### Danielle Navarro

I am a computational cognitive scientist at the University of New South Wales. My research focuses on human concept learning, reasoning and decision making.

Danielle Navarro (@djnavarro)

https://slides.com/djnavarro/scienceandstatistics2

I briefly considered giving a talk about preregistration...

... but decided against it

(https://psyarxiv.com/x36pz/)

A __request__: if you tweet about my talk, please think about the framing & consider adding a link to my slides

**https://slides.com/djnavarro/scienceandstatistics2**

Statistics is a __tool__ that can assist scientists develop, evaluate and modify theoretical claims

Statistical theory provides the logic of and the __rules__ for scientific reasoning

- Scientists must follow the rules
- Statistics dictates what is "questionable"
- Breaking the rules is "p-hacking"
- Researcher "degrees of freedom" are bad
- Human judgment is not to be trusted

"Whatever. Those rules aren't real"

"Without rules there is chaos"

- Scientists should select a suitable tool
- Scientists decide what is "questionable"
- The rules aren't much more than guidelines
- Researcher "degrees of freedom" are good
- Statistical calculations are not to be trusted

"Without rules there is chaos"

I am __deeply__ opposed to all forms of statistical prescriptivism... and my goal in this talk is to discuss why I feel this way

original artwork made with github.com/djnavarro/jasmines

Thomas Kuhn

"Science does not deal in all possible laboratory manipulations. Instead, it selects those relevant to the juxtaposition of a paradigm with the immediate experience that that paradigm has partially determined. As a result, scientists with different paradigms engage in different concrete laboratory manipulations"

Okay, so I want to study human concept learning and inductive reasoning?

Let's consider two strategies I typically follow...

(https://psyarxiv.com/szr4u)

Operationalising the phenomenon of interest

(Yay math psych! I don't have to hide the equations)

Experiments based on my operationalisation yield very clean data that discriminate between competing computational models, yay!!!

What does my Bayes factor tell me about the relationship between my models and human reasoning outside of the experiment?

But I have an external validity problem... does this map onto __ anything __in the world?

There are more things in human reasoning than dreamt of within my operationalisation!

(https://psyarxiv.com/mb93p/)

The SWOW norms encode common sense knowledge

... about science

The SWOW norms encode common sense knowledge

... about clothes

We can use SWOW to study reasoning about lexicalised concepts...

(https://psyarxiv.com/s3k79/)

If I __don't__ want sexist assumptions embedded in experiments that rely on SWOW norms, it is unwise to take those norms at face value

Buuuuut....

http://blog.conceptnet.io/posts/2017/how-to-make-a-racist-ai-without-really-trying/

(Mikolov et al 2013)

But... does this __really__ matter?

A cautionary example of how to misuse real world data in an applied context

Yeah, yeah, the model achieves 95% cross-validation accuracy, whatever...

Looking good!

For lab studies, the data analysis is only useful if you know how your operationalisation affects the way you to __generalise__ outside the lab

... either way, the limitations to your design and your data ensure that __the scientific problem you care about is more difficult than the one your statistical tools are built to solve__

For naturalistic studies, the data analysis is only useful if you know which aspects of your uncontrolled data are __relevant__ to the thing you are trying to study

original artwork made with github.com/djnavarro/jasmines

Statistical inference as I learned it in my Ph.D.

Life is too short to take p-values seriously

Bayes factors: A tool for confidently selecting the "best" "model"...

... where "__best__" is weird and the "__models__" are fantasies

Here be dragons.

Gronau and Wagenmakers (2018)

A toy problem that implicitly asserts a prescriptivist view of statistics

...which is unfortunate, because it's not in your model space

Selecting a horribly broken model with absolute confidence just because it's the "least wrong" (in KL-divergence terms) is a transparently insane inferential strategy

In real life everything falls apart when __all__ your models are wrong in terrible ways

(https://psyarxiv.com/39q8y/)

P(X|M) = \int P(X|\theta) P(\theta | M) d\theta

The researcher's belief (or "knowledge") about the plausible values of the model parameters.

The prior predictive P(X|M) is quite sensitive to this prior, including the parts we don't think much about, like the *heaviness of the tails*

The more carefully you look, the stranger things become...

image via Michael Betancourt

The more parameters in your model, the more "tail" there is. So the closer we come to having genuinely __ plausible models__ of human reasoning, the less likely it is we can write down a

Oh and also the researcher is a human being who doesn't have perfect access to their own "beliefs" or "knowledge" (remember, we're psychologists????)

Anyone care to specify a prior for this model?

One that is precise enough for a Bayes factor calculation to actually * mean *something?

Lake et al (2015)

original artwork made with github.com/djnavarro/jasmines

Since all models are wrong the scientist must be alert to what is importantly wrong. It is inappropriate to be concerned about mice when there are tigers abroad.

- George Box (1976)

Model fitting the way I was taught it as a naive young thing ... quantify the degree of agreement between model and data

(https://psyarxiv.com/2m83v/)

Correlations range from .91 to .95. About what I'd expect for a decent model, but is it ... (gasp) ... ** overfitting**?

The middle-aged cynic, having found a way to "break" every model selection criterion she has tried...

(e.g., https://djnavarro.net/post/a-personal-essay-on-bayes-factors/)

What I do now...

What counts as a __meaningful__ pattern in the data? To what extent is are such patterns a priori predictions of the model?

(https://psyarxiv.com/43auj/)

The same data set and model fits replotted.

Huh. Maybe I'm __underfitting__???

(https://psyarxiv.com/2m83v/)

This theoretically meaningful model failure is barely noticeable on the scatterplot, and a correlation of 0.92 rarely leads us to worry about * underfitting*, does it?

Fit looks good, but is the model overfitting???

Theoretical agreement looks good, but is the model underfitting???

Alas, this iterative process means Sir Ronald Fisher & I are "double dipping". This is purported to be a *questionable research practice*.

Oh well

(1) When __statistical inferences don't work as advertised__, they lose their usual meaning for confirmatory tests. So why be so petrified of making tentative inferences in exploratory analysis?

(2) Science is hard. __Transparency, openness, audit trails__, and scrupulous honesty are absolutely critical. This does **not** mean we must endorse the "remove researcher degrees of freedom to avoid p-hacking" opinion currently popular among methodological reformists

**Thank you**

https://slides.com/djnavarro/scienceandstatistics2

original artwork made with github.com/djnavarro/jasmines

By Danielle Navarro

Slides for my invited talk for the mathematical psychology satellite day at the 2019 psychonomics conference. This is a variation on an earlier talk I gave at the Aarhus open science workshop. http://mathpsych.org/conferences/psychonomics2019/

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I am a computational cognitive scientist at the University of New South Wales. My research focuses on human concept learning, reasoning and decision making.

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