about · email me · subscribe
Spurious correlation #3,829 · 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 Decatur, Illinois and the second variable is Total Points scored by the New England Patriots in the NFL season.  The chart goes from 1980 to 2022, and the two variables track closely in value over that time. Small Image
Download png
, svg

AI explanation

As air pollution in Decatur increased, it created a haze that drifted all the way to New England. This haze acted as a smokescreen, making it harder for the opposing teams to tackle and intercept the Patriots. It's like the pollution particles were saying, "You can't catch us, we're the Beli-chicks!"

Model: dalle-3
Prompt: Generate a comic-book-style illustration with muted colors and a dotted halftone pattern from the 1960s. Depict a scene where in Decatur, Illinois, the air is filled with thick smog as mutant butterflies flutter around, their population booming due to the rising pollution. Meanwhile, in New England, the Patriots players look up distractedly as the mutant butterflies swarm around the field, causing them to fumble and miss scoring opportunities, leading to a decrease in their total points for the NFL season. Ensure the visual depiction is simple without any words or speech bubbles. 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 Decatur, Illinois and Total Points scored by the New England Patriots in the NFL season. 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: inspired by bauhaus Woodblock painting Celtic art A comic-book-style illustration with muted colors and a dotted halftone pattern from the 1960s Minimalism
ChatGPT: A comic-book-style illustration with muted colors and a dotted halftone pattern from the 1960s

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 Decatur, Illinois and Total Points scored by the New England Patriots in the NFL season, in the following situation: Because the increase in air pollution in Decatur, Illinois caused a surge in the local population of mutant butterflies, which then traveled to New England and distracted the Patriots players during games, resulting in a decrease in total points scored for the season.. Keep the description simple.
ChatGPT: In Decatur, Illinois, the air is filled with thick smog as mutant butterflies flutter around, their population booming due to the rising pollution. Meanwhile, in New England, the Patriots players look up distractedly as the mutant butterflies swarm around the field, causing them to fumble and miss scoring opportunities, leading to a decrease in their total points for the NFL season.

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 comic-book-style illustration with muted colors and a dotted halftone pattern from the 1960s ] and depicting this scene: In Decatur, Illinois, the air is filled with thick smog as mutant butterflies flutter around, their population booming due to the rising pollution. Meanwhile, in New England, the Patriots players look up distractedly as the mutant butterflies swarm around the field, causing them to fumble and miss scoring opportunities, leading to a decrease in their total points for the NFL season. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate a comic-book-style illustration with muted colors and a dotted halftone pattern from the 1960s. Depict a scene where in Decatur, Illinois, the air is filled with thick smog as mutant butterflies flutter around, their population booming due to the rising pollution. Meanwhile, in New England, the Patriots players look up distractedly as the mutant butterflies swarm around the field, causing them to fumble and miss scoring opportunities, leading to a decrease in their total points for the NFL season. Ensure the visual depiction is simple without any words or speech bubbles.

*Variations in the User Prompts from chart to chart are just the result of random number generation in Python. I wrote a few arrays of various styles and methods to ask questions to change up the results. Every time this site writes an explanation or generates an image, the script picks from each at random.

I sequence the requests into multiple prompts because I find GPT 3.5 to perform much better with short, well-managed contexts. Thus, I track the context directly in Python and only ask ChatGPT targeted questions.

Model: gpt-3.5-turbo-1106 (fine-tuned)
System prompt: You provide humorous responses in the form of plausible sounding explanations for correlations. You assume the correlation is causative for the purpose of the explanation even if it is ridiculous. You do not chat with the user, you only reply with the causal connection explanation and nothing else.
User prompt: Please make up a funny explanation for how increases in Air pollution in Decatur, Illinois positively influenced Total Points scored by the New England Patriots in the NFL season. Include one good pun.

AI academic paper

(Because p < 0.01)
A Breath of Fresh Air: Uncovering the Air Pollution versus Football Points Paradox

The Journal of Environmental Sports Science

Jan 2024

Reminder: This paper is AI-generated. Not real!
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 researcher writing an academic paper.You write titles and abstracts of goofy academic research papers.
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, and add unexpected twists in your writing.

Please draft the title and abstract of an academic research paper presenting the findings of the connection between Air pollution in Decatur, Illinois and Total Points scored by the New England Patriots in the NFL season. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

Make the title punny if you can come up with clever pun. If not, just make it sound clever.

Your research team used data from Environmental Protection Agency and Pro-football-reference to assess this nagging question. You found a correlation coefficient of 0.6471551 and p < 0.01 for 1980 to 2022.

Please respond in this format (replace "Lorem ipsum dolor sit" with your title and abstract)

[[TITLE]]
Lorem ipsum dolor sit

[[ABSTRACT]]
Lorem ipsum dolor sit



ChatGPT:
[[TITLE]]
A Breath of Fresh Air: Uncovering the Air Pollution versus Football Points Paradox

[[ABSTRACT]]
In this paper, we delve into an unconventional analysis of the relationship between air pollution levels in Decatur, Illinois, and the total points scored by the New England Patriots in the NFL season. Leveraging EPA data on air quality and Pro-football-reference statistics, our research team has unearthed a startling correlation between these seemingly disparate phenomena. The correlation coefficient of 0.6471551 and p < 0.01 from 1980 to 2022 indicates a significant relationship that warrants further inquiry.

