduate programs is still quite sketchy. For example, as a grad student at Ohio State, in 1999 or 2000 or so, I did a four-week intensive course on statistics, after which I could do t-tests and ANOVAs on my data using JMP. Even in psychology departments, the amount of exposure students get to statistics varies a lot.
As part of Potsdam’s graduate linguistics/cognitive science/cognitive systems programs, we teach a sequence of five courses involving data analysis and statistics:
- (Winter) Statistical data analysis 1
- (Winter) Bayesian statistical inference 1
- (Winter) Case studies in psycholinguistics
- (Summer) Statistical data analysis 2
- (Winter) Bayesian statistical inference 2
In addition, we teach (in winter) a Foundations of Mathematics course that covers undergraduate calculus, probability theory, and linear algebra. This course is designed for people who plan to take the machine learning classes in computer science, as part of the MSc in Cognitive Systems.
Students sometimes have difficulties while doing these courses. This is because there is an art to taking these courses that is not obvious. This short note is aimed at spelling out some important aspects of this art.
In my experience, anyone can learn this way of approaching the study of statistics, which is inherently difficult. Keep in mind that when learning something new, one might not understand everything, but that’s OK. The whole world is built on partial understanding (I myself have only a very incomplete picture of statistics, and it’s likely to stay that way). Someone once told me that that the key difference between a mathematician and a “normal” preson is that the mathematician will keep reading or listening even if they are not following the details of the presentation. One can learn to become comfortable with partial understanding, safe in the knowledge that one can come back to the open questions later.
Below, I am shamelessly going to borrow from this (to my mind) classic book:
Burger, E. B., & Starbird, M. (2012). The 5 elements of effective thinking. Princeton University Press.
I strongly advise you to read the Burger and Starbird book; it’s short and very practically oriented. I re-read it once a year on average just to remind myself of the main ideas.
My comments below are specifically oriented towards the learning of statistics as my colleagues and I teach it at Potsdam, so my examples are very specifically about the material I teach. The examples are really the only thing I add beyond what’s in the Burger and Starbird book.
Developing the right mindset: A checklist
Understand the “easy” stuff deeply
Ask yourself: when starting the study of statistics, what is the basic knowledge I will need (I review all these topics in my introductory classes)? You will not be in a position to answer this question when you start your studies, but after completing one or two courses you should revisit this question.
- The basic elements of probability theory (sum rule, product rule, conditional probability, law of total probability)
- Basic high-school algebra (e.g., given \(y = \frac{x}{1-x}\), solve for \(x\))
- How to deal with exponents: \(x^2 \times x^3 = ?\) Is it \(x^5\) or \(x^6\)? We learnt this in school but we forgot it because we didn’t use it for many years. But now we need this knowledge!
- What is a log? What is log(1)? What is log(0)? How to find out if one has forgotten?
- What is a probability distribution? This requires some careful navigation. The key concepts here are the probability mass function (discrete case), probability density functions (continuous case), cumulative distribution functions. In bivariate/multivariate distributions, conditional, marginal, and joint distributions must be well-understood intuitively. The key here is to develop graphical intuition, using simulation. I teach this approach in my courses. Statisticians use calculus when discussing the properties of probability distributions. However, we can do all this graphically and lose no information. In practice, we rarely or never need to do any analytical work involving mathematical derivations; the software does all the work. However, it is important to understand the details intuitively, and here figures help a lot. A basic rule of thumb is: whenever trying to understand something, try to visualize it graphically. Even something mundane like repeated coin tosses can be graphically visualized, and then everything becomes clear.
Going back repeatedly to these foundational ideas as one advances through the courses is very important. The goal should be to internalize them deeply, through graphical intuition.
Mistakes are your friend and teacher
Throughout our school years, we are encouraged to deliver the right answers, and penalized for delivering wrong answers. This style of schooling misses the point that mistakes can teach us more than our correct answers, if we compare the expectd answer with ours and try to work out what we got wrong and why. This is called “error learning” or something like that in machine learning, and it works with humans too. Don’t be afraid to make mistakes, but try to make only new mistakes, and keep learning from them.
Students generally assume that I will judge them if they get something wrong. This is a false impression. As I say above, you can learn more from a mistake than from a correct answer. In my own studies of statistics, you can see that my grades are not stellar, they are all online:
https://vasishth-statistics.blogspot.com/2015/02/getting-statistics-education-review-of.html
Despite my mediocre grades, I still learnt a lot. Similarly, in graduate school, at Ohio State, my grades were just OK to so-so, nothing to write home about. In computer science (Ohio State), my grades were usually in the range of B+. I rarely got an A-. I still learnt important and useful stuff.
How to develop curiosity: Solve the same problem more than one way, and generate your own questions
The Burger and Starlight book encourages the reader to become curious about a problem. Here, I suggest a very concrete strategy, e.g., when doing homework assignments.
- First, create some mental space and time. Don’t try to squeeze the homework assignment into the last two hours before the submission deadline. Create a clear day ahead of you to explore a problem. I know that courses are designed these days to require at most 2-3 hours of work per week at home. This is an unfortunate productionalization of education that is now hurting the education system in Europe. If you need to stick to that tght schedule, do what you can in the limited time, but even there it is good to not leave the work to the last hours before submission. If you create more time, use it to explore in the following way.
- Second, assuming you have some extra time, try to solve the given problem using different approaches. E.g., if the assignment asks you to use a lognormal likelihood in a linear mixed model, ask yourself if there is some way to solve the problem with the standard normal likelihood. If the problem asks you to work with brms, try to also solve the problem using Stan or even rstanarm, even if the assignment doesn’t ask you to do this. You are doing this for yourself, not for submitting the assignment. Even if the assignment doesn’t ask you to change the priors in a model, fool around with them to see what happens to the posteriors. If there is an LKJ(2) prior on a correlation parameter in the linear mixed model, find out what happens if you use LKJ(0.5) or LKJ(10). Etc.
