Spurious correlation #5,660 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Votes for Libertarian Senators in Illinois and the second variable is Customer satisfaction with Dillard's. The chart goes from 1994 to 2020, and the two variables track closely in value over that time.

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Votes for Libertarian Senators in Illinois and the second variable is Customer satisfaction with Dillard's. The chart goes from 1994 to 2020, and the two variables track closely in value over that time.

Download png, svg

AI explanation

The increase in Libertarian votes for Senators in Illinois caused Customer satisfaction with Dillard's to increase because as more people embraced the idea of personal freedom and responsibility, they also started taking a more laissez-faire approach to their shopping experiences. This led to a greater sense of autonomy and choice in the aisles, ultimately allowing customers to truly 'vote' for the products and services that best suited their needs. After all, when it comes to Dillard's, it's all about pursuing shopping 'pursuits' without government intervention!

^{Show image generation prompt} Model: dalle-3
Prompt: [ Celtic art ] In downtown Chicago, Illinois, a group of people wearing "Vote Libertarian" shirts march in a procession towards the polling station. They carry signs that read "Personal Freedom, Personal Responsibility". As they walk, the swirling patterns of Celtic art intertwine with the urban landscape, creating an enchanting scene. Meanwhile, at Dillard's department store, customers leisurely browse through the aisles, surrounded by intricate Celtic knots and patterns that adorn the store's decor. The satisfaction on their faces is evident as they enjoy the newly introduced self-checkout kiosks, with the interwoven Celtic motifs adding a touch of magic to the scene. 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: Votes for Libertarian Senators in Illinois and Customer satisfaction with Dillard's. 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: Voxel art Celtic art a Polaroid photo Surrealism Celtic art
ChatGPT: Celtic 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 Votes for Libertarian Senators in Illinois and Customer satisfaction with Dillard's, in the following situation: The increase in Libertarian votes for Senators in Illinois caused Customer satisfaction with Dillard's to increase because as more people embraced the idea of personal freedom and responsibility, they also started taking a more laissez-faire approach to their shopping experiences. This led to a greater sense of autonomy and choice in the aisles, ultimately allowing customers to truly 'vote' for the products and services that best suited their needs. After all, when it comes to Dillard's, it's all about pursuing shopping 'pursuits' without government intervention!. Keep the description simple.
ChatGPT: In downtown Chicago, Illinois, a crowd of people wearing "Vote Libertarian" shirts march towards the polling station, holding signs that read "Personal Freedom, Personal Responsibility". Meanwhile, at Dillard's department store, customers leisurely browse through the aisles, smiling and chatting with staff, with satisfaction evident on their faces as they enjoy the newly introduced self-checkout kiosks.

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: [ Celtic art ] and depicting this scene: In downtown Chicago, Illinois, a crowd of people wearing "Vote Libertarian" shirts march towards the polling station, holding signs that read "Personal Freedom, Personal Responsibility". Meanwhile, at Dillard's department store, customers leisurely browse through the aisles, smiling and chatting with staff, with satisfaction evident on their faces as they enjoy the newly introduced self-checkout kiosks. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: [ Celtic art ] In downtown Chicago, Illinois, a group of people wearing "Vote Libertarian" shirts march in a procession towards the polling station. They carry signs that read "Personal Freedom, Personal Responsibility". As they walk, the swirling patterns of Celtic art intertwine with the urban landscape, creating an enchanting scene. Meanwhile, at Dillard's department store, customers leisurely browse through the aisles, surrounded by intricate Celtic knots and patterns that adorn the store's decor. The satisfaction on their faces is evident as they enjoy the newly introduced self-checkout kiosks, with the interwoven Celtic motifs adding a touch of magic to the scene.

*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.
^{Show prompt for explanation} 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 Libertarian votes for Senators in Illinois caused Customer satisfaction with Dillard's to increase. Include one good pun.

AI academic paper

(Because p < 0.01)

Vote Libertarian, Feel Delightful: The Bizarre Link Between Illinois Senatorial Preferences and Dillard's Customer Satisfaction

The Journal of Political Peculiarities

Jan 2024

Reminder: This paper is AI-generated. Not real!

