# Shravan Vasishth's Slog (Statistics blog)

This blog is a repository of cool things relating to statistical computing, simulation and stochastic modeling.

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## Friday, May 27, 2022

### Summer School “Methods in Language Sciences” (16-20 August 2022, Ghent, Belgium): Registrations open

## Saturday, April 16, 2022

### Ever wondered how the probability of the null hypothesis being true changes given a significant result?

**TRIGGER WARNING: These simulations might fundamentally shake your belief system. USE WITH CARE.**

In a recently accepted paper in the open access journal Quantitative Methods for Psychology that Daniel Schad led, we discuss how, using Bayes' rule, one can explore the change in the probability of a null hypothesis being true (call it theta) when you get a significant effect. The paper, which was inspired by a short comment in McElreath's book (first edition), shows that theta does not necessarily change much even if you get a significant result. The probability theta **can** change dramatically under certain conditions, but those conditions are either so stringent or so trivial that it renders many of the significance-based conclusions in psychology and psycholinguistics questionable at the very least.

You can do your own simulations, under assumptions that you consider more appropriate for your own research problem, using this shiny app (below), or play with the source code: here.

## Thursday, March 31, 2022

### New(ish) paper: Share the code, not just the data: A case study of the reproducibility of JML articles published under the open data policy

Here's an important new paper led by Dr. Anna Laurinavichyute on the reproducibility of published analyses. This paper by commissioned by the editor in chief of the Journal of Memory and Language, Kathy Rastle.

**Title**: Share the code, not just the data: A case study of the reproducibility of JML articles published under the open data policy

**Abstract**:

In 2019 the Journal of Memory and Language instituted an open data and code policy; this policy requires that, as a rule, code and data be released at the latest upon publication. How effective is this policy? We compared 59 papers published before, and 59 papers published after, the policy took effect. After the policy was in place, the rate of data sharing increased by more than 50%. We further looked at whether papers published under the open data policy were reproducible, in the sense that the published results should be possible to regenerate given the data, and given the code, when code was provided. For 8 out of the 59 papers, data sets were inaccessible. The reproducibility rate ranged from 34% to 56%, depending on the reproducibility criteria. The strongest predictor of whether an attempt to reproduce would be successful is the presence of the analysis code: it increases the probability of reproducing reported results by almost 40%. We propose two simple steps that can increase the reproducibility of published papers: share the analysis code, and attempt to reproduce one’s own analysis using only the shared materials.

PDF: here.

## Wednesday, March 23, 2022

### Short course and keynote on statistical methods at Ghent Summer School on Methods in Language Sciences

I will be teaching an in-person course on linear mixed modeling at the summer school at Ghent (below) August 2022.

The summer school home page: https://www.mils.ugent.be/

1. 2.5 day course: Introduction to linear mixed modelling for linguists

When and where: August 18, 19, 20, 2022 in Ghent.

**Prerequisites and target audience**

The target audience is graduate students in linguistics.

I assume familiarity with graphical descriptive summaries of data of the type

encountered in linguistics; the most important theoretical distributions

(normal, t, binomial, chi-squared); description of univariate and bivariate data

(mean, variance, standard deviation, correlation, cross-tabulations);

graphical presentation of univariate and bivariate/multivariate data

(bar chart, histogram, boxplot, qq-plot, etc.);

point estimators and confidence intervals for population averages

with normal data or large samples;

null hypothesis significance testing;

t-test, Chi-square test, simple linear regression.

A basic knowledge of R is assumed.

**Curriculum**:

I will cover some important ideas relating to linear mixed models

and how they can be used in linguistics research. I will loosely follow

my textbook draft: https://vasishth.github.io/Freq_CogSci/

Topics to be covered:

- Linear mixed models: basic theory and applications

- Contrast coding

- Generalized Linear Mixed Models (binomial link)

- Using simulation for power analysis and for understanding one’s model

2. Keynote lecture

** Using Bayesian Data Analysis in Language Research**

Bayesian methods are becoming a standard part of the toolkit for

psycholinguists, linguists, and psychologists. This transition has

been sped up by the arrival of easy-to-use software like brms, a

front-end for the probabilistic programming language Stan. In this

talk, I will show how Bayesian analyses differ from frequentist

analogues, focusing on the linear mixed model. I will illustrate the

main advantages of Bayes: a direct, nuanced, and conservative answer

to the research question at hand, flexible model specification, the

ability to incorporate prior knowledge in the model, and a focus on

uncertainty quantification.

