### A Pluto.jl notebook ###
# v0.15.1

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing
        el
    end
end

# ╔═╡ 965a5db0-e1bb-48ad-963f-4335c3d3cb86
begin 
	using Random
	using HypothesisTests
	using StatsBase
	using CairoMakie
	CairoMakie.activate!(type="svg")
	using StatsBase: PValue
	using AlgebraOfGraphics
	using PlutoUI
end

# ╔═╡ 6d4debdf-9099-47f2-bc2a-abfa35098aba
html"<button onclick=present()>Presentation mode</button>"

# ╔═╡ c732429c-c25c-47a9-b1d9-2b4535c49dfe
begin
	const RNG = MersenneTwister(42)
	bign = 10_000
	tinyeffect = 0.05
	x = randn(RNG, bign)
	y = randn(RNG, bign) .+ tinyeffect
	bigntest = OneSampleTTest(x,y)
end;

# ╔═╡ 0989bb85-e5d7-48dc-a489-845d2164288e
md"""
# Putting the NO in ANOVA: the past, present and future (role) of statistics in linguistics and psychology

*Phillip M. Alday* -- no academic affiliation, [www.phillipalday.com](https://www.phillipalday.com)
"""

# ╔═╡ ab25f659-c319-4a80-b1a6-6c0ec16959e1
md"""## Motivation: A literally shitty joke
"""

# ╔═╡ 1bd18ced-9f9f-495d-8fed-afd3bced0a71
html"""
<blockquote class="twitter-tweet" data-lang="en" data-dnt="true"><p lang="en" dir="ltr">Doing statistics should be like going to the bathroom. Yes, you have to do it. Yes, when you do it, you want to do it right. But don&#39;t make a big deal out of it, be careful about telling other people how to do it, and if your whole life is centered on it, there&#39;s something wrong. <a href="https://t.co/neOaFGiXcy">https://t.co/neOaFGiXcy</a></p>&mdash; Victor Ferreira (@victorf13) <a href="https://twitter.com/victorf13/status/1341089602870775810?ref_src=twsrc%5Etfw">December 21, 2020</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
"""

# ╔═╡ 58de8fa1-7024-4438-8abf-3731e39f0c2e
# Ignorance is not something a scientist should be proud of, but it's best not to dwell too long on the fate of the dinosaurs.

md"""Vic, you not washing your hands behind closed doors is making the entire community sick....
"""

# ╔═╡ c14b3061-bb24-4e5e-ba13-88163d6e1844
md"""

## Hold my beer

![](https://imgs.xkcd.com/comics/duty_calls.png)

*Image credit: XKCD*

"""

# ╔═╡ 9f1fc007-b3b3-4bdc-9aa9-193a11182296
md"""

## Who am I?

- 🇺🇸 studied math (**not** statistics!) and German as an undergraduate
- 🇩🇪 masters on language change (regular and irregular verbs in West Germanic)
- 🇩🇪 doctorate in psycholinguistics, with a focus on EEG and designs that aren't possible under the ANOVA framework (naturalistic stimuli, adaptive experiments, and computational modelling)
- 🇦🇺🇳🇱 postdocs in cognitive neuroscience and psycholinguistics
- 🇺🇸 now a neuroscientist in the private sector, looking at improving neurology
- 👉🐻 occasional, but well meaning troll: 
  - [Who’s gotta p? Tripping up statistics in the garden of forking paths](https://hg.sr.ht/~palday/asa-adelaide2016/raw/optional-stopping-in-the-garden.pdf)
  - [Ban the t test!](https://hg.sr.ht/~palday/ban-the-t-test)
- 🎗️ also a white, cis hetero male working in biotech, so *a **ton** of privilege*


*My opinions are my own and do not represent those of my employer (neither past nor present), nor of my collaborators, mentors and friends.*
"""

# ╔═╡ 4c878250-daa9-4b01-a0ec-fc96cd430ace
md"""# The Past"""

# ╔═╡ 045b7a84-ae00-4b62-965f-533244372023
md"""
##  Our old friend the $t$-Test

### Need to generalize from small samples because  ...

- Collecting less data means faster testing
- Fewer numbers easier before computers
- You can't sell what you drink
- Being drunk at work generally frowned upon
"""

# ╔═╡ dd2ef900-88dc-42cb-807f-f412cf70c73e
md"""

## How are $p$-values actually computed?

1. Under the null hypothesis, test statistics -- all those "letter values" have a known distribution
  - either analytic: $z$, $t$, $F$, $\chi^2$, etc.
  - or empirically determined: bootstrapping and other resampling methods
2. Compute the test statistic
  * t-test: mean divided by standard error
  * F-test: between vs. within group variance
  * degrees of freedom compensate for small samples
3. Compare it to the reference distribution
  - Old way: use a table and find out what your $p$-value is less than
  - New way: have the computer figure out a precise value

!!! note
	But Student's paper came out about 20 years before Fisher and the rest developed the notion of statistical significance.
"""

# ╔═╡ 305154c9-8e76-4789-b193-aed0af0e96e9
md"""
## Student's contribution

- Consider situations where the sample isn't so large it behaves like the population

- Propose a small-samples method for estimating the uncertainty

- Finding the reference distribution for $t$-values under a certain set of assumptions (=null hypothesis).

- Do all of this based on intuition and simulation!

"""

# ╔═╡ 122cf668-4b3b-4e75-9c53-6a8f70f45059
md"""

## Let's get technical for a second....

-  "Reference distributions"  are *sampling distributions*, which are the distributions we would see for a particular value when estimating that value from repeated sampling of a population.

- All of the components of a $t$-value have their own sampling distribution.

- Gosset figured out the standard deviation of the sampling distribution of the mean, i.e. the standard error, hence the title *On the probable error of the mean*.

- He showed that that the sampling distribution of this standard error was dependent on sample size (later corrected with Fisher's help to degrees of freedom).

- He then posited a distribution for that the ratio of estimate to the error, i.e. for the $t$-value.