^{Show prompt used to generate this paper} Quick note: This sequence is long and repetitive. That's how the prompt engineering works for this one. I manage the output in Python to format it into this PDF.

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.You draft a literature review section of an academic research paper, that starts out dry for the first few sentences but then becomes hilarious and goofy.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up a literature review section of an academic research paper presenting the findings of the connection between Libertarian votes for Senators in Illinois and Customer satisfaction with Dillard's. Make lots of jokes, goofy observations, and puns.

Speak in the present tense for this section (the authors find...), as is common in academic research paper literature reviews. Name the sources in a format similar to this: In "Book," the authors find lorem and ipsum.

Make up the lorem and ipsum part, but make it sound related to the topic at hand.

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then you might move on to cartoons and children's shows that you watched for research.

Here is the title and abstract of the paper:
[[TITLE]]
Vote Libertarian, Feel Delightful: The Bizarre Link Between Illinois Senatorial Preferences and Dillard's Customer Satisfaction

[[ABSTRACT]]
This research delves into the unorthodox and whimsical relationship between the ofttimes forgotten Libertarian party voters in Illinois and the delightfulness experienced by patrons of the esteemed department store chain, Dillard's. Leveraging data from the MIT Election Data and Science Lab, Harvard Dataverse, and the American Customer Satisfaction Index, our investigation uncovered a surprising correlation coefficient of 0.9569001 and p < 0.01 for the period spanning from 1994 to 2020. While the conventional wisdom may struggle to comprehend the linkage between political inclinations and retail euphoria, our findings shed light on this peculiar phenomenon, leaving researchers and readers equally enchanted and bemused.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The intricate dance between political choices and consumer satisfaction has long puzzled researchers and laymen alike. The notion that casting a vote for a particular political party could have any bearing on the delightful experiences of department store shoppers may seem utterly preposterous to the uninitiated. However, the field of political economy has a long history of uncovering surprising and inexplicable connections, and the bizarre link between libertarian votes for senators in Illinois and customer satisfaction with Dillard's is no exception.
While most studies focus on the more traditional and expected relationships between political leanings and economic outcomes, our investigation into this peculiar relationship aims to unravel the enigmatic influence of libertarian votes on the shopping whims of Dillard's patrons. The findings of our research may raise eyebrows, elicit guffaws, and perhaps even prompt a quizzical tilt of the head, but our methodology and results stand as a testament to the perplexing and intriguing nature of this phenomenon.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The scholarly literature on the connection between Illinois Senatorial preferences and customer satisfaction with Dillard's is surprisingly scant, given the complexity of the relationship under investigation. Smith (2010) found no direct link between voter choices and retail preferences, while Doe (2015) suggested that such a relationship was highly unlikely. Jones (2018) similarly dismissed any potential correlation. However, as we delve into more recent research, we discover a trove of unexpected and whimsical findings that challenge the conventional wisdom on this topic.

Turning our attention to the broader realm of political economy and consumer behavior, "Free to Choose" by Milton Friedman and "The Affluent Society" by John Kenneth Galbraith shed light on the intersection of individual choices and market phenomena. In a more tangential but nevertheless thought-provoking manner, the fiction novel "The Fountainhead" by Ayn Rand and "Confessions of a Shopaholic" by Sophie Kinsella provide intriguing insights into the human psyche and its intricate relationships with commerce.

As our investigation took a turn towards the absurdly delightful, our research team engaged with unconventional sources to further unravel the enigmatic influence of libertarian votes on the shopping whims of Dillard’s patrons. The watching of classic cartoons such as "The Pink Panther" and children's shows exemplified by "Sesame Street" offered unexpected but surprisingly relevant perspectives on human behavior and the pursuit of joy. The grandiloquent absurdity of "Monty Python's Flying Circus" and the whimsical charm of "The Muppet Show" also sparked inspiration in our exploration of this peculiar phenomenon. While not your traditional academic sources, the insights gained from these unconventional platforms proved to be remarkably enlightening.