References

Daniel J. Schad, Bruno Nicenboim, Paul-Christian Bürkner, Michael

Betancourt, and Shravan Vasishth. Workflow Techniques for the Robust

Use of Bayes Factors. Psychological Methods, 2022.

https://doi.apa.org/doiLanding

Shravan Vasishth and Andrew Gelman. How to embrace variation and

accept uncertainty in linguistic and psycholinguistic data analysis.

Linguistics, 59:1311--1342, 2021.

https://www.degruyter.com/docu

2019-0051/html

Shravan Vasishth. Some right ways to analyze (psycho)linguistic data.

Submitted, 2022.

https://osf.io/5wzyg/

### New paper: Some right ways to analyze (psycho)linguistic data

** New paper (under review): **

**Title: Some right ways to analyze (psycho)linguistic data**

**Abstract**:

Much has been written on the abuse and misuse of statistical methods, including p-values, statistical significance, etc. I present some of the best practices in statistics using a running example data analysis. Focusing primarily on frequentist and Bayesian linear mixed models, I illustrate some defensible ways in which statistical inference—specifically, hypothesis testing using Bayes factors vs. estimation or uncertainty quantification—can be carried out. The key is to not overstate the evidence and to not expect too much from statistics. Along the way, I demonstrate some powerful ideas, the most important ones being using simulation to understand the design properties of one’s experiment before running it, visualizing data before carrying out a formal analysis, and simulating data from the fitted model to understand the model’s behavior.

**PDF**: https://psyarxiv.com/y54va/

### Summer School on Statistical Methods for Linguistics and Psychology, Sept. 12-16, 2022 (applications close April 1)

**Summer School on Statistical Methods for Linguistics and Psychology**will be held in Potsdam, Germany,

**September 12-16, 2022**. Like the previous editions of the summer school, this edition will have two frequentist and two Bayesian streams. Currently, this summer school is being planned as an in-person event.

The application form closes **April 1, 2022**. We will announce
the decisions on or around April 15, 2022.

**Course fee**: There is no fee because the summer school is funded by the Collaborative Research Center (Sonderforschungsbereich 1287). However, we will charge 40 Euros to cover costs for coffee and snacks during the breaks and social hours. And participants will have to pay for their own accommodation.

For details, see: https://vasishth.github.io/

**Curriculum**:

1. **Introduction to Bayesian data analysis** (maximum 30 participants). Taught by Shravan Vasishth, assisted by Anna Laurinavichyute, and Paula Lissón

**Course Materials**Previous year's course web page: all materials (videos etc.) from the previous year are available here.

Textbook: here. We will work through the first six chapters.

**Advanced Bayesian data analysis**(maximum 30 participants). Taught by Bruno Nicenboim, assisted by Himanshu Yadav

This course assumes that participants have some experience in Bayesian modeling already using brms and want to transition to Stan to learn more advanced methods and start building simple computational cognitive models. Participants should have worked through or be familiar with the material in the first five chapters of our book draft: Introduction to Bayesian Data Analysis for Cognitive Science. In this course, we will cover Parts III to V of our book draft: model comparison using Bayes factors and k-fold cross validation, introduction and relatively advanced models with Stan, and simple computational cognitive models.

**Course Materials**Textbook here. We will start from Part III of the book (Advanced models with Stan). Participants are expected to be familiar with the first five chapters.

**Foundational methods in frequentist statistics**(maximum 30 participants). Taught by Audrey Buerki, Daniel Schad, and João Veríssimo.

Participants will be expected to have used linear mixed models before, to the level of the textbook by Winter (2019, Statistics for Linguists), and want to acquire a deeper knowledge of frequentist foundations, and understand the linear mixed modeling framework more deeply. Participants are also expected to have fit multiple regressions. We will cover model selection, contrast coding, with a heavy emphasis on simulations to compute power and to understand what the model implies. We will work on (at least some of) the participants' own datasets.

*This course is not appropriate for researchers new to R or to frequentist statistics*.

**Course Materials**Textbook draft here.

**Advanced methods in frequentist statistics with Julia**(maximum 30 participants). Taught by Reinhold Kliegl, Phillip Alday, Julius Krumbiegel, and Doug Bates.

Applicants must have experience with linear mixed models and be interested in learning how to carry out such analyses with the Julia-based MixedModels.jl package) (i.e., the analogue of the R-based lme4 package). MixedModels.jl has some significant advantages. Some of them are: (a) new and more efficient computational implementation, (b) speed — needed for, e.g., complex designs and power simulations, (c) more flexibility for selection of parsimonious mixed models, and (d) more flexibility in taking into account autocorrelations or other dependencies — typical EEG-, fMRI-based time series (under development). We

**do not expect**profound knowledge of Julia from participants; the necessary subset of knowledge will be taught on the first day of the course. We do expect a readiness to install Julia and the confidence that with some basic instruction participants will be able to adapt prepared Julia scripts for their own data or to adapt some of their own lme4-commands to the equivalent MixedModels.jl-commands. The course will be taught in a hybrid IDE. There is already the option to execute R chunks from within Julia, meaning one needs Julia primarily for execution of MixedModels.jl commands as replacement of lme4. There is also an option to call MixedModels.jl from within R and process the resulting object like an lme4-object. Thus, much of pre- and postprocessing (e.g., data simulation for complex experimental designs; visualization of partial-effect interactions or shrinkage effects) can be carried out in R.

