Spurious correlation #1,712 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Wind power generated in Poland and the second variable is Number of websites on the internet. The chart goes from 1995 to 2018, 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 Wind power generated in Poland and the second variable is Number of websites on the internet. The chart goes from 1995 to 2018, and the two variables track closely in value over that time.

Download png, svg

AI explanation

The spinning wind turbines in Poland created a vortex of technological inspiration, leading to a surge in website creation as people felt the urge to share their electrifying ideas with the world. As the saying goes, when the wind of change blows, it powers up the internet in the most unexpected ways!

^{Show image generation prompt} Model: dalle-3
Prompt: Generate an image of a futuristic scene set in a rural area of Poland. A vast field of sleek, modern wind turbines gracefully spin in the breeze, standing as monuments to clean energy and progress. In the distance, a group of people diligently set up servers and computer infrastructure, symbolizing the expansion of the digital landscape. The juxtaposition of traditional rural tranquility and high-tech innovation creates a visually striking and thought-provoking image. 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: Wind power generated in Poland and Number of websites on the internet. 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 Futuristic Art nouveau High-tech Cybernetic art
ChatGPT: High-tech

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 Wind power generated in Poland and Number of websites on the internet together. Keep the description simple.
ChatGPT: In a rural area of Poland, a large field of wind turbines is seen spinning steadily in the breeze. In the distance, a group of people are working on setting up servers and computers, symbolizing the increasing number of websites on the internet.

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: [ High-tech ] and depicting this scene: In a rural area of Poland, a large field of wind turbines is seen spinning steadily in the breeze. In the distance, a group of people are working on setting up servers and computers, symbolizing the increasing number of websites on the internet. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image of a futuristic scene set in a rural area of Poland. A vast field of sleek, modern wind turbines gracefully spin in the breeze, standing as monuments to clean energy and progress. In the distance, a group of people diligently set up servers and computer infrastructure, symbolizing the expansion of the digital landscape. The juxtaposition of traditional rural tranquility and high-tech innovation creates a visually striking and thought-provoking image.

*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 Wind power generated in Poland caused Number of websites on the internet to increase.

AI academic paper

(Because p < 0.01)

The Wind Power Grind: A Correlation Between Poland's Breeze and Web-sites

The Journal of Environmental Zephyr 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 Wind power generated in Poland and Number of websites on the internet. 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 devolve ever further, and mention something completely ridiculous, like you conducted literature review by reading the backs of shampoo bottles.

Here is the title and abstract of the paper:
[[TITLE]]
The Wind Power Grind: A Correlation Between Poland's Breeze and Web-sites

[[ABSTRACT]]
This research investigates the perplexing puzzle of the relationship between wind power generated in Poland and the number of websites on the internet. Using data from the Energy Information Administration and Internet Live Stats spanning from 1995 to 2018, a correlation coefficient of 0.9720003 and a p-value less than 0.01 were calculated, revealing a robust association between these two seemingly disparate phenomena. The findings of this study prompt contemplation on the winds of change blowing through the digital landscape and the potential impact of a gusty website expansion. It leaves room for wry humor, as the internet grows and the wind blows, stirring up a tempest of technological progress.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The relationship between wind power and the virtual expanse of the internet is a gusty conundrum that has long intrigued researchers and technophiles alike. While one may be inclined to dismiss this correlation as a mere breezy coincidence, our study aims to unravel the turbulent connection between Poland's breezes and the blooming of web-sites.
As we delve into this windswept investigation, it becomes evident that the interplay between these two variables is not to be taken lightly. The wind, with its invisible force, and the internet, with its intangible web of connectivity, converge in a dance of data and wind turbines. This enigmatic relationship raises questions as profound as the wind itself, such as: Can the gusts of Poland's zephyrs truly stir the ether of the digital realm?
In the realm of statistical analysis, it is crucial to remain grounded, but also open to the winds of possibility. By harnessing the power of correlation coefficients and p-values, we set out to navigate this windswept landscape of numerical significance. As we unveil our findings, it becomes clear that the association between wind power and the digital domain is not just a passing breeze, but a robust and persistent bond that we cannot simply blow off.
Through this study, we seek to shed light on the stormy intersection of technology and natural forces, all while maintaining a sense of humor that is as refreshing as a cool breeze on a hot summer day. After all, who said scientific inquiry couldn't have a dash of whimsy and a gust of wit?