The landscape of literature on the topic spanned various genres and mediums, reflecting the multifaceted nature of the peculiar relationship we sought to investigate. As we dig deeper into the findings of this wacky connection, it becomes increasingly apparent that the unorthodox and whimsical bond between libertarian votes for Senators in Illinois and customer satisfaction with Dillard's is a subject that defies easy explanation, leaving many a reader equally enchanted and bemused.

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.You draft the discussion section of an academic research paper.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up the discussion section of an academic research paper presenting the findings of the connection between Libertarian votes for Senators in Illinois and Customer satisfaction with Dillard's. Make lots of jokes, goofy observations, and puns.

Limit your response to 500 tokens.

Here are the title, abstract, literature review, and results sections. Please harken back to 1-2 of the goofy items in the literature review, but pretend to take them completely seriously. Discuss how your results supported the prior research.

Do not write a conclusion. I will add a conclusion after this.

[[TITLE]]
Vote Libertarian, Feel Delightful: The Bizarre Link Between Illinois Senatorial Preferences and Dillard's Customer Satisfaction

[[ABSTRACT]]
This research delves into the unorthodox and whimsical relationship between the ofttimes forgotten Libertarian party voters in Illinois and the delightfulness experienced by patrons of the esteemed department store chain, Dillard's. Leveraging data from the MIT Election Data and Science Lab, Harvard Dataverse, and the American Customer Satisfaction Index, our investigation uncovered a surprising correlation coefficient of 0.9569001 and p < 0.01 for the period spanning from 1994 to 2020. While the conventional wisdom may struggle to comprehend the linkage between political inclinations and retail euphoria, our findings shed light on this peculiar phenomenon, leaving researchers and readers equally enchanted and bemused.

[[LITERATURE REVIEW]]
The scholarly literature on the connection between Illinois Senatorial preferences and customer satisfaction with Dillard's is surprisingly scant, given the complexity of the relationship under investigation. Smith (2010) found no direct link between voter choices and retail preferences, while Doe (2015) suggested that such a relationship was highly unlikely. Jones (2018) similarly dismissed any potential correlation. However, as we delve into more recent research, we discover a trove of unexpected and whimsical findings that challenge the conventional wisdom on this topic.
Turning our attention to the broader realm of political economy and consumer behavior, "Free to Choose" by Milton Friedman and "The Affluent Society" by John Kenneth Galbraith shed light on the intersection of individual choices and market phenomena. In a more tangential but nevertheless thought-provoking manner, the fiction novel "The Fountainhead" by Ayn Rand and "Confessions of a Shopaholic" by Sophie Kinsella provide intriguing insights into the human psyche and its intricate relationships with commerce.
As our investigation took a turn towards the absurdly delightful, our research team engaged with unconventional sources to further unravel the enigmatic influence of libertarian votes on the shopping whims of Dillard’s patrons. The watching of classic cartoons such as "The Pink Panther" and children's shows exemplified by "Sesame Street" offered unexpected but surprisingly relevant perspectives on human behavior and the pursuit of joy. The grandiloquent absurdity of "Monty Python's Flying Circus" and the whimsical charm of "The Muppet Show" also sparked inspiration in our exploration of this peculiar phenomenon. While not your traditional academic sources, the insights gained from these unconventional platforms proved to be remarkably enlightening.
The landscape of literature on the topic spanned various genres and mediums, reflecting the multifaceted nature of the peculiar relationship we sought to investigate. As we dig deeper into the findings of this wacky connection, it becomes increasingly apparent that the unorthodox and whimsical bond between libertarian votes for Senators in Illinois and customer satisfaction with Dillard's is a subject that defies easy explanation, leaving many a reader equally enchanted and bemused.

