Spurious correlation #2,891 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air pollution in Boulder and the second variable is Kerosene used in Iraq. 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 Air pollution in Boulder and the second variable is Kerosene used in Iraq. The chart goes from 1980 to 2021, and the two variables track closely in value over that time.

Download png, svg

AI explanation

Boulder's extra smog somehow created a kerosene magnet, leading to a surge in demand all the way in Iraq! Who knew pollution could have such a far-reaching impact on the fuel trade?

^{Show image generation prompt} Model: dalle-3
Prompt: Style: Sci-fi fantasy Scene: A hazy sky hovers over the city of Boulder, with visible pollutants in the air. Meanwhile, in Iraq, a group of people is seen using kerosene lamps due to a redirection of a shipment. Prompt: Generate an image of a sprawling futuristic cityscape, bathed in a hazy, ethereal light. The city of Boulder should be depicted with towering skyscrapers and advanced technology, while the sky above is tinged with pollutants, creating an otherworldly atmosphere. In stark contrast, depict a group of diverse individuals in a dimly lit space in Iraq, using kerosene lamps as their primary source of light due to a disrupted shipment of advanced energy sources. The juxtaposition should capture the stark disparities between the two locations, blending elements of advanced sci-fi technology with the gritty reality of resource limitations. The depiction should include only scenes, people, and objects, it should not include text or speech bubbles.

This image generation prompt was also generated by AI, using the following sequence:

Model: gpt-3.5-turbo-1106
System prompt: You select one of a few potential scene descriptors that seems to go along with the variables described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here are two variables: Air pollution in Boulder and Kerosene used in Iraq. 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: Pop art Minimalism a Polaroid photo Sci-fi fantacy Oragami
ChatGPT: Sci-fi fantasy

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both Air pollution in Boulder and Kerosene used in Iraq, in the following situation: Because Boulder air pollution caused an uptick in airborne particulates, it disrupted global wind patterns, inadvertently redirecting kerosene from its intended destination to Iraq.. Keep the description simple.
ChatGPT: In a scene, a hazy sky hovers over the city of Boulder, with visible pollutants in the air. Meanwhile, in Iraq, a group of people is seen using kerosene lamps due to a redirection of a shipment.

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: [ Sci-fi fantasy ] and depicting this scene: In a scene, a hazy sky hovers over the city of Boulder, with visible pollutants in the air. Meanwhile, in Iraq, a group of people is seen using kerosene lamps due to a redirection of a shipment. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Style: Sci-fi fantasy Scene: A hazy sky hovers over the city of Boulder, with visible pollutants in the air. Meanwhile, in Iraq, a group of people is seen using kerosene lamps due to a redirection of a shipment. Prompt: Generate an image of a sprawling futuristic cityscape, bathed in a hazy, ethereal light. The city of Boulder should be depicted with towering skyscrapers and advanced technology, while the sky above is tinged with pollutants, creating an otherworldly atmosphere. In stark contrast, depict a group of diverse individuals in a dimly lit space in Iraq, using kerosene lamps as their primary source of light due to a disrupted shipment of advanced energy sources. The juxtaposition should capture the stark disparities between the two locations, blending elements of advanced sci-fi technology with the gritty reality of resource limitations.

*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 Air pollution in Boulder caused Kerosene used in Iraq to increase.

AI academic paper

(Because p < 0.01)

Boulder's Smog and Iraq's Kerosene: Is There a Connection Bubbling Unseen?

Journal of Eclectic Environmental 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 Air pollution in Boulder and Kerosene used in Iraq. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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 CVS receipts.

Here is the title and abstract of the paper:
[[TITLE]]
Boulder's Smog and Iraq's Kerosene: Is There a Connection Bubbling Unseen?

[[ABSTRACT]]
This paper delves into the unorthodox exploration of the potential link between air pollution in Boulder and the use of kerosene in Iraq. The study utilized data from the Environmental Protection Agency and the Energy Information Administration to address this peculiar conundrum. Our findings revealed a correlation coefficient of 0.6023490 and a p-value less than 0.01 for the years 1980 to 2021.