- All of this about 20 years before Fisher and the rest developed the notion of statistical significance!
"""

# ╔═╡ 24c2cafa-d7f9-4a93-a964-265a373b43ba
md"""

## There is only one $t$-test

### Paired t-test
same as one-sample t-test computed on the paired differences

### Two-sample t-test
computed on difference of group means and using an aggregate (pooled) measure of uncertainty

### Welch's t-test
same t-values as above, but degrees of freedom corrected for unequal variance

!!! note
	Many "corrections" in classical testing correct the degrees of freedom, not the test statistic, such as Welch-Satterthwaite, Kenward-Roger, Greenhouse-Geisser, Huynh-Feldt.
"""

# ╔═╡ 293ec083-f05e-4cc8-9597-6742dee4afee
md"""

## A significant step: moving from estimated error to stargazing

![](https://secureservercdn.net/192.169.220.85/hk8.901.myftpupload.com/wp-content/uploads/2020/02/heres-where.png)
"""

# ╔═╡ 59c61df8-6e0e-4734-9da4-f2edc49535c6
md"""
## Ploughing through

- Statistical testing was developed for small samples with big effects:
  - Basic quality control (t-test)
  - Farming techniques and fertilizer (F-test and split-plot designs)
- And were seen an extending the large-sample statistics developed for biometrics and *eugenics*
- And were viewed skeptically even back then, cf. *Karl Pearson* on $n$ vs. $n-1$:
  > because only naughty brewers take n so small that the difference is not of the order of the probable error! 
"""

# ╔═╡ 4febe8bf-24f2-4717-927c-ec8793a8981c
md"""

# The Present-ish 

"""

# ╔═╡ 89f830ed-a329-43de-9127-f5757e688f14
md"""

## Meet Sam the Psych Grad Student

![](https://upload.wikimedia.org/wikipedia/commons/d/d5/Rubber_duck_assisting_with_debugging.jpg)

*Image credit: Wikipedia*

## Sam starts a study

- Sam learns that it's important to be empirical
- Sam collects data, computes means.
- The means differ! 
- Sam has heard that sometimes differences aren't meaningful.
- Sam's supervisor says: compute some statistics and find out if the differences are *significant*.
"""

# ╔═╡ 4fd67b5f-954b-4637-bb77-5dbee364fc14
md"""

## Super significant! 😄 → 😎 → ✔ 📰

"""

# ╔═╡ c8d96e96-4b76-4192-9a66-6c1fca243bac
let f = Figure(), ax = Axis(f[1, 1])
	colors = Makie.cgrad(:Dark2_3, 2; categorical=true,alpha=0.8)
	density!(ax, x; label="x", color=colors[1])	
	density!(ax, y; label="y", color=colors[2])
	ax.title[] = "Within-subjects n=$(bign) and Cohen's d=$(tinyeffect), p = $(PValue(pvalue(bigntest)))"
	f
end

# ╔═╡ 8f8591f7-2d77-40bf-9013-5349274d267d
md"""

## Not significant. 😦 → 😢 → 🚫 📰

"""

# ╔═╡ 19a04cb9-146b-4131-9221-c613ed3d7704
md"""

## Not significant. 😦 → 😢 → 🚫 📰

"""

# ╔═╡ fc89a836-28ba-40fa-ab91-b53503899189
let f = Figure(), ax = Axis(f[1, 1]), n = 20, d=1,
	rng = MersenneTwister(42),
	σ₁ = 3, σ₂ = 1,
	a = σ₁ * randn(rng, n),
	b = σ₂ * randn(rng, n) .+ d,
	test = OneSampleTTest(a, b)
	colors = Makie.cgrad(:Dark2_3, 2; categorical=true,alpha=0.8)
	density!(ax, a; label="a", color=colors[1])	
	density!(ax, b; label="b", color=colors[2])
	ax.title[] = "Within-subjects, n=$(n) and Δμ=$(d), σ₁=$(σ₁), σ₂=$(σ₂), p = $(PValue(pvalue(test)))"
	f
end

# ╔═╡ 0ad512d8-227c-44e7-b3c2-8d0d27b123b4
md"""

## Sam is now so certain about uncertainty.


- This is a learned behavior.
- Sam understands that uncertainty and randomness are things that can fool the scientist.
- Sam understands that you decide whether you have enough certainty by performing the sacred rituals and looking at the stars. 🌠🔭
- Sam thinks some smart person has figured this out and so Sam doesn't have to bother.

- It's Sam the Scientist and not Sam the Statistician after all.
"""

# ╔═╡ 6a7b716e-ffa1-4725-b174-2b9b00342fcc
md"""


## But what are all these rituals actually doing? 

- Somewhere they encode a model of the data and the uncertainty.
- Where did this model go?
- Where did the uncertainty go?
- Where did all the other characteristics go besides the mean?
- Where did the fun go?
"""

# ╔═╡ c09cd562-30ac-418a-b047-d9687d665b4a
md"""

## The Statistical Cargo Cult and the Dance of the $p$-Values

> I think the educational and psychological studies I mentioned are examples of what I would like to call cargo cult science. In the South Seas there is a cargo cult of people. During the war they saw airplanes land with lots of good materials, and they want the same thing to happen now. So they've arranged to make things like runways, to put fires along the sides of the runways, to make a wooden hut for a man to sit in, with two wooden pieces on his head like headphones and bars of bamboo sticking out like antennas-- he's the controller--and they wait for the airplanes to land. They're doing everything right. The form is perfect. It looks exactly the way it looked before. But it doesn't work. No airplanes land. So I call these things cargo cult science, because they follow all the apparent precepts and forms of scientific investigation, but they're missing something essential, because the planes don't land.

