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Spurious correlation #5,247 · View random

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air pollution in Lafayette, Indiana and the second variable is How trendy Numberphile YouTube video titles are.  The chart goes from 2011 to 2023, and the two variables track closely in value over that time. Small Image
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AI explanation

As the smog thickened, so did the fascination with numbers, creating a prime environment for viral math content. It seems like the air wasn't the only thing getting squared in Lafayette!

Model: dalle-3
Prompt: Prompt: Generate an image in the style of a Polaroid photo that depicts a smog-covered Lafayette, Indiana skyline. In the foreground, include a group of people gathered around a screen, watching a Numberphile YouTube video with a trendy, attention-grabbing title. The contrast between the hazy air and the vibrant interest in numbers should be striking. The depiction should include only scenes, people, and objects, it should not include text or speech bubbles.
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: Air pollution in Lafayette, Indiana and How trendy Numberphile YouTube video titles are. 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: Steampunk a Polaroid photo Cutsy graphics Vaporwave Whimsical illustration
ChatGPT: a Polaroid photo

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 Air pollution in Lafayette, Indiana and How trendy Numberphile YouTube video titles are, in the following situation: As the smog thickened, so did the fascination with numbers, creating a prime environment for viral math content. It seems like the air wasn't the only thing getting squared in Lafayette!. Keep the description simple.
ChatGPT: In Lafayette, Indiana, the city's skyline is shrouded in a thick blanket of smog, with cars and factories emitting pollution into the air. Amidst this, a group of people gathers around a screen, excitedly watching a Numberphile YouTube video with a trendy, attention-grabbing title. The contrast between the hazy air and the vibrant interest in numbers is striking.

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 Polaroid photo ] and depicting this scene: In Lafayette, Indiana, the city's skyline is shrouded in a thick blanket of smog, with cars and factories emitting pollution into the air. Amidst this, a group of people gathers around a screen, excitedly watching a Numberphile YouTube video with a trendy, attention-grabbing title. The contrast between the hazy air and the vibrant interest in numbers is striking. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Prompt: Generate an image in the style of a Polaroid photo that depicts a smog-covered Lafayette, Indiana skyline. In the foreground, include a group of people gathered around a screen, watching a Numberphile YouTube video with a trendy, attention-grabbing title. The contrast between the hazy air and the vibrant interest in numbers should be striking.

*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.

Model: gpt-3.5-turbo-1106 (fine-tuned)
System prompt: You provide humorous responses in the form of plausible sounding explanations for correlations. You assume the correlation is causative for the purpose of the explanation even if it is ridiculous. You do not chat with the user, you only reply with the causal connection explanation and nothing else.
User prompt: Please make up a funny explanation for how an increase in Air pollution in Lafayette, Indiana caused How trendy Numberphile YouTube video titles are to increase.


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Data details

Air pollution in Lafayette, Indiana
Detailed data title: Percentage of days with air quality at 'unhealthy for sensitive groups' or worse in Lafayette-West Lafayette, IN
Source: Environmental Protection Agency
See what else correlates with Air pollution in Lafayette, Indiana

How trendy Numberphile YouTube video titles are
Detailed data title: How trendy Numberphile YouTube video titles are, as rated by an AI.
Source: AI analysis of Numberphile YouTube video titles
Additional Info: I asked a large language model, 'On a scale of 1-10, how _______ do you think this YouTube video title is?' for every video.

See what else correlates with How trendy Numberphile YouTube video titles are

Correlation r = 0.5195516 (Pearson correlation coefficient)
Correlation is a measure of how much the variables move together. If it is 0.99, when one goes up the other goes up. If it is 0.02, the connection is very weak or non-existent. If it is -0.99, then when one goes up the other goes down. If it is 1.00, you probably messed up your correlation function.

r2 = 0.2699339 (Coefficient of determination)
This means 27% of the change in the one variable (i.e., How trendy Numberphile YouTube video titles are) is predictable based on the change in the other (i.e., Air pollution in Lafayette, Indiana) over the 13 years from 2011 through 2023.

p < 0.10(Null hypothesis significance test)
The p-value is 0.069. 0.0688035226770472700000000000
The p-value is a measure of how probable it is that we would randomly find a result this extreme. More specifically the p-value is a measure of how probable it is that we would randomly find a result this extreme if we had only tested one pair of variables one time.

