Catch a wild distribution

A practice of the most basic bit of applied statistics you can do, and a foundation for what comes next.

To warm up for this class we will conduct a brief exercise. This exercise serves a few purposes.

It will help us to think about data generating processes.
It will introduce us to some of the bestiary of statistical distributions that have been invented.
It will help us practice the whole cycle of applied statistics: question, simulation, data collection, fitting and checking a model, interpretation.

Most importantly, it will help us to get to know each other a bit!

Group Exercise

Separate yourselves into groups. The groups should be at least 2 people. Suggestion pair with people you’ve only just met.

Each group should pick a different quantity that they will measure repeatedly. This can be anything that you can measure rooughly 30 times in the next 90 minutes. Your measurements should be of the SAME thing. Here are some ideas to get you started:

How long can someone hop on one foot ?
Amount of change in everyone’s pockets ?
How many birds can you hear in 2 minutes ?

Hypothesize

What statiscal distribution might describe the observations you are sampling/measuring? What are its property? Think about the kind of statistical distribution that might represent this phenomenon! Take a moment and write down the name of the distribution, and why it might describe the thing you’re going to measure.

Simulate

create a simulation of the data you’re about to collect. Every statistical distribution has four functions in R, and here you can use two of them:

Density function (starting with d)
Random generation function (starting with r).

For example, dnorm() and rnorm. Simulate about as many number as you hope to collect. There’s a quick example below.

Collect

After you have an idea of what your data might look like, go and get some! Try to get a good number (30 or more), this should take roughly 1 hour.

Visualize and fit

Enter the data into R and visualize them. Do they match your hypothesized distribution? How do you know? If it doesn’t match, why might that be? For this step you have a couple of choices:

Compare histograms
hist() (base R) or geom_hist (ggplot2 R package)
fitdistr (MASS R package)
optim (base R)
Stan (we’ll do this one tomorrow!)

Discuss

We’ll go around the room and each group will do a brief show-and-tell of their chosen distribution, their measurement methods, their results and what they might mean!

--- title: "Catch a wild distribution" description: | A practice of the most basic bit of applied statistics you can do, and a foundation for what comes next. execute: freeze: true comments: hypothesis: false format: html: code-tools: true --- To warm up for this class we will conduct a brief exercise. This exercise serves a few purposes. 1. It will help us to think about data generating processes. 2. It will introduce us to some of the bestiary of statistical distributions that have been invented. 3. It will help us practice the whole cycle of applied statistics: question, simulation, data collection, fitting and checking a model, interpretation. Most importantly, it will help us to get to know each other a bit! ## Group Exercise <aside>What makes things the "same" from the point of view of this exercise? Please take some time with your group to talk about what we mean by the word "same"!</aside> Separate yourselves into groups. The groups should be at least 2 people. _Suggestion_ pair with people you've only just met. Each group should pick a different quantity that they will measure repeatedly. This can be anything that you can measure rooughly 30 times in the next 90 minutes. Your measurements should be of the **SAME** thing. Here are some ideas to get you started: - How long can someone hop on one foot ? - Amount of change in everyone's pockets ? - How many birds can you hear in 2 minutes ? ### Hypothesize What statiscal distribution might describe the observations you are sampling/measuring? What are its property? Think about the kind of statistical distribution that might represent this phenomenon! Take a moment and write down the name of the distribution, and why it might describe the thing you're going to measure. ### Simulate create a simulation of the data you're about to collect. Every statistical distribution has four functions in R, and here you can use two of them: - Density function (starting with `d`) - Random generation function (starting with `r`). For example, `dnorm()` and `rnorm`. Simulate about as many number as you hope to collect. There's a quick example below. ### Collect After you have an idea of what your data might look like, go and get some! Try to get a good number (30 or more), this should take roughly 1 hour. ### Visualize and fit Enter the data into R and visualize them. Do they match your hypothesized distribution? How do you know? If it doesn't match, why might that be? For this step you have a couple of choices: - Compare histograms - `hist()` (base R) or `geom_hist` (ggplot2 R package) - `fitdistr` (MASS R package) - `optim` (base R) - `Stan` (we'll do this one tomorrow!) ### Discuss We'll go around the room and each group will do a brief show-and-tell of their chosen distribution, their measurement methods, their results and what they might mean!