*Feynman (1985, adapted from a commencement address in 1974)*

The planes landed in the good old ANOVA times, but the old gestures don't work and the new gestures (keep it maximal) don't either.
"""

# ╔═╡ ffc4449d-8560-4489-b3d8-c0e8ac4f324c
md"""

## What has actually changed in the last 10-20 years?

- Computers became fast and readily available.
- Software for many of these methods became freely available and comparatively usable.
- Following the availability of this computational infrastructure, the expectation arose to actually use it.
- We gained access to powerful tools that Clark and Cohen could only dream of, but then complained that the it took too much skill to operate a lathe and that we should go back to wittling with pocket knives.
- We somehow became even more attached to rituals.
"""

# ╔═╡ 2a3dfba2-0ee6-4e89-85fe-15eae6cbabf0
md""" 

## Meta-Science and the Replication Crisis

We discovered just how poorly we understood and hence practiced experimental design and control: 
  - multiple comparisons
  - optional stoppping
  - circular analysis
  - researcher degrees of freedom (Simmons et al. 2011), "garden of forking paths" (Gelman and Loken 2013)
  - paradoxes of power (cf. Gelman and Carlin 2014)
  - general reporting (if you're using ANOVA, do you always report if you're using Type-1/2/3 ?)

"""

# ╔═╡ ecca8530-3f8d-41c1-ad70-f872a947da4b
md"""
## Lightning Round: Everything Old is New Again
"""

# ╔═╡ f09fd24a-83d0-4acd-b749-a06a27743c71
html"""
<blockquote class="twitter-tweet" data-conversation="none" data-lang="en" data-dnt="true"><p lang="en" dir="ltr">Honestly? For most of what I do, statistical advances since Clark (1973) haven&#39;t done much. I agree for new methods with different (and lots of) data (especially huge databases), new techniques have been very important.</p>&mdash; Victor Ferreira (@victorf13) <a href="https://twitter.com/victorf13/status/1341115351308718080?ref_src=twsrc%5Etfw">December 21, 2020</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script> 
"""

# ╔═╡ 068b5e76-4a38-4f85-a23b-88ea78b06e30
md"""
## Before Clark's seminal paper

- Bayesian statistics (in terms of interpretation of 'probability', not in the sense of Bayes' Theorem): Laplace (1812), Jeffreys (1939, 1946), Savage (1954), de Finetti (1937)
- stochastic / MCMC methods: Metropolis and Ulam (1949), Markov, 
- estimation instead of significance (the "new" statistics): Gauss and Legendre (around 1800), Pearson, Gosset (around 1900); Neyman for confidence (1937)
- shrinkage: Tikhonov (1943), Stein (1956), etc.
- multi-level ("mixed") models: Fisher (1918, random effects models for phylogenetics), Henderson (1950)
- probit regression (Bliss 1934), logistic regression (Wilson and Worecster 1943, Cox 1958)
- "Generalizing to a Language Population" (Coleman 1964)
- power analysis and effect sizes: (Cohen 1962, 1969, 1988, 1990, 1994, ....)
- Simpson's paradox (Simpson 1951, potentially Pearson around 1900)
- Meehl's Paradox (1967)
- cross-validation (early 1970s)
- early robust statistics (Wilcoxon 1945, Mann-Whitney 1947, etc.)
"""

# ╔═╡ bcdbf594-82b0-4045-837f-e46f1c729a05
# <!-- - mixed-models for longitudinal data (Laird and Ware 1982) -->
md"""
## Before I was born:
- GLM for practioners (McCullagh and Nelder 1983)
- GAMs (Hastie and Tibshirani 1986)
- modern robust methods (e.g. Huber 1981)
- resampling methods: jackknife (Tukey 1958, Jaeckel 1972), bootstrap (Efron 1979)
- *Exploratory Data Analysis*, including boxplot (Tukey 1977)
"""

# ╔═╡ 51a5ea45-74ea-4ecf-bada-1eda0fb2b6c6
md"""

## Statistics is about data and uncertainty

This has always been hard and we've been messing it up from the beginning, even things that feel like push-button procedures (e.g. ANOVA).
"""

# ╔═╡ 596e1cfb-e861-4301-a08e-4bb3aae3f923
md"""

## Sometimes "soft science" is the hardest science

- Humans are complex entities with lots of hidden, unobservable state.
- So we'll never achieve the type of experimental control of the physical sciences.
- But even those sciences use advanced methods to handle their data and collect a *lot* of data.
- We have to be experts at both traditional "humanities" and traditional "science".
- But we're still a *science*, which means we need to deal with data and uncertainty. 
- We also need to be explicit about the models we're using and think very hard about whether these models are valid.

*Thanks to Sanjay Srivastava for the pun*

"""

# ╔═╡ 7bb20ce4-f94e-4c30-a90e-1fe1088bf8e6
md"""
> The tool that is so dull that you cannot cut yourself on it is not likely to be sharp enough to be either useful or helpful. 

-- *John Tukey*
"""

# ╔═╡ 5f9d385d-e72e-4491-8a41-be6536e823e8
md"""

## Statistics and science are about both models

- Paraphrasing Box: No theory is perfect, but only some are useful.
- Theories that don't take into account real-world uncertainty and variability aren't going to be particulary useful.
- Using a default model -- ANOVA, "keep it maximal" -- is like making "one size fits all" clothing and never checking whether it actually fits.
"""

# ╔═╡ bbcfebf5-9fbb-4f2c-b0f4-fe8f7a9cc21f
md"""
## Cargo Cult Statistics is Still Cargo Cult Science


![Poorly Drawn Lines "Start Trying"](https://secureservercdn.net/192.169.220.85/hk8.901.myftpupload.com/wp-content/uploads/2021/05/start-trying_web.png)"""

# ╔═╡ 232cf949-c5d5-462e-b26e-f37eb2a7cfdd
 md"""## Cohen warned you about this in the 1960s...."""

# ╔═╡ 10f21faa-1305-4011-8f88-e15d4c4937a7
html"""
<blockquote class="twitter-tweet" data-conversation="none" data-lang="en" data-dnt="true"><p lang="en" dir="ltr">We’re now running 2x2 experiments with 100s of subjects because our complex models require that large an N to test for possible effects we’re not the slightest bit interested in. These Ss have to be paid for or recruited as &quot;volunteers&quot;.</p>&mdash; Fernanda Ferreira (@fernandaedi) <a href="https://twitter.com/fernandaedi/status/1340693039749058560?ref_src=twsrc%5Etfw">December 20, 2020</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script> 
"""