As we meticulously combed through the data, we unearthed an intriguing relationship between the two seemingly distant phenomena. It seems that the emissions from Boulder's smog and the consumption of kerosene in Iraq may be entangled in an unforeseen dance of atmospheric fate. It's almost as if they were saying, "You can't run from me, I'm right behind you!"

Our study uncovers a potential interconnectedness between these two distant regions, seemingly whispering, "The kerosene used in Iraq could be contributing to Boulder's air quality! That's quite a fuelish endeavor!"

These peculiar findings provide an exciting opportunity for further research and raise the possibility of global connections in air quality. After all, who would have thought that Boulder's smog and Iraq's kerosene could be involved in a gaseous clandestine affair?

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
Air pollution is a pressing global issue with significant implications for public health and environmental sustainability. The adverse effects of air pollution on human health, ecosystems, and climate change have garnered widespread attention from policymakers, researchers, and the public alike. As the saying goes, "When it comes to air pollution, the sky's the limit!"
The city of Boulder, Colorado, renowned for its picturesque landscapes and commitment to environmental conservation, has been grappling with air quality challenges in recent decades. At the same time, Iraq, a country nestled in the heart of the Middle East, has been reliant on kerosene for various domestic and industrial purposes. Looking into the connection between these two seemingly disparate areas, one might be inclined to wonder, "What could possibly link the Rocky Mountains and the Mesopotamian plains, aside from their shared history of geological upheavals?"
This study seeks to unravel the potential link between the air pollution woes of Boulder and the extensive use of kerosene in Iraq. As we delve into this investigation, it's undeniable that we're venturing into uncharted territory, akin to exploring uncharted atmospheric territories!

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

This literature review encompasses a comprehensive synthesis of existing research ventures that have endeavored to untangle the enigmatic web of interconnectedness between air pollution in Boulder and the consumption of kerosene in Iraq.

In "The Impact of Air Pollution on Public Health" by Smith, the authors find compelling evidence linking air pollution to adverse respiratory outcomes. Similarly, Doe's study "Kerosene: From Combustion to Complex Chemical Reactions" reveals the intricate chemical processes associated with kerosene usage.

Moving into the realm of non-fiction books, "Choked: Life and Breath in the Age of Air Pollution" by Beth Gardiner provides a poignant exploration of the global air pollution crisis, shedding light on the profound repercussions of deteriorating air quality.

Transitioning to fiction, "The Kerosene Assassin" by A. Parker presents a thrilling narrative that may, inconceivably, contain hidden insights regarding the elusive connection between Boulder's smog and Iraq's kerosene usage.

Further delving into the depths of literature review, we turned to unusual sources of information, including overly enthusiastic travel brochures, cryptic fortune cookies, and, perhaps most notably, a series of CVS receipts. While unconventional, these sources proved to be surprisingly insightful, albeit laden with promotional coupons for assorted snacks and hair care products.

In "The Uncharted Territories of Air Pollution: A CVS Receipt Analysis," our findings revealed an unexpected correlation between excessive kerosene purchases and the prevalence of air freshener coupons on the receipts. While not scientifically rigorous, the evidence was curiously compelling.

In concluding the literature review, we emphasize the necessity of undertaking further studies to decipher the cryptic relationship between Boulder's smog and Iraq's kerosene usage. The implications of this potential connection are nothing short of momentous, akin to a revelation that a helium balloon factory and a pin factory are, in fact, rivals in a bitter rivalry over air superiority.

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 Air pollution in Boulder and Kerosene used in Iraq. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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]]
Boulder's Smog and Iraq's Kerosene: Is There a Connection Bubbling Unseen?

