Spurious correlation #3,039 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is UFO sightings in Ohio and the second variable is Electricity generation in Yemen. The chart goes from 1980 to 2021, 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 UFO sightings in Ohio and the second variable is Electricity generation in Yemen. The chart goes from 1980 to 2021, and the two variables track closely in value over that time.

Download png, svg

AI explanation

The UFOs were actually giant, energy-guzzling intergalactic toasters, and their presence somehow beamed extra toastiness to the Earth, but only in a small, remote village in Yemen.

^{Show image generation prompt} Model: dalle-3
Prompt: Title: "Extraterrestrial Energies" Description: A vivid and bustling UFO-themed store in a lively Ohio town draws animated customers, with colorful alien-inspired gadgets filling the shelves and captivating the shoppers. Meanwhile, the skyline of Yemen is dotted with construction cranes, hinting at the rapid development of new electricity generation infrastructure fueling the sudden surge in demand for the otherworldly merchandise. 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: UFO sightings in Ohio and Electricity generation in Yemen. 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: Symbolism Glitch art A Discovery magazine cover image Art nouveau Low poly
ChatGPT: A Discovery 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 UFO sightings in Ohio and Electricity generation in Yemen, in the following situation: Because the increase in UFO sightings in Ohio generated so much excitement and demand for alien-themed merchandise, it caused a surge in global consumer spending. This led to an unexpected influx of capital investment into Yemen, resulting in the expansion of electricity generation infrastructure to power all the UFO-inspired gadgets and gizmos. It's shocking how extraterrestrial encounters can spark economic currents across continents!. Keep the description simple.
ChatGPT: In a bustling Ohio town, colorful UFO-themed merchandise fills the shelves of a local store, attracting excited customers. Meanwhile, in Yemen, the skyline is dotted with construction cranes as new electricity generation infrastructure springs up, powering the alien-inspired gadgets that have suddenly surged in demand.

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 Discovery magazine cover image ] and depicting this scene: In a bustling Ohio town, colorful UFO-themed merchandise fills the shelves of a local store, attracting excited customers. Meanwhile, in Yemen, the skyline is dotted with construction cranes as new electricity generation infrastructure springs up, powering the alien-inspired gadgets that have suddenly surged in demand. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Title: "Extraterrestrial Energies" Description: A vivid and bustling UFO-themed store in a lively Ohio town draws animated customers, with colorful alien-inspired gadgets filling the shelves and captivating the shoppers. Meanwhile, the skyline of Yemen is dotted with construction cranes, hinting at the rapid development of new electricity generation infrastructure fueling the sudden surge in demand for the otherworldly merchandise.

*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 increases in UFO sightings in Ohio positively influenced Electricity generation in Yemen.

AI academic paper

(Because p < 0.01)

An Electrifying Encounter: Unveiling the Shocking Connection Between UFO Sightings in Ohio and Electricity Generation in Yemen

The Journal of Paranormal Energy Studies

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 UFO sightings in Ohio and Electricity generation in Yemen. 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]]
An Electrifying Encounter: Unveiling the Shocking Connection Between UFO Sightings in Ohio and Electricity Generation in Yemen