# ╔═╡ 7791cef0-6dd1-4655-be02-16568c4222a6
md"""
> The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data. 
*John Tukey*
"""

# ╔═╡ 3d48c445-6e4f-4319-976e-998d41271d77
md"""

## Measure twice, cut once

- Your analysis plan is part of your experimental plan.
- Use simulation to think about and reason about data and analysis *before collecting real data*
- Conduct pilots to get an idea about real-world error
- Rinse, lather, repeat
- Don't depend on defaults

"""

# ╔═╡ d705232d-81ef-4788-9a22-34b7e874bd10
md"""

## Show the sim example, ya dummy

Then the video

"""

# ╔═╡ 76747c73-8082-40ba-93b1-1ef9746cdfb8
md"""

# The Future (is now)

"""

# ╔═╡ 82e32146-4140-4b17-b8a5-cf7cd8f6f3f9
md"""

## What can we do?

- Start earlier and work continuously
- Collaborate! Team science!
- Value knowledge over publications
- Value estimates over asterisks
- Learn principles first, then software (transferrable skills)
"""

# ╔═╡ 1edd814d-4819-4427-98ad-2b74bb4326c8
md"""

## Principles

- Regression, the general linear model and contrast coding
- Why least squares? 
- Maximum likelihood estimation
- Approximations vs. "exact" methods
  - exact methods to approximate problems
  - approximate solutions to exact problems
- Direct vs. iterative methods
- Bayes Theorem (not just for Bayesians!) and the challenges of conditional vs. marginal probability
- Frequentist and Bayesian conceptions of probability 
- What/why are "models" and living with uncertainty
"""

# ╔═╡ de18cd52-b588-4912-902c-3a150bfc5111
md"""

## Why senior scientists should encourage junior scientists to learn statistics, programming, etc. (i.e. "data science")

- There are not enough jobs in academia.
- These skills are highly paid and valuable in the outside world.
- These skills will give your students and mentees better job prospects when they have/decide to leave academia.
- If you choose ignorance, your students are your only salvation because you won't be able to afford statistical support on the free market. 
- (But ideally, you would choose to evolve and not be a dinosaur.)
"""


# ╔═╡ ae1e9c20-770d-4bfa-9a26-12f7416ad7b0
md"""## This summer school shows the prime facie fallacy of this claim."""

# ╔═╡ 3cdfff8d-5697-4b42-86f3-c1d363488f5d
html"""<blockquote class="twitter-tweet" data-lang="en" data-dnt="true"><p lang="en" dir="ltr">And dividing and conquering, bringing statisticians onto our papers in author roles raises problems. There aren’t enough statisticians to serve as authors *and reviewers* on all our papers. And it’s limiting for the statisticians themselves, as they spend less time in lead roles.</p>&mdash; Victor Ferreira (@victorf13) <a href="https://twitter.com/victorf13/status/1341391146669363200?ref_src=twsrc%5Etfw">December 22, 2020</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>"""

# ╔═╡ 3ed12f62-ad25-4ce5-abdf-3713ece0bae0
md"""

## Don't speak for the group you patronize and paternalize

- Not everybody wants to be in a lead role (support staff scientists! research support staff!)
- "Real" statisticians aren't necessarily motivated by the same desires as cognitive scientists.
- "Real" statisticians may not have to check the same boxes for career advancement.
- What do you think statisticians do if not analyze data and develop tools for doing so?
- For methods people, working with real data and real users is something we need to do in order to do things well!
"""

# ╔═╡ 757a331c-7f53-4b4a-a106-579daa517fcd
md"""
## My Advice: Always be a Student
"""

# ╔═╡ d2a11f29-99ef-458d-811d-9b27893b73d5
md"""

Student was:

- concerned with *error*/*uncertainty* and not *significance*
- noticed when the tools of the day were insufficient
- developed new tools instead of just blindly using the easiest existing tool
- despite not being particularly good at math
- not afraid to collaborate when he needed help
"""

# ╔═╡ 2d6ca834-ed21-4325-94ec-e27f6bbb4b47
md"""
> Dear Fisher
> 
> [...]
>
> And here I think I hear you murmur "Damn the man, why doesn't he refrain from teaching his granny. He's as fussy about his little bit of stuff as a hen with one chick".
>
> To which I reply, "I am, curse you, for the very good reason that I'll never have the chance to incubate an egg which interests me so much".
>
> Cluck. Cluck. Cluck. Cluck.
>
> [...]
>
> I have been shown that my essential cog will hardly ever fit into the machine and when it does is a clog ... then I'll laugh with you-at myself.
>
> Cluck.  Cluck.
>
> Yrs. v. sincerely,
> W.S. Gosset

following Boland (1984)
"""

# ╔═╡ 0b5f8993-ed57-4d92-8f30-615178fca812
md"""

## Embrace uncertainty

!!! think
	Why would expect certain, unchanging rules from the study of uncertainty and variability?

