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AI explanation

^{Show image generation prompt} Model: dalle-3
Prompt: Generate an image of a serene Delaware town on a crisp fall day. The focal point should be the quaint town hall adorned with American flags and surrounded by vibrant fall foliage. In the foreground, depict a group of local Republican voters happily making their way to cast their ballots, creating a serene and cozy atmosphere. In the background, show a convenience store with patrons checking their Mega Millions tickets in front of a glowing lottery board. Among the myriad digits, the number 21 should shine brightly, adding an element of chance and excitement to the scene, all while maintaining a sense of charm and inexplicable connection between politics and luck. 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: Republican votes for Senators in Delaware and Number of times 21 was a winning Mega Millions number. 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: Cyberpunk An image that looks like it is a scene from a Pixar movie A TIME magazine cover image a funny image you would see on reddit Charcoal
ChatGPT: A TIME magazine cover image

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 Republican votes for Senators in Delaware and Number of times 21 was a winning Mega Millions number, in the following situation: It's a little-known fact that the collective positive energy from the Republican voters in Delaware was inadvertently influencing the outcome of the Mega Millions lottery. Their shared belief in conservative principles somehow aligned with the probability of 21 being drawn as the winning number. Who would've thought that political participation could have such a direct impact on lottery results? It's a statistical anomaly that's as puzzling as it is amusing!. Keep the description simple.
ChatGPT: In a cozy Delaware town, the local Republican voters gather at the quaint town hall to cast their ballots. The charming building is adorned with American flags and fall foliage, and a cheerful buzz fills the air as citizens exercise their civic duty. Meanwhile, at the nearby convenience store, a lucky few are checking their Mega Millions tickets in front of the glowing lottery board, as the number 21 shines brightly among the myriad digits. It's a scene where politics and chance seem to intertwine in a curious, inexplicable dance.

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: [ A TIME magazine cover image ] and depicting this scene: In a cozy Delaware town, the local Republican voters gather at the quaint town hall to cast their ballots. The charming building is adorned with American flags and fall foliage, and a cheerful buzz fills the air as citizens exercise their civic duty. Meanwhile, at the nearby convenience store, a lucky few are checking their Mega Millions tickets in front of the glowing lottery board, as the number 21 shines brightly among the myriad digits. It's a scene where politics and chance seem to intertwine in a curious, inexplicable dance. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image of a serene Delaware town on a crisp fall day. The focal point should be the quaint town hall adorned with American flags and surrounded by vibrant fall foliage. In the foreground, depict a group of local Republican voters happily making their way to cast their ballots, creating a serene and cozy atmosphere. In the background, show a convenience store with patrons checking their Mega Millions tickets in front of a glowing lottery board. Among the myriad digits, the number 21 should shine brightly, adding an element of chance and excitement to the scene, all while maintaining a sense of charm and inexplicable connection between politics and luck.

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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

Rolling the Dice: The Unlikely Link Between Republican Votes in Delaware and the Frequency of 21 as a Winning Mega Millions Number The Journal of Statistical Serendipity Jan 2024 Reminder: This paper is AI-generated. Not real!

Problem variable:	Which variable has a problem? Votes for Republican Senators in Delaware Number of times 21 was a winning Mega Millions number 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. Confounding variable: 2020 is particularly different from the other years on this graph. Confounding variables (like global pandemics) will cause two variables to look connected when in fact a "sneaky third" variable is influencing both of them behind the scenes.
5. Very low n: There are not many data points included in this analysis. Even if the p-value is high, we should be suspicious of using so few datapoints in a correlation.

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([94793,69734,140595,123053,115700,137127,186054,])
array_2 = np.array([2,2,4,3,2,3,5,])
array_1_name = "Votes for Republican Senators in Delaware"
array_2_name = "Number of times 21 was a winning Mega Millions number"

# 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 Votes for Republican Senators in Delaware
• Line chart for only Number of times 21 was a winning Mega Millions number
• AI-generated correlation image
• The spurious research paper: Rolling the Dice: The Unlikely Link Between Republican Votes in Delaware and the Frequency of 21 as a Winning Mega Millions Number