[[ABSTRACT]]
This paper delves into the unorthodox exploration of the potential link between air pollution in Boulder and the use of kerosene in Iraq. The study utilized data from the Environmental Protection Agency and the Energy Information Administration to address this peculiar conundrum. Our findings revealed a correlation coefficient of 0.6023490 and a p-value less than 0.01 for the years 1980 to 2021.

As we meticulously combed through the data, we unearthed an intriguing relationship between the two seemingly distant phenomena. It seems that the emissions from Boulder's smog and the consumption of kerosene in Iraq may be entangled in an unforeseen dance of atmospheric fate. It's almost as if they were saying, "You can't run from me, I'm right behind you!"

Our study uncovers a potential interconnectedness between these two distant regions, seemingly whispering, "The kerosene used in Iraq could be contributing to Boulder's air quality! That's quite a fuelish endeavor!"

These peculiar findings provide an exciting opportunity for further research and raise the possibility of global connections in air quality. After all, who would have thought that Boulder's smog and Iraq's kerosene could be involved in a gaseous clandestine affair?

[[LITERATURE REVIEW]]
This literature review encompasses a comprehensive synthesis of existing research ventures that have endeavored to untangle the enigmatic web of interconnectedness between air pollution in Boulder and the consumption of kerosene in Iraq.
In "The Impact of Air Pollution on Public Health" by Smith, the authors find compelling evidence linking air pollution to adverse respiratory outcomes. Similarly, Doe's study "Kerosene: From Combustion to Complex Chemical Reactions" reveals the intricate chemical processes associated with kerosene usage.
Moving into the realm of non-fiction books, "Choked: Life and Breath in the Age of Air Pollution" by Beth Gardiner provides a poignant exploration of the global air pollution crisis, shedding light on the profound repercussions of deteriorating air quality.
Transitioning to fiction, "The Kerosene Assassin" by A. Parker presents a thrilling narrative that may, inconceivably, contain hidden insights regarding the elusive connection between Boulder's smog and Iraq's kerosene usage.
Further delving into the depths of literature review, we turned to unusual sources of information, including overly enthusiastic travel brochures, cryptic fortune cookies, and, perhaps most notably, a series of CVS receipts. While unconventional, these sources proved to be surprisingly insightful, albeit laden with promotional coupons for assorted snacks and hair care products.
In "The Uncharted Territories of Air Pollution: A CVS Receipt Analysis," our findings revealed an unexpected correlation between excessive kerosene purchases and the prevalence of air freshener coupons on the receipts. While not scientifically rigorous, the evidence was curiously compelling.
In concluding the literature review, we emphasize the necessity of undertaking further studies to decipher the cryptic relationship between Boulder's smog and Iraq's kerosene usage. The implications of this potential connection are nothing short of momentous, akin to a revelation that a helium balloon factory and a pin factory are, in fact, rivals in a bitter rivalry over air superiority.

[[RESULTS]]
The analysis of data collected from the Environmental Protection Agency and the Energy Information Administration revealed a significant and positive correlation between air pollution in Boulder and the usage of kerosene in Iraq. The correlation coefficient was found to be 0.6023490, indicating a moderate to strong relationship between the two variables. This suggests that as one variable increases, the other variable tends to increase as well. It's as if they were doing the atmospheric tango!
The r-squared value of 0.3628243 indicates that approximately 36.28% of the variability in air pollution in Boulder can be explained by the consumption of kerosene in Iraq. This provides a notable insight into the potential influence of kerosene usage in Iraq on the air quality of Boulder. It's almost like a mystery novel where the guilty party is finally revealed, and it turns out to be the unexpected character!
The p-value of less than 0.01 suggests that the correlation observed is statistically significant, further emphasizing the robustness of the relationship between air pollution in Boulder and kerosene usage in Iraq. It's as if the data were saying, "I'm so statistically significant, you can't ignore me!"
The scatterplot (Fig. 1) visually illustrates the strong correlation between the two variables, affirming the quantitative findings in a visually striking manner. It's like a photo of the elusive Bigfoot – hard to capture, but once you do, there's no denying its existence!
These results bring to light a previously unrecognized connection between seemingly unrelated phenomena, urging further exploration of the interplay between regional air quality and international fuel consumption. It's like stumbling upon a hidden treasure in the depths of statistical analysis – unexpected and exhilarating!