[[RESULTS]]
The statistical analysis revealed a remarkably strong correlation coefficient of 0.9569001 between the percentage of Libertarian votes for Senators in Illinois and the customer satisfaction with Dillard's. The r-squared value of 0.9156577 indicates that a substantial portion of the variation in Dillard's customer satisfaction can be explained by the variation in Libertarian votes.
It is quite baffling to contemplate the notion that the preferences of voters for a relatively obscure political party can wield such an influential force on the contentment levels of Dillard's shoppers. One might even say it seems as improbable as finding a stylish pair of shoes on sale during a clearance event in the Midwest in the middle of winter!
Furthermore, the p-value of less than 0.01 signifies that the observed correlation is highly unlikely to have occurred by chance. The probability is so minuscule, it's almost as if a snowball's chance in hell were competing with a unicorn for a spot in a popular vote.
The scatterplot (Fig. 1) unequivocally displays the tight relationship between the two variables, outlining the striking alignment of Libertarian votes and Dillard's customer satisfaction. It's as if the data points on the graph are holding hands and singing in perfect harmony, serenading the bewildered onlookers with a curious melody of political whimsy and shopper serenity.
In conclusion, our findings highlight the captivating and whimsical nature of the connection between political predilections and retail bliss. While the mechanism behind this peculiar relationship remains shrouded in mystery, it undoubtedly warrants further investigation and contemplation, eliciting laughter, perplexity, and perhaps a touch of delight from researchers and readers alike.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The results of our study provide compelling evidence in support of the previously unexplored relationship between Libertarian votes for Senators in Illinois and customer satisfaction with Dillard's. Despite the initial skepticism expressed by Smith (2010), Doe (2015), and Jones (2018), our findings challenge the conventional wisdom and whimsically affirm the unexpected influence of political inclinations on retail euphoria.

The observed correlation coefficient of 0.9569001 and the r-squared value of 0.9156577 align with the broader literature on political economy and consumer behavior, elucidating the peculiar mechanism underlying this relationship. Our results echo the sentiments of Milton Friedman and John Kenneth Galbraith, showcasing the intricate intersection of individual choices and market phenomena. While Smith, Doe, and Jones might have dismissed the plausibility of such a connection, our study underscores the whimsical bond between political predilections and shopper serenity, leaving them perhaps a bit mystified and tickled by the unexpectedness of our findings.

Harkening back to our literature review, the unconventional sources we engaged with, including classic cartoons and children's shows, provided remarkably enlightening perspectives on human behavior and the pursuit of joy. These seemingly far-fetched sources have lent credence to the unlikely relationship we have unearthed, challenging the expectations of traditional academic inquiry. Our study embodies the spirited exploration of this peculiar phenomenon, underscoring the delightful and enigmatic nature of the connection we aimed to unravel.

The unorthodox and whimsical nature of our findings is exemplified by the p-value of less than 0.01, signifying the highly improbable occurrence of the observed correlation by chance. This probability is akin to a snowball's chance in hell competing with a unicorn for a spot in a popular vote, illustrating the sheer unlikeliness of this unexpected linkage. The scatterplot, like a visual metaphor, encapsulates the remarkable alignment of Libertarian votes and Dillard's customer satisfaction, evoking a sense of wonder and amusement among the bewildered onlookers.

While this study adds an intriguing layer to the peculiar relationship at hand, it opens the door to further investigation and contemplation, eliciting a delightful blend of laughter, perplexity, and perhaps a touch of delight from researchers and readers alike. The mechanism behind this unanticipated connection remains shrouded in mystery, inviting a whimsical pursuit of understanding and an appreciation for the unexpected quirks of human behavior.

Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of academic journals. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding research, scientific, or academic journal that would publish a paper entited Vote Libertarian, Feel Delightful: The Bizarre Link Between Illinois Senatorial Preferences and Dillard's Customer Satisfaction. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Political Peculiarities

Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of nonprofit research organizations and associations. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding nonprofit, academic, or scientific association or organization that would sponsor research that resulted in a paper entited Vote Libertarian, Feel Delightful: The Bizarre Link Between Illinois Senatorial Preferences and Dillard's Customer Satisfaction. Respond only with the name of a fictional organization.

ChatGPT:

The Institute for Political Fashion and Consumer Behavior

Model: gpt-3.5-turbo-1106
System prompt: You provide potential search keywords separated by commas. You say nothing else, and you do not chat with the user.
User prompt: Please provide potential search keywords for a paper titled Vote Libertarian, Feel Delightful: The Bizarre Link Between Illinois Senatorial Preferences and Dillard's Customer Satisfaction with an abstract of This research delves into the unorthodox and whimsical relationship between the ofttimes forgotten Libertarian party voters in Illinois and the delightfulness experienced by patrons of the esteemed department store chain, Dillard's. Leveraging data from the MIT Election Data and Science Lab, Harvard Dataverse, and the American Customer Satisfaction Index, our investigation uncovered a surprising correlation coefficient of 0.9569001 and p < 0.01 for the period spanning from 1994 to 2020. While the conventional wisdom may struggle to comprehend the linkage between political inclinations and retail euphoria, our findings shed light on this peculiar phenomenon, leaving researchers and readers equally enchanted and bemused.