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

In "Smith et al. (2015)," the authors find a correlation between wind power generation and various environmental factors, such as air quality and climate patterns. Similarly, Doe and Jones (2017) explore the impacts of renewable energy sources on global carbon emissions and energy consumption. These studies underscore the significance of wind power as a sustainable energy resource and its effects on the natural environment.

Moving on to related non-fiction literature, "The Weather Makers" by Tim Flannery provides insight into the interconnectedness of weather patterns and energy production, offering a broader context for understanding the potential influence of wind power on digital phenomena. Additionally, "The Sixth Extinction" by Elizabeth Kolbert delves into the complex interplay between human activity and ecological changes, shedding light on the broader implications of energy-related environmental shifts.

Transitioning to fiction literature with thematic relevance, J.K. Rowling's "Harry Potter and the Goblet of Fire" features the magical use of wind in various spells and enchantments, offering a whimsical perspective on the elemental forces that may influence digital landscapes. Similarly, in the dystopian novel "1984" by George Orwell, the omnipresent gaze of the internet-like "Big Brother" looms over a society shaped by surveillance and control, invoking contemplation on the power dynamics inherent in digital expansion.

Furthermore, the researchers conducted an extensive review of unconventional sources, venturing into uncharted territories to uncover potential insights. This included delving into the back of shampoo bottles for cryptic messages that could offer unexpected wisdom on the winds of change and digital innovation. While these unconventional sources may raise eyebrows, they serve as a testament to the researchers' commitment to exploring the unconventional in pursuit of knowledge.

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 Wind power generated in Poland and Number of websites on the internet. 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]]
The Wind Power Grind: A Correlation Between Poland's Breeze and Web-sites

[[ABSTRACT]]
This research investigates the perplexing puzzle of the relationship between wind power generated in Poland and the number of websites on the internet. Using data from the Energy Information Administration and Internet Live Stats spanning from 1995 to 2018, a correlation coefficient of 0.9720003 and a p-value less than 0.01 were calculated, revealing a robust association between these two seemingly disparate phenomena. The findings of this study prompt contemplation on the winds of change blowing through the digital landscape and the potential impact of a gusty website expansion. It leaves room for wry humor, as the internet grows and the wind blows, stirring up a tempest of technological progress.

[[LITERATURE REVIEW]]
In "Smith et al. (2015)," the authors find a correlation between wind power generation and various environmental factors, such as air quality and climate patterns. Similarly, Doe and Jones (2017) explore the impacts of renewable energy sources on global carbon emissions and energy consumption. These studies underscore the significance of wind power as a sustainable energy resource and its effects on the natural environment.
Moving on to related non-fiction literature, "The Weather Makers" by Tim Flannery provides insight into the interconnectedness of weather patterns and energy production, offering a broader context for understanding the potential influence of wind power on digital phenomena. Additionally, "The Sixth Extinction" by Elizabeth Kolbert delves into the complex interplay between human activity and ecological changes, shedding light on the broader implications of energy-related environmental shifts.
Transitioning to fiction literature with thematic relevance, J.K. Rowling's "Harry Potter and the Goblet of Fire" features the magical use of wind in various spells and enchantments, offering a whimsical perspective on the elemental forces that may influence digital landscapes. Similarly, in the dystopian novel "1984" by George Orwell, the omnipresent gaze of the internet-like "Big Brother" looms over a society shaped by surveillance and control, invoking contemplation on the power dynamics inherent in digital expansion.
Furthermore, the researchers conducted an extensive review of unconventional sources, venturing into uncharted territories to uncover potential insights. This included delving into the back of shampoo bottles for cryptic messages that could offer unexpected wisdom on the winds of change and digital innovation. While these unconventional sources may raise eyebrows, they serve as a testament to the researchers' commitment to exploring the unconventional in pursuit of knowledge.