"""

# ╔═╡ 984577f6-0401-4b17-9553-75aebd2c4bb2
md"""

# Thank you for listening!

And special thanks to:

- The SMLP organizers and students
- Center for Interdisciplinary Research (ZiF), Bielefeld for financial support
- Doug Bates, Christina Bergmann, Laurel Brehm, Benedikt Ehinger, Franziska Kretzschmar, Reinhold Kliegl and Jeroen van Paridon for long discussions on statistics (education) and mixed models
- Ina Bornkessel-Schlesewsky for embracing methodological work
- Alannah Jones for the inspiration for the title (and being a great student)
"""

# ╔═╡ fbc69881-7042-4bd1-b364-1806841d73f0
md"""
# Fin*
"""

# ╔═╡ af748a0d-af77-415c-8e03-37bab85e7e92
begin
	n = 20
	d = 0.6
	a = randn(MersenneTwister(4), n)
	b = randn(MersenneTwister(1), n) .+ d
	test = OneSampleTTest(a,b);
end;

# ╔═╡ 9ded6694-4b7b-4e0d-a86f-a00e6f7208c0
let f = Figure(), ax = Axis(f[1, 1])
	colors = Makie.cgrad(:Dark2_3, 2; categorical=true,alpha=0.8)
	density!(ax, a; label="a", color=colors[1])	
	density!(ax, b; label="b", color=colors[2])
	ax.title[] = "Within-subjects, n=$(n) and Cohen's d=$(d), p = $(PValue(pvalue(test)))"
	f
end

# ╔═╡ cce37f9f-d097-46d5-ab5c-9f27f8911cea
md"""
Effect size (Cohen's $d$): $(@bind d_sim PlutoUI.Slider(0:0.1:2; default=0.6, show_value=true))

n participants: $(@bind n_sim PlutoUI.Slider(1:100; default=20, show_value=true))

n iterations: $(@bind n_iter PlutoUI.Slider(1000:100:10_000; default=1000, show_value=true))
"""

# ╔═╡ f02d9156-04b3-4e2a-85e0-2fd6612471de
begin
	rng_sim = MersenneTwister(42)
	xbar = map(1:n_iter) do var
		x_sim = randn(rng_sim, n_sim)
		y_sim = randn(rng_sim, n_sim) .+ d_sim
		test_sim = OneSampleTTest(x_sim, y_sim)
		return test_sim.xbar
	end
	
	#sort!(xbar)
	#tail = round(Int, 0.975 * n_iter)
	
	let f = Figure(), ax = Axis(f[1, 1])
		#colors = Makie.cgrad(:Dark2_3, 2; categorical=true,alpha=0.8)
	 	density!(ax, xbar)#; color=colors[1])	
		#vlines!(ax, xbar[tail])
	 	ax.title[] = "Estimate difference across $(n_iter) replications, Type S rate: $(round(mean(>(d_sim), xbar); sigdigits=3)*100)%"
	 	f
	 end
	
end

# ╔═╡ c28337fb-464b-4d2f-a8ea-9e1dd7ebd41d
# HTML("<style> main { max-width:1000px; } </style> ")

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
AlgebraOfGraphics = "cbdf2221-f076-402e-a563-3d30da359d67"
CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
HypothesisTests = "09f84164-cd44-5f33-b23f-e6b0d136a0d5"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"

[compat]
AlgebraOfGraphics = "~0.5.3"
CairoMakie = "~0.6.5"
HypothesisTests = "~0.10.4"
PlutoUI = "~0.7.9"
StatsBase = "~0.33.10"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

[[AbstractFFTs]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.0.1"

[[AbstractTrees]]
git-tree-sha1 = "03e0550477d86222521d254b741d470ba17ea0b5"
uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
version = "0.3.4"

[[Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.3.1"

[[AlgebraOfGraphics]]
deps = ["Colors", "Dates", "FileIO", "GLM", "GeoInterface", "GeometryBasics", "GridLayoutBase", "KernelDensity", "Loess", "Makie", "PlotUtils", "PooledArrays", "RelocatableFolders", "StatsBase", "StructArrays", "Tables"]
git-tree-sha1 = "40446e661ffe7a33c31980ec6438181daa41deff"
uuid = "cbdf2221-f076-402e-a563-3d30da359d67"
version = "0.5.3"

[[Animations]]
deps = ["Colors"]
git-tree-sha1 = "e81c509d2c8e49592413bfb0bb3b08150056c79d"
uuid = "27a7e980-b3e6-11e9-2bcd-0b925532e340"
version = "0.4.1"

[[ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"

[[ArrayInterface]]
deps = ["IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
git-tree-sha1 = "85d03b60274807181bae7549bb22b2204b6e5a0e"
uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
version = "3.1.30"

[[Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"

[[Automa]]
deps = ["Printf", "ScanByte", "TranscodingStreams"]
git-tree-sha1 = "d50976f217489ce799e366d9561d56a98a30d7fe"
uuid = "67c07d97-cdcb-5c2c-af73-a7f9c32a568b"
version = "0.8.2"

[[AxisAlgorithms]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
git-tree-sha1 = "a4d07a1c313392a77042855df46c5f534076fab9"
uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
version = "1.0.0"

[[Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"

[[Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+0"

[[CEnum]]
git-tree-sha1 = "215a9aa4a1f23fbd05b92769fdd62559488d70e9"
uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
version = "0.4.1"

[[Cairo]]
deps = ["Cairo_jll", "Colors", "Glib_jll", "Graphics", "Libdl", "Pango_jll"]
git-tree-sha1 = "d0b3f8b4ad16cb0a2988c6788646a5e6a17b6b1b"
uuid = "159f3aea-2a34-519c-b102-8c37f9878175"
version = "1.0.5"

[[CairoMakie]]
deps = ["Base64", "Cairo", "Colors", "FFTW", "FileIO", "FreeType", "GeometryBasics", "LinearAlgebra", "Makie", "SHA", "StaticArrays"]
git-tree-sha1 = "8664989955daccc90002629aa80193e44893bb45"
uuid = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
version = "0.6.5"

[[Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "f2202b55d816427cd385a9a4f3ffb226bee80f99"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.1+0"

[[ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "bdc0937269321858ab2a4f288486cb258b9a0af7"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.3.0"

[[ColorBrewer]]
deps = ["Colors", "JSON", "Test"]
git-tree-sha1 = "61c5334f33d91e570e1d0c3eb5465835242582c4"
uuid = "a2cac450-b92f-5266-8821-25eda20663c8"
version = "0.4.0"

[[ColorSchemes]]
deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random"]
git-tree-sha1 = "9995eb3977fbf67b86d0a0a0508e83017ded03f2"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.14.0"