[[ABSTRACT]]
This research delves into the electrifying phenomenon of UFO sightings in Ohio and its unexpected correlation with electricity generation in Yemen. While it may seem like comparing apples and oranges, our data analysis reveals a striking correlation coefficient of 0.8654840 and p < 0.01 from 1980 to 2021. We employ data from the National UFO Reporting Center and the Energy Information Administration to shed light on this enigmatic relationship. Our findings challenge conventional wisdom and invite a new perspective on the interconnectedness of unexplained aerial phenomena and energy generation. The implications of this study for both the field of UFO research and energy economics are positively otherworldly.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The study of UFO sightings has long been a topic of both fascination and skepticism, often sparking heated debates and raising eyebrows. On the other hand, electricity generation in Yemen may not immediately capture the same level of public intrigue, but it is a crucial component of the country's infrastructure and economic stability. In this research, we embark upon a journey that traverses the realms of the mysterious and the mundane, aiming to uncover an electrifying connection between these seemingly disparate phenomena.
While some may consider the link between UFO sightings in Ohio and electricity generation in Yemen as far-fetched as a conspiracy theory, we venture to examine this unexpected relationship with scientific rigor and a dash of whimsy. With the aid of statistics and data analysis, we peer into the realms of the unknown and the unassuming, seeking to shed light on a correlation that is truly out of this world.
When considering the variables at play, one might be forgiven for thinking it's akin to comparing the weight of a black hole to a helium balloon. The esoteric nature of UFO sightings collides with the practicality of electricity generation, creating an intellectual playground where unexpected connections may spark like electricity in a storm. Through our research, we aim to bring levity to the gravity of this correlation, and perhaps, illuminate the path for future inquiries into the peculiar interplay between the enigmatic and the empirical.
As we delve into this electrifying encounter, we invite our readers to suspend disbelief, embrace curiosity, and join us in this unconventional pursuit of knowledge. After all, in the great laboratory of science, the most unexpected connections often yield the most illuminating insights.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

In their seminal work, Smith and Doe (2005) explore the unexplained aerial phenomena reported in the state of Ohio. The authors find a notable increase in UFO sightings during the 1990s, coinciding with the widespread adoption of dial-up internet and the popularization of the X-Files television series. Such findings compellingly illustrate the potential influence of popular culture and technological advancements on public perceptions of celestial encounters.

Adding to the discourse, Jones (2010) delves into the intricacies of electricity generation in Yemen, shedding light on the challenges and innovations within the country's energy sector. The author’s analysis unveils the complex interplay of geopolitical tensions, infrastructure development, and environmental sustainability in shaping Yemen’s energy landscape. This comprehensive overview sets the stage for examining the potential interdimensional forces at play.

Expanding beyond scholarly works, "The UFO Experience" by Edgar J. Evans (1971) provides a historical and cultural perspective on UFO sightings, offering insights into the societal impact of extraterrestrial encounters. The book discusses the psychological effects of UFO experiences and their implications for our understanding of human consciousness. Though not an empirical study, the work encourages a broader consideration of the emotional and cognitive dimensions of UFO phenomena.

Turning to fictional narratives, "The War of the Worlds" by H.G. Wells (1898) presents a classic portrayal of alien invasion, inciting widespread panic and fascination upon its publication. While a work of science fiction, the novel reflects the enduring human interest in cosmic exploration and the potential consequences of alien contact. Its relevance to our present inquiry lies in its portrayal of extraterrestrial visitations and their impact on terrestrial civilizations.

In an unconventional approach to sourcing, the researchers also drew inspiration from animated series such as "The Jetsons" and "Futurama," which depict futuristic scenarios with advanced technological capabilities, including flying saucers and advanced energy sources. While not scientifically rigorous, these sources offer a lighthearted lens through which to view the interplay of technology and otherworldly phenomena.

In adopting a multidisciplinary approach, this literature review provides a comprehensive foundation for understanding the intersection of UFO sightings in Ohio and electricity generation in Yemen. By incorporating diverse sources, from scholarly investigations to imaginative flights of fancy, the review sets the stage for uncovering the electrifying connection between these seemingly disparate domains.

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 UFO sightings in Ohio and Electricity generation in Yemen. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

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]]
An Electrifying Encounter: Unveiling the Shocking Connection Between UFO Sightings in Ohio and Electricity Generation in Yemen

[[ABSTRACT]]
This research delves into the electrifying phenomenon of UFO sightings in Ohio and its unexpected correlation with electricity generation in Yemen. While it may seem like comparing apples and oranges, our data analysis reveals a striking correlation coefficient of 0.8654840 and p < 0.01 from 1980 to 2021. We employ data from the National UFO Reporting Center and the Energy Information Administration to shed light on this enigmatic relationship. Our findings challenge conventional wisdom and invite a new perspective on the interconnectedness of unexplained aerial phenomena and energy generation. The implications of this study for both the field of UFO research and energy economics are positively otherworldly.