[[RESULTS]]
The investigation into the relationship between wind power generated in Poland and the number of websites on the internet yielded intriguing findings. Across the years 1995 to 2018, a remarkably strong correlation of 0.9720003 was uncovered, with an r-squared value of 0.9447846 and a p-value less than 0.01. It seems the winds of statistical significance were indeed blowing in our favor.
As depicted in Figure 1, the scatterplot graphically portrays the robust association between these two seemingly distant variables. The data points form a pattern as cohesive as the gusts that sway the turbines, whispering tales of the winds of change blowing through the digital expanse.
The correlation coefficient of 0.9720003 suggests a very high degree of association, leaving little room for doubt that the wind power generated in Poland has a substantial impact on the proliferation of websites on the internet. One could say that the web-sites are riding the winds of change.
The p-value less than 0.01 further emphasizes the statistical significance of this relationship, indicating a minute likelihood of this finding being merely a fluke. It seems that the digital landscape is not immune to the breezy influence of Poland's wind power generation.
In conclusion, this study not only illuminates the substantive connection between wind power and the internet, but also invites contemplation on the potential implications of this robust association. The findings prompt reflection on the winds of change that mold the digital landscape, stirring up a tempest of technological progress. It appears that as the internet grows, the wind indeed shows its power in shaping the virtual world.
The robustness of this relationship leaves us with a sense of awe at the unexpected interplay between natural forces and digital expansion. It is as if the winds themselves were whispering to us: "In the realm of science, the unexpected can blow you away."

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The results of this study provide substantial support for prior research demonstrating the unexpectedly strong correlation between wind power generation in Poland and the number of websites on the internet. These findings echo the work of Smith et al. (2015) and Doe and Jones (2017), who unearthed correlations between wind power and environmental factors, shedding light on the interconnectedness of natural phenomena. In a whimsical turn of events, the thematic relevance of J.K. Rowling's "Harry Potter and the Goblet of Fire," where wind is utilized in spells, appears to hold more weight in reality than initially anticipated.

This study's findings also align with the unconventional exploration of sources, including shampoo bottles, as a testament to the researchers' dedication to unearthing unconventional insights. It seems that the winds of change, be they literal or metaphorical, may indeed carry unexpected wisdom. The robust correlation coefficient of 0.9720003 and the p-value less than 0.01 underscore the statistical significance of the relationship between wind power and internet growth, reminding us that even in the realm of science, the unexpected can make a compelling case for itself.

The findings encourage contemplation not only on the interconnectedness of seemingly disparate phenomena but also on the potential implications of wind power on the digital landscape. The winds of statistical significance were indeed blowing in our favor, leaving little room for doubt that the winds of change may hold more sway over the digital realm than previously imagined. As the internet continues to grow and evolve, it seems that the breezy influence of Poland's wind power generation has a substantial impact, metaphorically and statistically speaking.

These results prompt reflection on the winds of change that mold the digital landscape, stirring up a tempest of technological progress. Just as the wind can power turbines and propel sailboats, it appears to also play a significant role in propelling the expansion of the virtual world. In the realm of science, it is often the unexpected associations and correlations that can blow us away, leaving us to marvel at the unforeseen interplay between natural forces and digital expansion.

In essence, this study provides a fresh perspective on the potential influence of wind power on the proliferation of websites, offering a lighthearted reminder that even in the world of science, the winds of change may hold more sway than we anticipate.

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 goofy academic research papers that sounds like it belongs based on the title and abstract provided.
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 short conclusion of an academic research paper presenting the findings of the connection between Wind power generated in Poland and Number of websites on the internet. 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 300 tokens. At the very end, assert that no more research is needed in this area.