**Course Materials**Github repo: here.

### New paper in Computational Brain and Behavior: Sample size determination in Bayesian Linear Mixed Models

We've just had a paper accepted in Computational Brain and Behavior, an open access journal of the Society for Mathematical Psychology.

Even though I am not a psychologist, I feel an increasing affinity to this field compared to psycholinguistics proper. I will be submitting more of my papers to this journal and other open access journals (Glossa Psycholx, Open Mind in particular) in the future.

Some things I liked about this journal:

- A fast and well-informed, intelligent, useful set of reviews. The reviewers actually understand what they are talking about! It's refreshing to find people out there who speak my language (and I don't mean English or Hindi). Also, the reviewers signed their reviews. This doesn't usually happen.

- **Free availability of the paper **after publication; I didn't have to do anything to make this happen. By contrast, I don't even have copies of my own articles published in APA journals. The same goes for Elsevier journals like the Journal of Memory and Language. Either I shell out $$$ to make the paper open access, or I learn to live with the arXiv version of my paper.

- **The proofing was *excellent***. By contrast, the Journal of Memory and Language adds approximately 500 mistakes into my papers every time they publish it (then we have to correct them, if we catch them at all). E.g., in this paper we had to issue a correction about a German example; this error was added by the proofer! Another surprising example of JML actually destroying our paper's formatting is this one; here, the arXiv version has better formatting than the published paper, which cost several thousand Euros!

- **LaTeX is encouraged**. By contrast, APA journals demand that papers be submitted in W**d.

Here is the paper itself: here, we present an approach, adapted from the work of two statisticians (Wang and Gelfand), for determining approximate sample size needed for drawing meaningful inferences using Bayes factors in hierarchical models (aka linear mixed models). The example comes from a psycholinguistic study but the method is general. Code and data are of course available online.

The pdf: https://link.springer.com/article/10.1007/s42113-021-00125-y

## Thursday, February 03, 2022

### EMLAR 2022 tutorial on Bayesian methods

At EMLAR 2022 I will teach two sessions that will introduce Bayesian methods. Here is the abstract for the two sessions:

EMLAR 2022: An introduction to Bayesian data analysis

Taught by Shravan Vasishth (vasishth.github.io)

**Session 1. Tuesday 19 April 2022, 1-3PM (Zoom link will be provided)**

Modern probabilistic programming languages like Stan (mc-stan.org)

have made Bayesian methods increasingly accessible to researchers

in linguistics and psychology. However, finding an entry point

into these methods is often difficult for researchers. In this

tutorial, I will provide an informal introduction to the

fundamental ideas behind Bayesian statistics, using examples

that illustrate applications to psycholinguistics.

I will also discuss some of the advantages of the Bayesian

approach over the standardly used frequentist paradigms:

uncertainty quantification, robust estimates through regularization,

the ability to incorporate expert and/or prior knowledge into

the data analysis, and the ability to flexibly define the

generative process and thereby to directly address the actual research

question (as opposed to a straw-man null hypothesis).

Suggestions for further reading will be provided. In this tutorial,

I presuppose that the audience is familiar with linear mixed models

(as used in R with the package lme4).

**Session 2. Thursday 21 April 2022, 9:30-11:30 (Zoom link will be provided)**

This session presupposed that the participant has attended

Session 1. I will show some case studies using brms and Stan

code that will demonstrate the major applications of

Bayesian methods in psycholinguistics. I will reference/use some of

the material described in this online textbook (in progress):

## Saturday, January 22, 2022

### Review of Writing Science by Joshua Shiemel: Good advice on writing, but ignore his advice on statistical inference because it's just plain wrong

These days I am quite obsessed with figuring out how to improve the writing that is coming out of my lab. My postdocs generally produce solid writing, but my students struggle, just as I struggled when I was a student. So I bought a bunch of books written by experts to try to figure out what the best advice is out there on writing scientific articles. One of the very best books I have read is by Schimel:

Schimel, Joshua. Writing Science. Oxford University Press. Kindle Edition.