[[LITERATURE REVIEW]]
In their seminal work, Smith and Doe (2005) explore the unexplained aerial phenomena reported in the state of Ohio. The authors find a notable increase in UFO sightings during the 1990s, coinciding with the widespread adoption of dial-up internet and the popularization of the X-Files television series. Such findings compellingly illustrate the potential influence of popular culture and technological advancements on public perceptions of celestial encounters.
Adding to the discourse, Jones (2010) delves into the intricacies of electricity generation in Yemen, shedding light on the challenges and innovations within the country's energy sector. The author’s analysis unveils the complex interplay of geopolitical tensions, infrastructure development, and environmental sustainability in shaping Yemen’s energy landscape. This comprehensive overview sets the stage for examining the potential interdimensional forces at play.
Expanding beyond scholarly works, "The UFO Experience" by Edgar J. Evans (1971) provides a historical and cultural perspective on UFO sightings, offering insights into the societal impact of extraterrestrial encounters. The book discusses the psychological effects of UFO experiences and their implications for our understanding of human consciousness. Though not an empirical study, the work encourages a broader consideration of the emotional and cognitive dimensions of UFO phenomena.
Turning to fictional narratives, "The War of the Worlds" by H.G. Wells (1898) presents a classic portrayal of alien invasion, inciting widespread panic and fascination upon its publication. While a work of science fiction, the novel reflects the enduring human interest in cosmic exploration and the potential consequences of alien contact. Its relevance to our present inquiry lies in its portrayal of extraterrestrial visitations and their impact on terrestrial civilizations.
In an unconventional approach to sourcing, the researchers also drew inspiration from animated series such as "The Jetsons" and "Futurama," which depict futuristic scenarios with advanced technological capabilities, including flying saucers and advanced energy sources. While not scientifically rigorous, these sources offer a lighthearted lens through which to view the interplay of technology and otherworldly phenomena.
In adopting a multidisciplinary approach, this literature review provides a comprehensive foundation for understanding the intersection of UFO sightings in Ohio and electricity generation in Yemen. By incorporating diverse sources, from scholarly investigations to imaginative flights of fancy, the review sets the stage for uncovering the electrifying connection between these seemingly disparate domains.

[[RESULTS]]
The analysis revealed a remarkably robust correlation coefficient of 0.8654840 between UFO sightings in Ohio and electricity generation in Yemen from 1980 to 2021, with an r-squared value of 0.7490626, and a p-value less than 0.01, suggesting a statistically significant relationship.
Upon scrutinizing the data, it became evident that the connection between these two variables was as clear as a UFO sighting on a cloudless night. The scatterplot (Fig. 1) visually demonstrates this striking relationship, leaving little room for doubt and much room for extraterrestrial speculation.
While some may find the association between UFO sightings and electricity generation as peculiar as a Martian landscape, our findings offer a spark of enlightenment in the twilight zone of research. The robustness of the correlation coefficient serves as a reminder that in the realm of statistical analysis, truth is often stranger than science fiction.
In conclusion, our research not only illuminates an unconventional relationship between UFO sightings in Ohio and electricity generation in Yemen but also sparks curiosity about the hidden forces at play in the cosmic dance of earthly phenomena. The implications of this discovery are positively electrifying and beckon further investigation into the intergalactic interplay between the inexplicable and the empirical.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The unearthly connection between UFO sightings in Ohio and electricity generation in Yemen has left us positively charged with excitement and a quantum of curiosity. Our findings not only confirm, but also illuminate the peculiar relationship hinted at by prior research. As Smith and Doe (2005) presciently observed, the increase in UFO sightings in Ohio during the 1990s coincided with the rise of the internet and cult sci-fi TV series, suggesting a link between technological advancements and public perceptions of celestial encounters. Likewise, Jones (2010) painstakingly unraveled the complexities of electricity generation in Yemen, shedding light on the geopolitical and environmental factors shaping the country's energy landscape. While their work may seem light-years away, our investigation corroborates their insights, extending the exploration of unforeseen connections into the next galaxy of knowledge.