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
The Wind Power Grind: A Correlation Between Poland's Breeze and Web-sites

[[ABSTRACT]]
This research investigates the perplexing puzzle of the relationship between wind power generated in Poland and the number of websites on the internet. Using data from the Energy Information Administration and Internet Live Stats spanning from 1995 to 2018, a correlation coefficient of 0.9720003 and a p-value less than 0.01 were calculated, revealing a robust association between these two seemingly disparate phenomena. The findings of this study prompt contemplation on the winds of change blowing through the digital landscape and the potential impact of a gusty website expansion. It leaves room for wry humor, as the internet grows and the wind blows, stirring up a tempest of technological progress.

[[INTRDUCTION]]
The relationship between wind power and the virtual expanse of the internet is a gusty conundrum that has long intrigued researchers and technophiles alike. While one may be inclined to dismiss this correlation as a mere breezy coincidence, our study aims to unravel the turbulent connection between Poland's breezes and the blooming of web-sites.
As we delve into this windswept investigation, it becomes evident that the interplay between these two variables is not to be taken lightly. The wind, with its invisible force, and the internet, with its intangible web of connectivity, converge in a dance of data and wind turbines. This enigmatic relationship raises questions as profound as the wind itself, such as: Can the gusts of Poland's zephyrs truly stir the ether of the digital realm?
In the realm of statistical analysis, it is crucial to remain grounded, but also open to the winds of possibility. By harnessing the power of correlation coefficients and p-values, we set out to navigate this windswept landscape of numerical significance. As we unveil our findings, it becomes clear that the association between wind power and the digital domain is not just a passing breeze, but a robust and persistent bond that we cannot simply blow off.
Through this study, we seek to shed light on the stormy intersection of technology and natural forces, all while maintaining a sense of humor that is as refreshing as a cool breeze on a hot summer day. After all, who said scientific inquiry couldn't have a dash of whimsy and a gust of wit?

[[RESULTS]]
The investigation into the relationship between wind power generated in Poland and the number of websites on the internet yielded intriguing findings. Across the years 1995 to 2018, a remarkably strong correlation of 0.9720003 was uncovered, with an r-squared value of 0.9447846 and a p-value less than 0.01. It seems the winds of statistical significance were indeed blowing in our favor.
As depicted in Figure 1, the scatterplot graphically portrays the robust association between these two seemingly distant variables. The data points form a pattern as cohesive as the gusts that sway the turbines, whispering tales of the winds of change blowing through the digital expanse.
The correlation coefficient of 0.9720003 suggests a very high degree of association, leaving little room for doubt that the wind power generated in Poland has a substantial impact on the proliferation of websites on the internet. One could say that the web-sites are riding the winds of change.
The p-value less than 0.01 further emphasizes the statistical significance of this relationship, indicating a minute likelihood of this finding being merely a fluke. It seems that the digital landscape is not immune to the breezy influence of Poland's wind power generation.
In conclusion, this study not only illuminates the substantive connection between wind power and the internet, but also invites contemplation on the potential implications of this robust association. The findings prompt reflection on the winds of change that mold the digital landscape, stirring up a tempest of technological progress. It appears that as the internet grows, the wind indeed shows its power in shaping the virtual world.
The robustness of this relationship leaves us with a sense of awe at the unexpected interplay between natural forces and digital expansion. It is as if the winds themselves were whispering to us: "In the realm of science, the unexpected can blow you away."

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

As we conclude this breezy exploration of Poland's wind power and the internet's digital sprawl, it is clear that the winds of statistical significance have left us winded. The robust correlation coefficient of 0.9720003 has blown our expectations away, with a p-value less than 0.01 that could knock the socks off even the most skeptical researcher. It seems the virtual expanse is indeed dancing to the tune of Poland's zephyrs, riding the winds of change like a technological kite soaring high.

The scatterplot's portrayal of the cohesive pattern between wind power and websites is as striking as a gale-force wind, whispering tales of a gusty relationship that is much more than a fleeting zephyr. The digital realm seems to be harnessing the power of Poland's winds, swirling and twirling in a techno-tango that defies conventional understanding.

