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AI explanation

^{Show image generation prompt} Model: dalle-3
Prompt: Prompt: [ Concept art ] In a twilight-lit town square, the once vibrant taper candle shop stands with fading signboards, surrounded by scattered remnants of empty shelves. A nostalgic air hangs over the deserted storefront, as the last few flickering tapers illuminate the fading name "Toby" etched into the signboard, now largely forgotten. The depiction should include only scenes, people, and objects, it should not include text or speech bubbles.

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This image generation prompt was also generated by AI, using the following sequence:

Model: gpt-3.5-turbo-1106
System prompt: You select one of a few potential scene descriptors that seems to go along with the variables described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here are two variables: Popularity of the first name Toby and The number of tapers in Texas. Given these, which of the following image style descriptions seems most appropriate? Pick the one that seems to be related to one of the variables at hand. Please respond with only one of the following potential descriptions: Concept art a meme Concept art Psychedelic Vaporwave
ChatGPT: Concept art

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both Popularity of the first name Toby and The number of tapers in Texas, in the following situation: Because as the popularity of the name Toby decreased, fewer parents were naming their children Toby. As a result, there were fewer people with the name Toby in Texas, and since Tobys are known for their affinity for taper candles, the demand for tapers decreased, leading to a drop in the number of tapers in Texas.. Keep the description simple.
ChatGPT: In a small Texas town, the name Toby used to be very popular, with many children named Toby. But as time passed, the popularity of the name Toby diminished, and there were fewer Tobys around. As a result, the local taper candle shop, which once had a bustling trade, now had fewer customers, and the shelves that were once filled with tapers were now sparsely stocked.

Model: gpt-3.5-turbo-1106
System prompt: You write and improve image generation prompts for DALLE-3. You maintain the same subjects, but enhance the visuals.
User prompt: Please respond with an image generation prompt that would be likely to create an interesting visual using DALLE-3, using the following style: [ Concept art ] and depicting this scene: In a small Texas town, the name Toby used to be very popular, with many children named Toby. But as time passed, the popularity of the name Toby diminished, and there were fewer Tobys around. As a result, the local taper candle shop, which once had a bustling trade, now had fewer customers, and the shelves that were once filled with tapers were now sparsely stocked. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Prompt: [ Concept art ] In a twilight-lit town square, the once vibrant taper candle shop stands with fading signboards, surrounded by scattered remnants of empty shelves. A nostalgic air hangs over the deserted storefront, as the last few flickering tapers illuminate the fading name "Toby" etched into the signboard, now largely forgotten.

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*Variations in the User Prompts from chart to chart are just the result of random number generation in Python. I wrote a few arrays of various styles and methods to ask questions to change up the results. Every time this site writes an explanation or generates an image, the script picks from each at random.

I sequence the requests into multiple prompts because I find GPT 3.5 to perform much better with short, well-managed contexts. Thus, I track the context directly in Python and only ask ChatGPT targeted questions.

AI academic paper

Toby or Not Toby: A Tantalizing Tale of Tapers in Texas Journal of Tapered Tales and Trivial Tidbits Jan 2024 Reminder: This paper is AI-generated. Not real!

Problem variable:	Which variable has a problem? Popularity of the first name Toby The number of tapers in Texas Neither / both
Issue:	What is the issue? The data is incorrect The chart isn't displaying properly There is a typo The source link is incorrect A calculation is wrong Something else
Additional details: Optional
Confirm you are a human:

Data details

Why this works

1. Data dredging: I have 25,153 variables in my database. I compare all these variables against each other to find ones that randomly match up. That's 632,673,409 correlation calculations! This is called “data dredging.” Instead of starting with a hypothesis and testing it, I instead abused the data to see what correlations shake out. It’s a dangerous way to go about analysis, because any sufficiently large dataset will yield strong correlations completely at random.
2. Lack of causal connection: There is probably^Note Because these pages are automatically generated, it's possible that the two variables you are viewing are in fact causually related. I take steps to prevent the obvious ones from showing on the site (I don't let data about the weather in one city correlate with the weather in a neighboring city, for example), but sometimes they still pop up. If they are related, cool! You found a loophole.
   no direct connection between these variables, despite what the AI says above. This is exacerbated by the fact that I used "Years" as the base variable. Lots of things happen in a year that are not related to each other! Most studies would use something like "one person" in stead of "one year" to be the "thing" studied.
3. Observations not independent: For many variables, sequential years are not independent of each other. If a population of people is continuously doing something every day, there is no reason to think they would suddenly change how they are doing that thing on January 1. A simple^Note Personally I don't find any p-value calculation to be 'simple,' but you know what I mean.
   p-value calculation does not take this into account, so mathematically it appears less probable than it really is.
4. Y-axis doesn't start at zero: I truncated the Y-axes of the graph above. I also used a line graph, which makes the visual connection stand out more than it deserves. ^Note Nothing against line graphs. They are great at telling a story when you have linear data! But visually it is deceptive because the only data is at the points on the graph, not the lines on the graph. In between each point, the data could have been doing anything. Like going for a random walk by itself!
   Mathematically what I showed is true, but it is intentionally misleading. Below is the same chart but with both Y-axes starting at zero.

Try it yourself

# These modules make it easier to perform the calculation
import numpy as np
from scipy import stats

# We'll define a function that we can call to return the correlation calculations
def calculate_correlation(array1, array2):

    # Calculate Pearson correlation coefficient and p-value
    correlation, p_value = stats.pearsonr(array1, array2)

    # Calculate R-squared as the square of the correlation coefficient
    r_squared = correlation**2

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([645,677,594,570,513,493,452,409,352,451,554,520,451,395,363,337,301,262,])
array_2 = np.array([900,1060,750,840,910,1080,810,470,350,510,1010,770,590,520,350,400,90,300,])
array_1_name = "Popularity of the first name Toby"
array_2_name = "The number of tapers in Texas"

# Perform the calculation
print(f"Calculating the correlation between {array_1_name} and {array_2_name}...")
correlation, r_squared, p_value = calculate_correlation(array_1, array_2)

# Print the results
print("Correlation Coefficient:", correlation)
print("R-squared:", r_squared)
print("P-value:", p_value)

Reuseable content

• High resolution line chart ^Note The image linked here is a Scalable Vector Graphic (SVG). It is the highest resolution that is possible to achieve. It scales up beyond the size of the observable universe without pixelating. You do not need to email me asking if I have a higher resolution image. I do not. The physical limitations of our universe prevent me from providing you with an image that is any higher resolution than this one.
  
  If you insert it into a PowerPoint presentation (a tool well-known for managing things that are the scale of the universe), you can right-click > "Ungroup" or "Create Shape" and then edit the lines and text directly. You can also change the colors this way.
  
  Alternatively you can use a tool like Inkscape.
  
• High resolution line chart, optimized for mobile
• Alternative high resolution line chart
• Scatterplot
• Portable line chart (png)
• Portable line chart (png), optimized for mobile
• Line chart for only Popularity of the first name Toby
• Line chart for only The number of tapers in Texas
• AI-generated correlation image
• The spurious research paper: Toby or Not Toby: A Tantalizing Tale of Tapers in Texas