The robust correlation coefficient we uncovered stands as solid proof, akin to a UFO caught on camera, of the tangible link between these seemingly distant phenomena. The statistical significance of our findings is as striking as a lightning bolt on a stormy night, reinforcing the importance of considering interstellar influences in energy economics. While some may find the correlation as implausible as a spaceship made of cheese, the data leave little room for skepticism and much room for speculation about celestial currents and terrestrial transformers.

In line with Edgar J. Evans's (1971) contemplation of the emotional and cognitive dimensions of UFO phenomena, our research prompts us to consider the psychological effects of intergalactic interactions on earthly systems. The emotional charge sparked by our discoveries begs for a deeper investigation into the cosmic consequences of these seemingly mundane statistics. Just as "The War of the Worlds" by H.G. Wells (1898) incited fascination and panic, our findings invite a reevaluation of the potential impacts of celestial encounters on earthly energy generation.

The unconventional approach of drawing inspiration from animated series such as "The Jetsons" and "Futurama" lends a lighthearted lens through which to view our findings, prompting us to ponder the futuristic implications of our research. Far from being light-years away, these sources add a dash of humor and imagination to our exploration of the interconnectedness of technological innovation and enigmatic aerial phenomena. In doing so, they reaffirm the multidimensional nature of our investigation and provoke a cosmic chuckle at the intricacies of our statistical sleuthing.

In sum, our study represents an astronomical leap in uncovering the electrifying connection between UFO sightings in Ohio and electricity generation in Yemen. By shedding a light beam of statistical rigor on this uncharted territory, we have demonstrated the potential of seemingly disparate fields to converge in unexpected ways, much like celestial bodies in the night sky. The implications of our findings may seem out of this world, but they beckon further investigation into the cosmic dance of earthly phenomena.

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 An Electrifying Encounter: Unveiling the Shocking Connection Between UFO Sightings in Ohio and Electricity Generation in Yemen. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Paranormal Energy Studies

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 An Electrifying Encounter: Unveiling the Shocking Connection Between UFO Sightings in Ohio and Electricity Generation in Yemen. Respond only with the name of a fictional organization.

ChatGPT:

National Institute for Extraterrestrial Studies

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 An Electrifying Encounter: Unveiling the Shocking Connection Between UFO Sightings in Ohio and Electricity Generation in Yemen with an abstract of This research delves into the electrifying phenomenon of UFO sightings in Ohio and its unexpected correlation with electricity generation in Yemen. While it may seem like comparing apples and oranges, our data analysis reveals a striking correlation coefficient of 0.8654840 and p < 0.01 from 1980 to 2021. We employ data from the National UFO Reporting Center and the Energy Information Administration to shed light on this enigmatic relationship. Our findings challenge conventional wisdom and invite a new perspective on the interconnectedness of unexplained aerial phenomena and energy generation. The implications of this study for both the field of UFO research and energy economics are positively otherworldly.

ChatGPT:

UFO sightings, Ohio, electricity generation, Yemen, correlation analysis, National UFO Reporting Center, Energy Information Administration, data analysis, unexplained aerial phenomena, energy economics

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

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Data details

UFO sightings in Ohio
Detailed data title: UFO sightings reported in Ohio
Source: National UFO Reporting Center
See what else correlates with UFO sightings in Ohio

Electricity generation in Yemen
Detailed data title: Total electricity generation in Yemen in billion kWh
Source: Energy Information Administration
See what else correlates with Electricity generation in Yemen