In the face of these compelling results, it is tempting to be swept away by thoughts of future research uncovering even more, but we assert that no further exploration is needed in this windswept domain. Our findings blow away doubt and uncertainty, leaving us with a sense of clarity akin to a pristine, cloudless sky. No need to tread where the winds have already blown their influence.

Thus, with a gust of finality, we bid adieu to this study, leaving it to drift away on the winds of scientific inquiry, its unexpected findings still swirling in the air, like the echoes of a well-timed pun at a symposium.

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 The Wind Power Grind: A Correlation Between Poland's Breeze and Web-sites. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Environmental Zephyr 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 The Wind Power Grind: A Correlation Between Poland's Breeze and Web-sites. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Analytical Wind 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 The Wind Power Grind: A Correlation Between Poland's Breeze and Web-sites with an abstract of This research investigates the perplexing puzzle of the relationship between wind power generated in Poland and the number of websites on the internet. Using data from the Energy Information Administration and Internet Live Stats spanning from 1995 to 2018, a correlation coefficient of 0.9720003 and a p-value less than 0.01 were calculated, revealing a robust association between these two seemingly disparate phenomena. The findings of this study prompt contemplation on the winds of change blowing through the digital landscape and the potential impact of a gusty website expansion. It leaves room for wry humor, as the internet grows and the wind blows, stirring up a tempest of technological progress.

ChatGPT:

Wind power Poland, internet websites, correlation, Energy Information Administration, Internet Live Stats, wind energy production, website growth, digital landscape, technological progress

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

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Data details

Wind power generated in Poland
Detailed data title: Total wind power generated in Poland in billion kWh
Source: Energy Information Administration
See what else correlates with Wind power generated in Poland

Number of websites on the internet
Detailed data title: Number of websites, measured by unique hostnames
Source: Internet Live Stats
See what else correlates with Number of websites on the internet

Correlation r = 0.9720003 (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 = 0.9447846 (Coefficient of determination)
This means 94.5% of the change in the one variable (i.e., Number of websites on the internet) is predictable based on the change in the other (i.e., Wind power generated in Poland) over the 24 years from 1995 through 2018.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 2.5E-15.^Show 0.0000000000000025103650157057
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 0.97 in 2.5E-13% of random cases. Said differently, if you correlated 398,348,444,845,136 random variables^Note You don't actually need 398 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 23 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 23 because we have two variables measured over a period of 24 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.

[ 0.94, 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.

	1995	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018
Wind power generated in Poland (Billion kWh)	0.001	0	0.002	0.004	0.004	0.005	0.014	0.061	0.124	0.142	0.135	0.256	0.522	0.837	1.077	1.664	3.187	4.709	5.939	7.579	10.728	12.2786	14.5742	12.4717
Number of websites on the internet (Websites)	23500	257601	1117260	2410070	3177450	17087200	29254400	38760400	40912300	51611600	64780600	85507300	121893000	172339000	238028000	206957000	346004000	697089000	672985000	968882000	863106000	1045530000	1766930000	1630320000

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.

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([0.001,0,0.002,0.004,0.004,0.005,0.014,0.061,0.124,0.142,0.135,0.256,0.522,0.837,1.077,1.664,3.187,4.709,5.939,7.579,10.728,12.2786,14.5742,12.4717,])
array_2 = np.array([23500,257601,1117260,2410070,3177450,17087200,29254400,38760400,40912300,51611600,64780600,85507300,121893000,172339000,238028000,206957000,346004000,697089000,672985000,968882000,863106000,1045530000,1766930000,1630320000,])
array_1_name = "Wind power generated in Poland"
array_2_name = "Number of websites on the internet"

# 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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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.

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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 Wind power generated in Poland
Line chart for only Number of websites on the internet
AI-generated correlation image
The spurious research paper: The Wind Power Grind: A Correlation Between Poland's Breeze and Web-sites

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Correlation ID: 1712 · Black Variable ID: 23904 · Red Variable ID: 370


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