ChatGPT:

Libertarian party, Illinois senatorial preferences, Dillard's customer satisfaction, correlation coefficient, MIT Election Data and Science Lab, Harvard Dataverse, American Customer Satisfaction Index, political inclinations, retail euphoria, peculiar phenomenon

*There is a bunch of Python happening behind the scenes to turn this prompt sequence into a PDF.

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Data details

Votes for Libertarian Senators in Illinois
Detailed data title: Total number of votes cast for Federal Libertarian Senate candidates in Illinois
Source: MIT Election Data and Science Lab, Harvard Dataverse
See what else correlates with Votes for Libertarian Senators in Illinois

Customer satisfaction with Dillard's
Source: American Customer Satisfaction Index
See what else correlates with Customer satisfaction with Dillard's

Correlation r = 0.9569001 (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 = 0.9156577 (Coefficient of determination)
This means 91.6% of the change in the one variable (i.e., Customer satisfaction with Dillard's) is predictable based on the change in the other (i.e., Votes for Libertarian Senators in Illinois) over the 8 years from 1994 through 2020.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 0.00019.^Show 0.0001937422668801657000000000
The p-value is a measure of how probable it is that we would randomly find a result this extreme.^Note 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 0.96 in 0.019% of random cases. Said differently, if you correlated 5,161 random variables^Note Which I absolutely did.
with the same 7 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 7 because we have two variables measured over a period of 8 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.

[ 0.77, 0.99 ] 95% correlation confidence interval (using the Fisher z-transformation)
^{Read more about the confidence interval} 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: ^Note 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.

	1996	2002	2004	2008	2010	2014	2016	2020
Votes for Libertarian Senators in Illinois (Total votes)	41218	57382	69253	50224	87247	135316	175988	75673
Customer satisfaction with Dillard's (Consumer Satisfaction)	74	75	77	75	78	81	83	79

Why this works

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.
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.
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.
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.
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

You can calculate the values on this page on your own! Try running the Python code to see the calculation results. ^{Show the steps to do this.} 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([41218,57382,69253,50224,87247,135316,175988,75673,])
array_2 = np.array([74,75,77,75,78,81,83,79,])
array_1_name = "Votes for Libertarian Senators in Illinois"
array_2_name = "Customer satisfaction with Dillard's"

# 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

You may re-use the images on this page for any purpose, even commercial purposes, without asking for permission. The only requirement is that you attribute Tyler Vigen. ^Note Attribution can take many different forms. If you leave the "tylervigen.com" link in the image, that satisfies it just fine. If you remove it and move it to a footnote, that's fine too. You can also just write "Charts courtesy of Tyler Vigen" at the bottom of an article.

You do not need to attribute "the spurious correlations website," and you don't even need to link here if you don't want to. I don't gain anything from pageviews. There are no ads on this site, there is nothing for sale, and I am not for hire.

For the record, I am just one person. Tyler Vigen, he/him/his. I do have degrees, but they should not go after my name unless you want to annoy my wife. If that is your goal, then go ahead and cite me as "Tyler Vigen, A.A. A.A.S. B.A. J.D." Otherwise it is just "Tyler Vigen."

When spoken, my last name is pronounced "vegan," like I don't eat meat.

Full license details.
For more on re-use permissions, or to get a signed release form, see tylervigen.com/permission.

Download images for these variables:

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 Libertarian Senators in Illinois
Line chart for only Customer satisfaction with Dillard's
AI-generated correlation image
The spurious research paper: Vote Libertarian, Feel Delightful: The Bizarre Link Between Illinois Senatorial Preferences and Dillard's Customer Satisfaction

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Correlation ID: 5660 · Black Variable ID: 26232 · Red Variable ID: 19845


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