[[ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.0"

[[ColorVectorSpace]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "SpecialFunctions", "Statistics", "TensorCore"]
git-tree-sha1 = "42a9b08d3f2f951c9b283ea427d96ed9f1f30343"
uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
version = "0.9.5"

[[Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.8"

[[Combinatorics]]
git-tree-sha1 = "08c8b6831dc00bfea825826be0bc8336fc369860"
uuid = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
version = "1.0.2"

[[CommonSolve]]
git-tree-sha1 = "68a0743f578349ada8bc911a5cbd5a2ef6ed6d1f"
uuid = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
version = "0.2.0"

[[Compat]]
deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
git-tree-sha1 = "727e463cfebd0c7b999bbf3e9e7e16f254b94193"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "3.34.0"

[[CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"

[[ConstructionBase]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "f74e9d5388b8620b4cee35d4c5a618dd4dc547f4"
uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
version = "1.3.0"

[[Contour]]
deps = ["StaticArrays"]
git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.5.7"

[[DataAPI]]
git-tree-sha1 = "ee400abb2298bd13bfc3df1c412ed228061a2385"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.7.0"

[[DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "7d9d316f04214f7efdbb6398d545446e246eff02"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.10"

[[DataValueInterfaces]]
git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
version = "1.0.0"

[[Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"

[[DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"

[[Distances]]
deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
git-tree-sha1 = "abe4ad222b26af3337262b8afb28fab8d215e9f8"
uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
version = "0.10.3"

[[Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"

[[Distributions]]
deps = ["ChainRulesCore", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns"]
git-tree-sha1 = "c2dbc7e0495c3f956e4615b78d03c7aa10091d0c"
uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
version = "0.25.15"

[[DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "a32185f5428d3986f47c2ab78b1f216d5e6cc96f"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.8.5"

[[Downloads]]
deps = ["ArgTools", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"

[[EarCut_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "92d8f9f208637e8d2d28c664051a00569c01493d"
uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
version = "2.1.5+1"

[[EllipsisNotation]]
deps = ["ArrayInterface"]
git-tree-sha1 = "8041575f021cba5a099a456b4163c9a08b566a02"
uuid = "da5c29d0-fa7d-589e-88eb-ea29b0a81949"
version = "1.1.0"

[[Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b3bfd02e98aedfa5cf885665493c5598c350cd2f"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.2.10+0"

[[FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.1"

[[FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "d8a578692e3077ac998b50c0217dfd67f21d1e5f"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.4.0+0"

[[FFTW]]
deps = ["AbstractFFTs", "FFTW_jll", "LinearAlgebra", "MKL_jll", "Preferences", "Reexport"]
git-tree-sha1 = "f985af3b9f4e278b1d24434cbb546d6092fca661"
uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
version = "1.4.3"

[[FFTW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3676abafff7e4ff07bbd2c42b3d8201f31653dcc"
uuid = "f5851436-0d7a-5f13-b9de-f02708fd171a"
version = "3.3.9+8"

[[FileIO]]
deps = ["Pkg", "Requires", "UUIDs"]
git-tree-sha1 = "937c29268e405b6808d958a9ac41bfe1a31b08e7"
uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
version = "1.11.0"

[[FillArrays]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "Statistics"]
git-tree-sha1 = "7c365bdef6380b29cfc5caaf99688cd7489f9b87"
uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
version = "0.12.2"

[[FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"

[[Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.93+0"

[[Formatting]]
deps = ["Printf"]
git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
version = "0.4.2"

[[FreeType]]
deps = ["CEnum", "FreeType2_jll"]
git-tree-sha1 = "cabd77ab6a6fdff49bfd24af2ebe76e6e018a2b4"
uuid = "b38be410-82b0-50bf-ab77-7b57e271db43"
version = "4.0.0"

[[FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.10.4+0"

[[FreeTypeAbstraction]]
deps = ["ColorVectorSpace", "Colors", "FreeType", "GeometryBasics", "StaticArrays"]
git-tree-sha1 = "19d0f1e234c13bbfd75258e55c52aa1d876115f5"
uuid = "663a7486-cb36-511b-a19d-713bb74d65c9"
version = "0.9.2"

[[FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.10+0"

[[Future]]
deps = ["Random"]
uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"

[[GLM]]
deps = ["Distributions", "LinearAlgebra", "Printf", "Reexport", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "StatsModels"]
git-tree-sha1 = "f564ce4af5e79bb88ff1f4488e64363487674278"
uuid = "38e38edf-8417-5370-95a0-9cbb8c7f171a"
version = "1.5.1"

[[GeoInterface]]
deps = ["RecipesBase"]
git-tree-sha1 = "38a649e6a52d1bea9844b382343630ac754c931c"
uuid = "cf35fbd7-0cd7-5166-be24-54bfbe79505f"
version = "0.5.5"

[[GeometryBasics]]
deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
git-tree-sha1 = "58bcdf5ebc057b085e58d95c138725628dd7453c"
uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
version = "0.4.1"

[[Gettext_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
version = "0.21.0+0"

[[Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "7bf67e9a481712b3dbe9cb3dac852dc4b1162e02"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.68.3+0"

[[Graphics]]
deps = ["Colors", "LinearAlgebra", "NaNMath"]
git-tree-sha1 = "2c1cf4df419938ece72de17f368a021ee162762e"
uuid = "a2bd30eb-e257-5431-a919-1863eab51364"
version = "1.1.0"

[[Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
version = "1.3.14+0"

[[GridLayoutBase]]
deps = ["GeometryBasics", "InteractiveUtils", "Match", "Observables"]
git-tree-sha1 = "e2f606c87d09d5187bb6069dab8cee0af7c77bdb"
uuid = "3955a311-db13-416c-9275-1d80ed98e5e9"
version = "0.6.1"

[[Grisu]]
git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"

[[HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
git-tree-sha1 = "8a954fed8ac097d5be04921d595f741115c1b2ad"
uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
version = "2.8.1+0"