But I am a p-villain. I absolutely did not test only one pair of variables one time. I correlated hundreds of millions of pairs of variables. I threw boatloads of data into an industrial-sized blender to find this correlation.

Who is going to stop me? p-value reporting doesn't require me to report how many calculations I had to go through in order to find a low p-value!
On average, you will find a correaltion as strong as 0.52 in 6.9% of random cases. Said differently, if you correlated 15 random variables Which I absolutely did.
with the same 12 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 12 because we have two variables measured over a period of 13 years. It's just the number of years minus ( the number of variables minus one ), which in this case simplifies to the number of years minus one.
you would randomly expect to find a correlation as strong as this one.

[ -0.04, 0.83 ] 95% correlation confidence interval (using the Fisher z-transformation)
The confidence interval is an estimate the range of the value of the correlation coefficient, using the correlation itself as an input. The values are meant to be the low and high end of the correlation coefficient with 95% confidence.

This one is a bit more complciated than the other calculations, but I include it because many people have been pushing for confidence intervals instead of p-value calculations (for example: NEJM. However, if you are dredging data, you can reliably find yourself in the 5%. That's my goal!


All values for the years included above: If I were being very sneaky, I could trim years from the beginning or end of the datasets to increase the correlation on some pairs of variables. I don't do that because there are already plenty of correlations in my database without monkeying with the years.

Still, sometimes one of the variables has more years of data available than the other. This page only shows the overlapping years. To see all the years, click on "See what else correlates with..." link above.
2011201220132014201520162017201820192020202120222023
Air pollution in Lafayette, Indiana (Bad air quality days)0.005602240.030219800.0059523800.0056818200.00821918000.0027397300.0452675
How trendy Numberphile YouTube video titles are (Trendiness score)6.66677.02116.73086.91437.08226.85296.86216.9026.93757.16.82937.02447.2353




Why this works

  1. Data dredging: I have 25,237 variables in my database. I compare all these variables against each other to find ones that randomly match up. That's 636,906,169 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 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 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. 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

You can calculate the values on this page on your own! Try running the Python code to see the calculation results. Step 1: Download and install Python on your computer.

Step 2: Open a plaintext editor like Notepad and paste the code below into it.

Step 3: Save the file as "calculate_correlation.py" in a place you will remember, like your desktop. Copy the file location to your clipboard. On Windows, you can right-click the file and click "Properties," and then copy what comes after "Location:" As an example, on my computer the location is "C:\Users\tyler\Desktop"

Step 4: Open a command line window. For example, by pressing start and typing "cmd" and them pressing enter.

Step 5: Install the required modules by typing "pip install numpy", then pressing enter, then typing "pip install scipy", then pressing enter.

Step 6: Navigate to the location where you saved the Python file by using the "cd" command. For example, I would type "cd C:\Users\tyler\Desktop" and push enter.

Step 7: Run the Python script by typing "python calculate_correlation.py"

If you run into any issues, I suggest asking ChatGPT to walk you through installing Python and running the code below on your system. Try this question:

"Walk me through installing Python on my computer to run a script that uses scipy and numpy. Go step-by-step and ask me to confirm before moving on. Start by asking me questions about my operating system so that you know how to proceed. Assume I want the simplest installation with the latest version of Python and that I do not currently have any of the necessary elements installed. Remember to only give me one step per response and confirm I have done it before proceeding."


# 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([0.00560224,0.0302198,0,0.00595238,0,0.00568182,0,0.00821918,0,0,0.00273973,0,0.0452675,])
array_2 = np.array([6.6667,7.0211,6.7308,6.9143,7.0822,6.8529,6.8621,6.902,6.9375,7.1,6.8293,7.0244,7.2353,])
array_1_name = "Air pollution in Lafayette, Indiana"
array_2_name = "How trendy Numberphile YouTube video titles are"

# 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)



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Correlation ID: 5247 · Black Variable ID: 21746 · Red Variable ID: 25482
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