- Ask yourself what-if questions. Suppose you are learning about power analysis using simulation, a topic I cover in all my advanced classes, Bayesian or frequentist. This topic is ripe for exploration. Power depends essentially on three variables: effect size, sample size, and standard deviation. That is a fertile playground! I have spent so much time playing with power analyses that I can give ballpark estimates for my research problems quite accurately, without any simulation (of course, I always check my answers using simulation!). There are actually several different ways to compute power; you can use power.t.test, you can do it using simulation, etc. This topic is perfect for developing a sense of curiosity, but youc an do this for really any topic.
Keep careful notes
Statistics is not to be trifled with. I don’t expect anyone to memorize any formulas, but the logic of the analytical steps can get confusing. Keep good records of your learning. As an example, here is my entire record of four years of formal statistics study at the University of Sheffield (I did an MSc online, part time). These are cheat sheets I prepared while studying:
https://github.com/vasishth/MScStatisticsNotes
These notes are way more mathematical than anything I will teach at Potsdam. However, the principle is: organize your understanding of the material yourself. Don’t just let the teacher organize it for you (the teacher does do that, through slides and lecture notes!). We only understand things if we can actively produce and reorganize them ourselves.
Have a real problem you want to solve, and start simple
Usually, you will learn the most when you are desperate to get the answer to a data analysis problem. You will be working in a very small world of your own, and you know your problem, you are motivated to solving it. This is very different from homework assignments given out of the blue by the teacher. For this reason, especially in statistics courses, it is useful to come to the course with a specific problem you want to solve. As the course unfolds, apply the methods you learn to your problem. For example, suppose your supervisor has already told you that you need to fit a generalized linear mixed model with a logit link function to the data. Where to start?
Suppose you are taking a frequentist course and know that at the end of the course you need to be able to complete the data analysis your supervisor asked you to deal with. You can start by simplifying the problem radically and working with what you already know. Could you run a t-test instead? It doesn’t matter that someone told you that that’s the wrong test; we are playing here. Could you just fit a simple linear model (again wrong, but this is exploration). Just these two exercises will leave us with a lot of interesting insights to explore. Once you learn about linear mixed models, you can start exploring whether you can fit the model with the standard lmer function and what it would tell you. Once you reach that point, you are close to getting to the analysis you were told to do. Even if I don’t teach it in class, you can use the last trick to get there, which I discuss next.
“Let me google that for you”: Learn to find information
Any time someone asks you a question you consider easily answered by googling, and you feel like being mean, you can use this website to deliver a sarcastic response: https://lmgtfy.com/. You simply type in the question, and then send the link to the person asking the question. When they click on it, the question is typed into the google search window, and you are invited to click on the search button. It’s a pretty passive aggressive thing to do, and I advise you to never use this approach. :)
But despite the nasty aspect of the LMFTY website, it does illustrate an important point: these days you can find a lot of information online. Here are some ways that I use the internet:
- When I get an error message in RStudio I don’t understand (this happens pretty much daily), I just copy it and paste it into google’s search engine. Almost always, someone has had that same problem before and posted a solution. You have to be patient sometimes and look at a lot of the search engine results; but eventually you will find the answer. One gets better at this with experience. Sometimes one can’t solve the problem (e.g., I have a minor ongoing problem with Cairo fonts); it’s OK to give up and move on when it isn’t critical to the work one is doing.
- For Bayesian data analysis, there are online forums one can ask questions at. E.g., discourse.mc-stan.org for Stan. For frequentist questions, there are R mailing lists (exercise: google them!).
- Stackexchange. I have gotten authoritative answers from distinguished scientists about math problems that I don’t have the technical knowledge to solve. Often, someone else has asked a similar question already, so it can happen that one doesn’t even need to ask.
- Google scholar gives you access to scientific articles via keyword search.
- Blogs: I use Feedly to follow R-bloggers and other blogs like Andrew Gelman’s. Over time I have learnt a lot from reading blog posts.
Obviously, googling is not a fail-safe strategy. Sometimes you will get incorrect information. What I generally do is try to cross-check any technical claims from other sources like textbooks.
A common complaint in my statistics courses is that I don’t teach enough R. That’s because one can never teach enough R. One has to keep looking stuff up as needed; this is the skill that I am suggesting that you acquire.
Look for connections between ideas
Often, statistics is taught like a random catalogue of tests: t-test, ANOVA, linear mixed model, Fisher exact test, etc., etc. Interestingly, however, many of these seemingly disparate ideas have deep connections. The t-value and the F-score are connected; the t-test and the linear mixed model are connected. Figuring out these relationships analytically is not difficult but one needs some background to work it out. For example, see
https://vasishth-statistics.blogspot.com/2018/04/a-little-known-fact-paired-t-test-is.html
Even if one doesn’t know enough to carry out this analytical derivation, one can play with data to get a feel for the connection. The way I first got a hint about the t-test and linear mixed model connection (discussed above analytically) was by simulating data and then analyzing it two different ways (t-test vs linear mixed model), and getting the exact same statistics. It was only much later that I saw how to work this out analytically. The point is that simulation will get you very far in such investigations. You may not be able to prove stuff mathematically (I usually can’t), but you can still gain insight.
Getting further in your study of statistics
It is possible to take the Potsdam courses and do solid statistical analyses. However, if you get curious about the underlying mathematics, or want to read more advanced textbooks, or want to get into the machine learning field, we teach a Foundations of Mathematics course that graduate students can take. Historically, people have benefitted from taking this course even if they had no previous math exposure in university. So this course is definitely optional and most people can skip it; but it’s available for anyone interested in going deeper.