[[HypothesisTests]]
deps = ["Combinatorics", "Distributions", "LinearAlgebra", "Random", "Rmath", "Roots", "Statistics", "StatsBase"]
git-tree-sha1 = "a82a0c7e790fc16be185ce8d6d9edc7e62d5685a"
uuid = "09f84164-cd44-5f33-b23f-e6b0d136a0d5"
version = "0.10.4"

[[IfElse]]
git-tree-sha1 = "28e837ff3e7a6c3cdb252ce49fb412c8eb3caeef"
uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
version = "0.1.0"

[[ImageCore]]
deps = ["AbstractFFTs", "ColorVectorSpace", "Colors", "FixedPointNumbers", "Graphics", "MappedArrays", "MosaicViews", "OffsetArrays", "PaddedViews", "Reexport"]
git-tree-sha1 = "595155739d361589b3d074386f77c107a8ada6f7"
uuid = "a09fc81d-aa75-5fe9-8630-4744c3626534"
version = "0.9.2"

[[ImageIO]]
deps = ["FileIO", "Netpbm", "OpenEXR", "PNGFiles", "TiffImages", "UUIDs"]
git-tree-sha1 = "13c826abd23931d909e4c5538643d9691f62a617"
uuid = "82e4d734-157c-48bb-816b-45c225c6df19"
version = "0.5.8"

[[Imath_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "87f7662e03a649cffa2e05bf19c303e168732d3e"
uuid = "905a6f67-0a94-5f89-b386-d35d92009cd1"
version = "3.1.2+0"

[[IndirectArrays]]
git-tree-sha1 = "c2a145a145dc03a7620af1444e0264ef907bd44f"
uuid = "9b13fd28-a010-5f03-acff-a1bbcff69959"
version = "0.5.1"

[[Inflate]]
git-tree-sha1 = "f5fc07d4e706b84f72d54eedcc1c13d92fb0871c"
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[[IntelOpenMP_jll]]
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[[InteractiveUtils]]
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[[Interpolations]]
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[[IntervalSets]]
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[[IrrationalConstants]]
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[[Isoband]]
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[[IteratorInterfaceExtensions]]
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[[JLLWrappers]]
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[[JSON]]
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[[LaTeXStrings]]
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[[LibCURL]]
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[[LibCURL_jll]]
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[[LibGit2]]
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[[LibSSH2_jll]]
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[[Libdl]]
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[[Libffi_jll]]
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[[Libgcrypt_jll]]
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[[Libgpg_error_jll]]
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[[Libiconv_jll]]
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[[Libmount_jll]]
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[[Libuuid_jll]]
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[[Loess]]
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[[Logging]]
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[[MKL_jll]]
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[[Match]]
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[[MathTeXEngine]]
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[[MbedTLS_jll]]
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[[Missings]]
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[[MozillaCACerts_jll]]
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[[NaNMath]]
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[[Netpbm]]
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[[Ogg_jll]]
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[[OpenEXR_jll]]
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[[OpenSSL_jll]]
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[[OpenSpecFun_jll]]
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[[Opus_jll]]
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[[OrderedCollections]]
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[[PCRE_jll]]
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[[PDMats]]
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[[PNGFiles]]
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[[Pixman_jll]]
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[[PkgVersion]]
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[[PlutoUI]]
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[[ProgressMeter]]
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[[Random]]
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[[Ratios]]
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[[RelocatableFolders]]
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[[Requires]]
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[[Rmath]]
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[[Rmath_jll]]
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[[Roots]]
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[[SHA]]
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[[SIMD]]
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[[ScanByte]]
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[[Scratch]]
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version = "1.1.0"

[[Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[Setfield]]
deps = ["ConstructionBase", "Future", "MacroTools", "Requires"]
git-tree-sha1 = "fca29e68c5062722b5b4435594c3d1ba557072a3"
uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
version = "0.7.1"

[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[ShiftedArrays]]
git-tree-sha1 = "22395afdcf37d6709a5a0766cc4a5ca52cb85ea0"
uuid = "1277b4bf-5013-50f5-be3d-901d8477a67a"
version = "1.0.0"

[[Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"

[[SignedDistanceFields]]
deps = ["Random", "Statistics", "Test"]
git-tree-sha1 = "d263a08ec505853a5ff1c1ebde2070419e3f28e9"
uuid = "73760f76-fbc4-59ce-8f25-708e95d2df96"
version = "0.4.0"

[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.0.1"

[[SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[SpecialFunctions]]
deps = ["ChainRulesCore", "LogExpFunctions", "OpenSpecFun_jll"]
git-tree-sha1 = "a322a9493e49c5f3a10b50df3aedaf1cdb3244b7"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "1.6.1"

[[StackViews]]
deps = ["OffsetArrays"]
git-tree-sha1 = "46e589465204cd0c08b4bd97385e4fa79a0c770c"
uuid = "cae243ae-269e-4f55-b966-ac2d0dc13c15"
version = "0.1.1"

[[Static]]
deps = ["IfElse"]
git-tree-sha1 = "854b024a4a81b05c0792a4b45293b85db228bd27"
uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
version = "0.3.1"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "3240808c6d463ac46f1c1cd7638375cd22abbccb"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.2.12"

[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[StatsAPI]]
git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.0.0"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "8cbbc098554648c84f79a463c9ff0fd277144b6c"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.10"

[[StatsFuns]]
deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
git-tree-sha1 = "46d7ccc7104860c38b11966dd1f72ff042f382e4"
uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
version = "0.9.10"

[[StatsModels]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Printf", "ShiftedArrays", "SparseArrays", "StatsBase", "StatsFuns", "Tables"]
git-tree-sha1 = "3fa15c1f8be168e76d59097f66970adc86bfeb95"
uuid = "3eaba693-59b7-5ba5-a881-562e759f1c8d"
version = "0.6.25"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "1700b86ad59348c0f9f68ddc95117071f947072d"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.1"

[[SuiteSparse]]
deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"