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The findings of this study provide compelling evidence of a significant and positive correlation between air pollution in Boulder and the usage of kerosene in Iraq, echoing and affirming previous research. The moderate to strong relationship revealed by the correlation coefficient aligns with the suggestive nature of the air pollution and kerosene usage dynamics. It's as if these two variables were engaging in an atmospheric pas de deux, with one seemingly mirroring the steps of the other.

The r-squared value of 0.3628243 indicates that approximately 36.28% of the variability in air pollution in Boulder can be ascribed to the consumption of kerosene in Iraq. This quantification reaffirms the substantial influence of kerosene usage on regional air quality, akin to discovering that a previously unseen supporting character is, in fact, the linchpin of the entire narrative.

The statistically significant p-value further validates the robustness of the relationship, emphasizing the veracity of the interconnection between air pollution in Boulder and kerosene usage in Iraq. It's akin to a Sherlock Holmes mystery where the clues are unequivocal and incriminating, leaving little room for doubt or dissent.

The visual representation of the relationship in the scatterplot mirrors the quantitative results, reinforcing the compelling nature of the evidence. It's as if the empirical data are donning a metaphorical deerstalker hat and magnifying glass, leaving no room for ambiguity or misinterpretation.

The interconnectedness between Boulder's air quality and Iraq's kerosene usage, while initially surprising, underscores the intricate and often unexpected global dynamics at play. It's as if the world were a complex and interwoven tapestry, where seemingly disparate threads are inevitably linked in an elaborate and surprising pattern.

In conclusion, these findings not only validate but also elucidate the potential connection between seemingly distant phenomena. Further exploration of the intricate relationship between regional air quality and international fuel consumption is warranted, offering the promise of uncovering even more unexpected and captivating connections. It's as if the scientific endeavor were akin to embarking on a thrilling treasure hunt, with each discovery revealing a new layer of intrigue and possibility.

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 Air pollution in Boulder and Kerosene used in Iraq. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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]]
Boulder's Smog and Iraq's Kerosene: Is There a Connection Bubbling Unseen?

[[ABSTRACT]]
This paper delves into the unorthodox exploration of the potential link between air pollution in Boulder and the use of kerosene in Iraq. The study utilized data from the Environmental Protection Agency and the Energy Information Administration to address this peculiar conundrum. Our findings revealed a correlation coefficient of 0.6023490 and a p-value less than 0.01 for the years 1980 to 2021.

As we meticulously combed through the data, we unearthed an intriguing relationship between the two seemingly distant phenomena. It seems that the emissions from Boulder's smog and the consumption of kerosene in Iraq may be entangled in an unforeseen dance of atmospheric fate. It's almost as if they were saying, "You can't run from me, I'm right behind you!"

Our study uncovers a potential interconnectedness between these two distant regions, seemingly whispering, "The kerosene used in Iraq could be contributing to Boulder's air quality! That's quite a fuelish endeavor!"

These peculiar findings provide an exciting opportunity for further research and raise the possibility of global connections in air quality. After all, who would have thought that Boulder's smog and Iraq's kerosene could be involved in a gaseous clandestine affair?

[[INTRDUCTION]]
Air pollution is a pressing global issue with significant implications for public health and environmental sustainability. The adverse effects of air pollution on human health, ecosystems, and climate change have garnered widespread attention from policymakers, researchers, and the public alike. As the saying goes, "When it comes to air pollution, the sky's the limit!"
The city of Boulder, Colorado, renowned for its picturesque landscapes and commitment to environmental conservation, has been grappling with air quality challenges in recent decades. At the same time, Iraq, a country nestled in the heart of the Middle East, has been reliant on kerosene for various domestic and industrial purposes. Looking into the connection between these two seemingly disparate areas, one might be inclined to wonder, "What could possibly link the Rocky Mountains and the Mesopotamian plains, aside from their shared history of geological upheavals?"
This study seeks to unravel the potential link between the air pollution woes of Boulder and the extensive use of kerosene in Iraq. As we delve into this investigation, it's undeniable that we're venturing into uncharted territory, akin to exploring uncharted atmospheric territories!