Schimel seems to be a heavy-weight in his field:

What I like most about his book is that he takes the attitude that the goal of writing is that people actually read your paper. He puts it differently: people should cite your paper. But I think he means that people should want to read your paper (it's unfortunately pretty common to cite someone's work without reading it, just because someone else cited it; one just copies over the citations).

His book treats writing as storytelling. A clear storyline has to be planned out before one puts pen to paper (or fingers to keyboard). Several types of openings are suggested, but the most sensible one for standard technical writing that is addressed to an expert audience is what he calls the OCAR style (the text below is quoted directly from his excellent blog: https://schimelwritingscience.wordpress.com/):

1. **Opening**: This should identify the larger problem you are contributing to, give readers a sense of the direction your paper is going, and make it clear why it is important. It should engage the widest audience practical. The problem may be applied or purely conceptual and intellectual—this is the reason you’re doing the work.

2. **Challenge**: What is your specific question or hypothesis? You might have a few, but there is often one overarching question, which others flesh out.

3. **Action**: What are the key results of your work? Identify no more than 2-3 points.

4. **Resolution**: What is your central conclusion and take home message? What have you learned about nature? If readers remember only one thing from your work, this should be it. The resolution should show how the results (*Action*) answer the question in the *Challenge*, and how doing so helps solve the problem you identified in the *Opening*.

The book spends a lot of time unpacking these ideas, I won't repeat the details here.

One problem I had with his examples was that they all lie outside my area of expertise, so I couldn't really appreciate what a good vs bad style was when looking at his specific examples. I think such books really have to be written for people working in particular fields; the title should reflect that. There is an urgent need for such a book specifically for psycholinguistics, with examples from our own field. I don't think that a student of psycholinguistics can pick up this book and learn anything much from the examples. The high-level advice is great, but it's hard to translate into actionable things in one's own field.

I have one major complaint about this book: Schimel gives absurdly incorrect advice to the reader about how to present and draw inferences from statistical results. To me it is quite surprising that you can become just a senior and well-cited scientist in an empirically driven field, and have absolutely zero understanding of basic statistical concepts. Schimel would fail my intro stats 1 class.

Here is what he has to say (p 78 in my Kindle edition) about how to present statistical results. I bold-face the most egregious statements.

"As an example, consider figure 8.3. In panel A there is a large difference (the treatment is 2.3 x the control) that is unquestionably statistically significant. Panel B shows data with the same statistical significance ( p = 0.02), but the difference between the treatments is smaller. You could describe both of these graphs by saying, “The treatment significantly increased the response ( p = 0.02).” That would be true, but the stories in panels A and B are different —

in panel A, there is a strong effect and in panel B, a weak one. I would describe panel A by saying, “The treatment increased the response by a factor of 2.3 ( p = 0.02)”; for panel B, I might write, “The treatment increased the response by only 30 percent, but this increase was statistically significant ( p = 0.02).”

Well, panel A is probably Type M error (just look at the uncertainty of the estimates compared to panel B), and what he calls a weak effect in panel B is more likely to be the accurate estimate (again, just look at those uncertainty intervals). So that's a very misleading statement to call A a strong effect and B a weak effect. If given data like in panels A and B, I would take panel B more seriously. I have ranted extensively about this point in a 2018 paper. And of course, others have long complained about this kind of misunderstanding (Gelman and Carlin, 2014).

But it gets worse. Here is what Schimel has to say about panel C. Again, I highlight the absurd part of his comments/advice:

"The tricky question is what to write about panel C. The difference between treatment and control is the same as in panel A (a factor of 2.3), but the data are more variable and so the statistics are weaker, in this case above the threshold that many use to distinguish whether there is a “significant” diff erence at all. Many would describe this panel by writing, “There was no significant effect of the treatment (p > 0.05).” Such a description, however, has several problems. The first problem is that many readers would infer that there was no difference between treatment and control. In fact though, they differed by a factor of 2.3. That is never the “same.” Also,

with a p value of 0.07, the probability that the effect was due to the experimental treatment is still greater than 90 percent. Thus, a statement like this is probably making a Type II error — rejecting a real effect.The second problem is that just saying there was no significant effect mixes results and interpretation. When you do a statistical test, the F and p values are results . Deciding whether the test is significant is interpretation. When you describe the data solely in terms of whether the difference was significant, you present an interpretation of the data as the data, which violates an important principle of science. Any specific threshold for significance is an arbitrary choice with no fundamental basis in either science or statistics."

## Thursday, January 20, 2022

### New opinion paper in Trends in Cognitive Sciences: Data Assimilation in Dynamical Cognitive Science (Engbert et al.)

Here's a new opinion paper in Trends in Cognitive Sciences, by Ralf Engbert, Max Rabe, et al.

Link to paper: here