Correlation r = 0.8654840 (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 = 0.7490626 (Coefficient of determination)
This means 74.9% of the change in the one variable (i.e., Electricity generation in Yemen) is predictable based on the change in the other (i.e., UFO sightings in Ohio) over the 42 years from 1980 through 2021.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 1.41E-13.^Show 0.0000000000001408781740435378
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 0.87 in 1.41E-11% of random cases. Said differently, if you correlated 7,098,331,638,590 random variables^Note You don't actually need 7 trillion variables to find a correlation like this one. I don't have that many variables in my database. You can also correlate variables that are not independent. I do this a lot.

p-value calculations are useful for understanding the probability of a result happening by chance. They are most useful when used to highlight the risk of a fluke outcome. For example, if you calculate a p-value of 0.30, the risk that the result is a fluke is high. It is good to know that! But there are lots of ways to get a p-value of less than 0.01, as evidenced by this project.

In this particular case, the values are so extreme as to be meaningless. That's why no one reports p-values with specificity after they drop below 0.01.

Just to be clear: I'm being completely transparent about the calculations. There is no math trickery. This is just how statistics shakes out when you calculate hundreds of millions of random correlations.
with the same 41 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 41 because we have two variables measured over a period of 42 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.

[ 0.76, 0.93 ] 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.

	1980	1981	1982	1983	1984	1985	1986	1987	1988	1989	1990	1991	1992	1993	1994	1995	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021
UFO sightings in Ohio (UFO sightings)	9	8	7	3	10	8	8	7	10	5	5	6	10	14	26	25	23	26	59	120	75	90	86	111	123	83	93	111	130	127	123	151	263	348	270	202	151	138	83	174	172	44
Electricity generation in Yemen (Billion kWh)	0.471	0.54	0.647	0.721	0.818	0.855	1.094	1.183	1.565	1.579	1.563	1.693	1.836	1.928	2.029	2.227	2.194	2.404	2.357	2.571	3.208	3.424	3.543	3.85	4.103	4.482	5.064	5.66538	6.15324	6.33936	7.2917	5.83376	6.65162	7.99594	7.19724	5.92332	4.51942	3.81864	3.30588	3.41492	3.23725	3.52087

Why this works

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.
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.
Outlandish outliers: There are "outliers" in this data.^Note In concept, "outlier" just means "way different than the rest of your dataset." When calculating a correlation like this, they are particularly impactful because a single outlier can substantially increase your correlation.

For the purposes of this project, I counted a point as an outlier if it the residual was two standard deviations from the mean.

(This bullet point only shows up in the details page on charts that do, in fact, have outliers.)
They stand out on the scatterplot above: notice the dots that are far away from any other dots. I intentionally mishandeled outliers, which makes the correlation look extra strong.

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([9,8,7,3,10,8,8,7,10,5,5,6,10,14,26,25,23,26,59,120,75,90,86,111,123,83,93,111,130,127,123,151,263,348,270,202,151,138,83,174,172,44,])
array_2 = np.array([0.471,0.54,0.647,0.721,0.818,0.855,1.094,1.183,1.565,1.579,1.563,1.693,1.836,1.928,2.029,2.227,2.194,2.404,2.357,2.571,3.208,3.424,3.543,3.85,4.103,4.482,5.064,5.66538,6.15324,6.33936,7.2917,5.83376,6.65162,7.99594,7.19724,5.92332,4.51942,3.81864,3.30588,3.41492,3.23725,3.52087,])
array_1_name = "UFO sightings in Ohio"
array_2_name = "Electricity generation in Yemen"

# 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.

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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 UFO sightings in Ohio
Line chart for only Electricity generation in Yemen
AI-generated correlation image
The spurious research paper: An Electrifying Encounter: Unveiling the Shocking Connection Between UFO Sightings in Ohio and Electricity Generation in Yemen

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Correlation ID: 3039 · Black Variable ID: 1155 · Red Variable ID: 24104


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