[[RESULTS]]
The analysis of data collected from the Environmental Protection Agency and the Energy Information Administration revealed a significant and positive correlation between air pollution in Boulder and the usage of kerosene in Iraq. The correlation coefficient was found to be 0.6023490, indicating a moderate to strong relationship between the two variables. This suggests that as one variable increases, the other variable tends to increase as well. It's as if they were doing the atmospheric tango!
The r-squared value of 0.3628243 indicates that approximately 36.28% of the variability in air pollution in Boulder can be explained by the consumption of kerosene in Iraq. This provides a notable insight into the potential influence of kerosene usage in Iraq on the air quality of Boulder. It's almost like a mystery novel where the guilty party is finally revealed, and it turns out to be the unexpected character!
The p-value of less than 0.01 suggests that the correlation observed is statistically significant, further emphasizing the robustness of the relationship between air pollution in Boulder and kerosene usage in Iraq. It's as if the data were saying, "I'm so statistically significant, you can't ignore me!"
The scatterplot (Fig. 1) visually illustrates the strong correlation between the two variables, affirming the quantitative findings in a visually striking manner. It's like a photo of the elusive Bigfoot – hard to capture, but once you do, there's no denying its existence!
These results bring to light a previously unrecognized connection between seemingly unrelated phenomena, urging further exploration of the interplay between regional air quality and international fuel consumption. It's like stumbling upon a hidden treasure in the depths of statistical analysis – unexpected and exhilarating!

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our study has shed light on the surprising link between air pollution in Boulder and the utilization of kerosene in Iraq. The findings revealed a moderate to strong positive correlation between these seemingly disparate variables, hinting at an unexpected interconnectedness that transcends geographical boundaries. It’s as if the atmospheric particles were whispering, "We're all in this together, air-where!"

The statistically significant correlation coefficient and p-value provide compelling evidence of the relationship, almost like a detective solving a case with a captivating twist – who knew that air pollution and kerosene could be in cahoots?

These unanticipated revelations point to the need for continued exploration of the complex dynamics underlying global air quality. It's as if the data were telling us, "There's more to this story than meets the eye – keep digging!"

While our findings open new avenues for inquiry, it is clear that no more research is needed in this specific area. The results have served their purpose, and it's time to let this particular curiosity be consigned to the annals of scientific history. As they say, "You can't squeeze blood from a turnip – or research from an exhausted topic!"

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 Boulder's Smog and Iraq's Kerosene: Is There a Connection Bubbling Unseen?. Respond only with the name of a fictional academic journal.

ChatGPT:

Journal of Eclectic Environmental 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 Boulder's Smog and Iraq's Kerosene: Is There a Connection Bubbling Unseen?. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Quirky Environmental Research

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 Boulder's Smog and Iraq's Kerosene: Is There a Connection Bubbling Unseen? with an abstract of This paper delves into the unorthodox exploration of the potential link between air pollution in Boulder and the use of kerosene in Iraq. The study utilized data from the Environmental Protection Agency and the Energy Information Administration to address this peculiar conundrum. Our findings revealed a correlation coefficient of 0.6023490 and a p-value less than 0.01 for the years 1980 to 2021.
As we meticulously combed through the data, we unearthed an intriguing relationship between the two seemingly distant phenomena. It seems that the emissions from Boulder's smog and the consumption of kerosene in Iraq may be entangled in an unforeseen dance of atmospheric fate. It's almost as if they were saying, "You can't run from me, I'm right behind you!"
Our study uncovers a potential interconnectedness between these two distant regions, seemingly whispering, "The kerosene used in Iraq could be contributing to Boulder's air quality! That's quite a fuelish endeavor!"
These peculiar findings provide an exciting opportunity for further research and raise the possibility of global connections in air quality. After all, who would have thought that Boulder's smog and Iraq's kerosene could be involved in a gaseous clandestine affair?

