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AI explanation

^{Show image generation prompt} Model: dalle-3
Prompt: Generate an image that combines the style of a TIME magazine cover with the following scene: In a bustling high school cafeteria, a large group of 12th grade public school students are engaged in a spirited game of dodgeball, while in a corner, a group of lawyers specializing in juvenile law are seen conferring with students and school administrators. The room hums with activity as more and more lawyers arrive to address the increasing number of legal matters arising from the growing student population, creating a lively and dynamic atmosphere. The image should capture the vibrant energy of the cafeteria and the juxtaposition between the students' recreational activities and the legal discussions taking place. 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: Number of public school students in 12th grade and Number of Lawyers in the United States. 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: A TIME magazine cover image An image that looks like it is a scene from 'Star Wars' a meme Pop art Art nouveau
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 Number of public school students in 12th grade and Number of Lawyers in the United States, in the following situation: Because as the number of 12th graders in public schools increases, so does the demand for legal expertise in dodgeball disputes and cafeteria food fights. The rise in students means more potential clients for budding lawyers specializing in juvenile law, leading to a surge in the number of lawyers in the United States. It's a case of educational escalation leading to legal proliferation, creating a jurisdictional jamboree!. Keep the description simple.
ChatGPT: In a bustling high school cafeteria, a large group of 12th grade public school students are engaged in a spirited game of dodgeball, while in a corner, a group of lawyers specializing in juvenile law are seen conferring with students and school administrators. The room hums with activity as more and more lawyers arrive to address the increasing number of legal matters arising from the growing student population, creating a lively and dynamic atmosphere.

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 bustling high school cafeteria, a large group of 12th grade public school students are engaged in a spirited game of dodgeball, while in a corner, a group of lawyers specializing in juvenile law are seen conferring with students and school administrators. The room hums with activity as more and more lawyers arrive to address the increasing number of legal matters arising from the growing student population, creating a lively and dynamic atmosphere. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image that combines the style of a TIME magazine cover with the following scene: In a bustling high school cafeteria, a large group of 12th grade public school students are engaged in a spirited game of dodgeball, while in a corner, a group of lawyers specializing in juvenile law are seen conferring with students and school administrators. The room hums with activity as more and more lawyers arrive to address the increasing number of legal matters arising from the growing student population, creating a lively and dynamic atmosphere. The image should capture the vibrant energy of the cafeteria and the juxtaposition between the students' recreational activities and the legal discussions taking place.

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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

Twelfth Graders and Legal Crusaders: A Quantitative Examination of the Relationship Between Public School Students in the 12th Grade and the Number of Lawyers in the United States The Journal of Educational Puzzles and Legal Trends Jan 2024 Reminder: This paper is AI-generated. Not real!

Problem variable:	Which variable has a problem? Number of public school students in 12th grade Number of Lawyers in the United States 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.

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([2381080,2392460,2430540,2424030,2487550,2487140,2586450,2672930,2721710,2781620,2802790,2862860,2989510,3046490,3094350,3180250,3277400,3374510,3399690,3431690,3471890,3451880,3477020,3476130,3496480,3537230,3571440,3631450,3648660,3621160,3663690,3670440,3661920,])
array_2 = np.array([755694,777119,799760,846036,865614,896140,953260,953260,985921,1000440,1022460,1048900,1049750,1058660,1084500,1104770,1116970,1143360,1162120,1180390,1203100,1225450,1245200,1268010,1281430,1300700,1312870,1335960,1342380,1352080,1328740,1327910,1327010,])
array_1_name = "Number of public school students in 12th grade"
array_2_name = "Number of Lawyers in the United States"

# 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 Number of public school students in 12th grade
• Line chart for only Number of Lawyers in the United States
• AI-generated correlation image
• The spurious research paper: Twelfth Graders and Legal Crusaders: A Quantitative Examination of the Relationship Between Public School Students in the 12th Grade and the Number of Lawyers in the United States