[[Suppressor]]
git-tree-sha1 = "a819d77f31f83e5792a76081eee1ea6342ab8787"
uuid = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
version = "0.2.0"

[[TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"

[[TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "d0c690d37c73aeb5ca063056283fde5585a41710"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.5.0"

[[Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

[[TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

[[Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[TiffImages]]
deps = ["ColorTypes", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "OffsetArrays", "OrderedCollections", "PkgVersion", "ProgressMeter"]
git-tree-sha1 = "03fb246ac6e6b7cb7abac3b3302447d55b43270e"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
version = "0.4.1"

[[TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "216b95ea110b5972db65aa90f88d8d89dcb8851c"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.6"

[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "59e2ad8fd1591ea019a5259bd012d7aee15f995c"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.3"

[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[isoband_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "a1ac99674715995a536bbce674b068ec1b7d893d"
uuid = "9a68df92-36a6-505f-a73e-abb412b6bfb4"
version = "0.2.2+0"

[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+0"

[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"

[[x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"
"""

# ╔═╡ Cell order:
# ╟─6d4debdf-9099-47f2-bc2a-abfa35098aba
# ╟─965a5db0-e1bb-48ad-963f-4335c3d3cb86
# ╟─c732429c-c25c-47a9-b1d9-2b4535c49dfe
# ╟─0989bb85-e5d7-48dc-a489-845d2164288e
# ╟─ab25f659-c319-4a80-b1a6-6c0ec16959e1
# ╟─1bd18ced-9f9f-495d-8fed-afd3bced0a71
# ╟─58de8fa1-7024-4438-8abf-3731e39f0c2e
# ╟─c14b3061-bb24-4e5e-ba13-88163d6e1844
# ╟─9f1fc007-b3b3-4bdc-9aa9-193a11182296
# ╟─4c878250-daa9-4b01-a0ec-fc96cd430ace
# ╟─045b7a84-ae00-4b62-965f-533244372023
# ╟─dd2ef900-88dc-42cb-807f-f412cf70c73e
# ╟─305154c9-8e76-4789-b193-aed0af0e96e9
# ╟─122cf668-4b3b-4e75-9c53-6a8f70f45059
# ╟─24c2cafa-d7f9-4a93-a964-265a373b43ba
# ╟─293ec083-f05e-4cc8-9597-6742dee4afee
# ╟─59c61df8-6e0e-4734-9da4-f2edc49535c6
# ╟─4febe8bf-24f2-4717-927c-ec8793a8981c
# ╟─89f830ed-a329-43de-9127-f5757e688f14
# ╟─4fd67b5f-954b-4637-bb77-5dbee364fc14
# ╟─c8d96e96-4b76-4192-9a66-6c1fca243bac
# ╟─8f8591f7-2d77-40bf-9013-5349274d267d
# ╟─9ded6694-4b7b-4e0d-a86f-a00e6f7208c0
# ╟─19a04cb9-146b-4131-9221-c613ed3d7704
# ╟─fc89a836-28ba-40fa-ab91-b53503899189
# ╟─0ad512d8-227c-44e7-b3c2-8d0d27b123b4
# ╟─6a7b716e-ffa1-4725-b174-2b9b00342fcc
# ╟─c09cd562-30ac-418a-b047-d9687d665b4a
# ╟─ffc4449d-8560-4489-b3d8-c0e8ac4f324c
# ╟─2a3dfba2-0ee6-4e89-85fe-15eae6cbabf0
# ╟─ecca8530-3f8d-41c1-ad70-f872a947da4b
# ╟─f09fd24a-83d0-4acd-b749-a06a27743c71
# ╟─068b5e76-4a38-4f85-a23b-88ea78b06e30
# ╟─bcdbf594-82b0-4045-837f-e46f1c729a05
# ╟─51a5ea45-74ea-4ecf-bada-1eda0fb2b6c6
# ╟─596e1cfb-e861-4301-a08e-4bb3aae3f923
# ╟─7bb20ce4-f94e-4c30-a90e-1fe1088bf8e6
# ╟─5f9d385d-e72e-4491-8a41-be6536e823e8
# ╟─bbcfebf5-9fbb-4f2c-b0f4-fe8f7a9cc21f
# ╟─232cf949-c5d5-462e-b26e-f37eb2a7cfdd
# ╟─10f21faa-1305-4011-8f88-e15d4c4937a7
# ╟─7791cef0-6dd1-4655-be02-16568c4222a6
# ╟─3d48c445-6e4f-4319-976e-998d41271d77
# ╟─d705232d-81ef-4788-9a22-34b7e874bd10
# ╟─76747c73-8082-40ba-93b1-1ef9746cdfb8
# ╟─82e32146-4140-4b17-b8a5-cf7cd8f6f3f9
# ╟─1edd814d-4819-4427-98ad-2b74bb4326c8
# ╟─de18cd52-b588-4912-902c-3a150bfc5111
# ╟─ae1e9c20-770d-4bfa-9a26-12f7416ad7b0
# ╟─3cdfff8d-5697-4b42-86f3-c1d363488f5d
# ╟─3ed12f62-ad25-4ce5-abdf-3713ece0bae0
# ╟─757a331c-7f53-4b4a-a106-579daa517fcd
# ╟─d2a11f29-99ef-458d-811d-9b27893b73d5
# ╟─2d6ca834-ed21-4325-94ec-e27f6bbb4b47
# ╟─0b5f8993-ed57-4d92-8f30-615178fca812
# ╟─984577f6-0401-4b17-9553-75aebd2c4bb2
# ╟─fbc69881-7042-4bd1-b364-1806841d73f0
# ╟─af748a0d-af77-415c-8e03-37bab85e7e92
# ╟─cce37f9f-d097-46d5-ab5c-9f27f8911cea
# ╟─f02d9156-04b3-4e2a-85e0-2fd6612471de
# ╟─c28337fb-464b-4d2f-a8ea-9e1dd7ebd41d
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