ChatGPT:

Boulder smog, air pollution, kerosene use, Iraq, environmental impact, correlation coefficient, atmospheric fate, EPA data, EIA data, air quality, global connections, research opportunities, interconnectedness, atmospheric chemistry, environmental impact, smog emissions, kerosene consumption, air quality study

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

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Data details

Air pollution in Boulder
Detailed data title: Percentage of days with moderate or worse air quality in Boulder, CO
Source: Environmental Protection Agency
See what else correlates with Air pollution in Boulder

Kerosene used in Iraq
Detailed data title: Volume of kerosene used consumed in Iraq in millions of barrels per day
Source: Energy Information Administration
See what else correlates with Kerosene used in Iraq

Correlation r = 0.6023490 (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 = 0.3628243 (Coefficient of determination)
This means 36.3% of the change in the one variable (i.e., Kerosene used in Iraq) is predictable based on the change in the other (i.e., Air pollution in Boulder) over the 42 years from 1980 through 2021.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 2.4E-5.^Show 0.0000243724580011152740000000
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 0.6 in 0.0024% of random cases. Said differently, if you correlated 41,030 random variables^Note You don't actually need 41 thousand variables to find a correlation like this one. 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.

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.

[ 0.37, 0.77 ] 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
Air pollution in Boulder (Bad air quality days)	7.16332	20.9945	27.9141	24.4506	30.663	32.6923	34.2466	38.0822	45.6284	34.2466	23.2877	27.9452	22.1311	27.3973	27.3973	20	24.0437	22.4658	32.3288	17.8082	25.1366	24.3836	24.6575	30.137	17.4863	29.589	38.0822	40.274	40.1639	29.863	35.6164	39.4521	46.7967	33.8889	27.5	27.3973	6.86275	32.7731	39.5028	37.8082	40.7104	44.1096
Kerosene used in Iraq (Million Barrels/Day)	22.5556	22.2437	21.3082	25.9857	24.9462	26.8172	29	28	29	28	31	12	16	23	26	24	24	21	21	20	26.4214	27.7645	27.5315	25.5408	29.695	32.2542	35.0921	35.9392	37.4461	39.9207	41	44	45	42	28	26	27	35.0441	36.0652	37.9554	33.784	33.784

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([7.16332,20.9945,27.9141,24.4506,30.663,32.6923,34.2466,38.0822,45.6284,34.2466,23.2877,27.9452,22.1311,27.3973,27.3973,20,24.0437,22.4658,32.3288,17.8082,25.1366,24.3836,24.6575,30.137,17.4863,29.589,38.0822,40.274,40.1639,29.863,35.6164,39.4521,46.7967,33.8889,27.5,27.3973,6.86275,32.7731,39.5028,37.8082,40.7104,44.1096,])
array_2 = np.array([22.5556,22.2437,21.3082,25.9857,24.9462,26.8172,29,28,29,28,31,12,16,23,26,24,24,21,21,20,26.4214,27.7645,27.5315,25.5408,29.695,32.2542,35.0921,35.9392,37.4461,39.9207,41,44,45,42,28,26,27,35.0441,36.0652,37.9554,33.784,33.784,])
array_1_name = "Air pollution in Boulder"
array_2_name = "Kerosene used in Iraq"

# 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 Air pollution in Boulder
Line chart for only Kerosene used in Iraq
AI-generated correlation image
The spurious research paper: Boulder's Smog and Iraq's Kerosene: Is There a Connection Bubbling Unseen?

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Correlation ID: 2891 · Black Variable ID: 20380 · Red Variable ID: 24552


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