thoughts+ideas: extreme heat example

[Jason Miller]

Hey EAPOST Community,

I just experienced the workshops on 4/26 at SLO and felt so engaged and interested.  Thank you to the presenters!

After spending some time reflecting on the workshops and writing up some notes, I remembered something I wrote up in 2021 when we had some extreme heat events on the West Coast.  I wanted to explore how rare the event was from an historical (data) context.  So I played with some data in R and wrote up this exploration:

http://thecoldfish.com/2021/07/03/june-28-weather-anomaly.html

I'm wondering how I could approach the question from a simulation perspective?  I'm also wondering how seasoned stats instructors might approach this question differently if they used it in a classroom.

I look forward to reading responses.

Jason

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Jason E. Miller, Ph.D.; KM6PSZ
C: 660-234-5028

If you have an apple and I have an apple and we exchange these apples then you and I will still each have one apple. But if you have an idea and I have an idea and we exchange these ideas, then each of us will have two ideas.
--George Bernard Shaw

[soma...@gmail.com]

Hi Jason,

Thanks for sharing your post! I have a similar dataset on global temps over the years that we look at, which I have only done descriptive statistics with, and looked at how far a particular year is using the methods you describe in your post. I have not used any simulation strategies with this yet. So, I am curious to hear too what others have tried or might suggest! :)

I am glad you found the workshop helpful! It was great to have you here!

Also, I love that G. B. Shaw quote in your signature.

Take care,

Soma

[nathan...@gmail.com]

Jason – yes, thanks for sharing this. Like Soma, I haven’t done a ton with simulation in contexts like this, however, I can think of a few ideas that I’m curious for others perspectives on.

 

1. I think the concept of a theoretical probability model (normal distribution) is not a ‘simple one’ for students to get (I think they get the shape idea easily, I’m not convinced they necessarily understand what it means). So, I think that you could envision a simulation where you sample from a normally distributed dataset (or randomly draw from a theoretical normal – rnorm function in R). You could use the “Sampling Words” applet for the former option (https://www.isi-stats.com/isi2nd/ISIapplets2021.html). This could make the idea of “normally distributed” more concrete for students, then you could use that sampled population/distribution to investigate the empirical probability of the 115 degree day and use that as a segue to the ‘true’ (long-run) likelihood of a 115 degree day IF the population was normally distributed.
   
   
2. I think that you also could then also think about how the normal approximation/distribution is an assumption and just use the actual data you have to compute the empirical probability of a 115 degree day on your actual observed data (in this case it’s 0 because you never got a day that high). You could then talk about the pros/cons of the “assumption based” approach (assumed normal – but probably not actually normal) vs. less assumptions -but “0” isn’t all that informative?
   
3. I could see students then naturally asking the question about some ‘better model’ – so, this could naturally lead into some other ‘standard’ probability distributions (log-normal?) and using a similar approach to #1 to evaluate fit and likelihood of 115 degree day.  
   
   
4. Finally, I think you could consider pulling in time as another variable as my guess is that the mean temp is probably going up over time. You could then use regression to predict the mean (and SD) of the normal distribution of temp’s for 2024 and do similar things. Opening the door to regression also then gives you more simulation options and related research questions, including prediction intervals vs. confidence intervals, R-squared, etc.

 

In general, I usually feel like anything we can do to make theoretical ideas (in this case theoretical distributions) more concrete is a good thing – hence sampling from a dataset that is actually normally distribution I think helps scaffold students understand of what the “smooth red lines” are in your graphs.

 

Thanks!

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[EAPOST Group]

I hope this is related to Nathan's post and the original question, apologies if not but rushing, but this is something new I tried this quarter.  It's a "jotform" but you can put in a few letters for your name and email to see the rest...

https://form.jotform.com/250908916466164