While the causal mechanisms underlying this connection remain enshrouded in mystery, our findings raise intriguing implications for both environmental science and sports analytics. We urge readers to inhale this research with cautious skepticism and an air of whimsy, as we leave no stone unturned in unraveling this offbeat enigma. Through this study, we aim to inject a breath of fresh air into the dry sphere of scholarly research, sparking laughter and curiosity in equal measure.


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.You draft the introduction 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 introduction section of an academic research paper presenting the findings of the connection between Air pollution in Decatur, Illinois and Total Points scored by the New England Patriots in the NFL season. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Here is the title and abstract of the paper:
[[TITLE]]
A Breath of Fresh Air: Uncovering the Air Pollution versus Football Points Paradox

[[ABSTRACT]]
In this paper, we delve into an unconventional analysis of the relationship between air pollution levels in Decatur, Illinois, and the total points scored by the New England Patriots in the NFL season. Leveraging EPA data on air quality and Pro-football-reference statistics, our research team has unearthed a startling correlation between these seemingly disparate phenomena. The correlation coefficient of 0.6471551 and p < 0.01 from 1980 to 2022 indicates a significant relationship that warrants further inquiry.

While the causal mechanisms underlying this connection remain enshrouded in mystery, our findings raise intriguing implications for both environmental science and sports analytics. We urge readers to inhale this research with cautious skepticism and an air of whimsy, as we leave no stone unturned in unraveling this offbeat enigma. Through this study, we aim to inject a breath of fresh air into the dry sphere of scholarly research, sparking laughter and curiosity in equal measure.

-------

Your response should start like this:

[[INTRODUCTION]]



ChatGPT:
[[INTRODUCTION]]

The relationship between air pollution and human health has long been a topic of concern and scholarly investigation. Decatur, Illinois, known for its industrial activity, has been a focal point for air quality studies. Conversely, in the realm of sports, the New England Patriots have garnered attention for their consistent performance in the NFL. These two seemingly unrelated domains converge in our research, as we embark on unraveling the enigmatic connection between air pollution in Decatur and the total points scored by the New England Patriots in the NFL season.

The city of Decatur, situated in Macon County, Illinois, has witnessed fluctuations in air quality over the years, primarily due to industrial emissions and vehicular activities. Meanwhile, the New England Patriots, based in the bustling metropolis of Foxborough, Massachusetts, have etched their name in NFL history with impressive offensive displays. Surprisingly, our preliminary analysis has uncovered a statistically significant correlation between air pollution levels in Decatur and the points amassed by the Patriots on the gridiron. The correlation coefficient of 0.6471551 and p < 0.01 from 1980 to 2022 has left our research team both captivated and perplexed.

This unexpected correlation beckons for a closer examination, delving into potential factors that might underpin such a peculiar association. While we remain cautious in drawing premature conclusions, we interpret these findings with a measure of playful curiosity, akin to unraveling a mystery novel with an unconventional plot twist. As we embark on this scholarly odyssey, we encourage our readers to adopt a lighthearted disposition, embracing this unorthodox exploration with open-mindedness and a hint of jest.

In the subsequent sections of this paper, we will discuss our methodology, present our empirical findings, and engage in a speculative discourse on the potential mechanisms that could engender such an improbable relationship. Brace yourselves for a journey that blends the solemnity of academic inquiry with the intrigue of uncovering an unexpected intersection between environmental factors and the realm of sports. Let us proceed with the gravity of scholarly rigor and the levity of inquisitive amusement as we unpick this most peculiar puzzle.


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.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 Decatur, Illinois and Total Points scored by the New England Patriots in the NFL season. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, 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]]
A Breath of Fresh Air: Uncovering the Air Pollution versus Football Points Paradox

[[ABSTRACT]]
In this paper, we delve into an unconventional analysis of the relationship between air pollution levels in Decatur, Illinois, and the total points scored by the New England Patriots in the NFL season. Leveraging EPA data on air quality and Pro-football-reference statistics, our research team has unearthed a startling correlation between these seemingly disparate phenomena. The correlation coefficient of 0.6471551 and p < 0.01 from 1980 to 2022 indicates a significant relationship that warrants further inquiry.

While the causal mechanisms underlying this connection remain enshrouded in mystery, our findings raise intriguing implications for both environmental science and sports analytics. We urge readers to inhale this research with cautious skepticism and an air of whimsy, as we leave no stone unturned in unraveling this offbeat enigma. Through this study, we aim to inject a breath of fresh air into the dry sphere of scholarly research, sparking laughter and curiosity in equal measure.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The relationship between air pollution and human health has long been a topic of concern and scholarly investigation. Decatur, Illinois, known for its industrial activity, has been a focal point for air quality studies. Conversely, in the realm of sports, the New England Patriots have garnered attention for their consistent performance in the NFL. These two seemingly unrelated domains converge in our research, as we embark on unraveling the enigmatic connection between air pollution in Decatur and the total points scored by the New England Patriots in the NFL season.
The city of Decatur, situated in Macon County, Illinois, has witnessed fluctuations in air quality over the years, primarily due to industrial emissions and vehicular activities. Meanwhile, the New England Patriots, based in the bustling metropolis of Foxborough, Massachusetts, have etched their name in NFL history with impressive offensive displays. Surprisingly, our preliminary analysis has uncovered a statistically significant correlation between air pollution levels in Decatur and the points amassed by the Patriots on the gridiron. The correlation coefficient of 0.6471551 and p < 0.01 from 1980 to 2022 has left our research team both captivated and perplexed.
This unexpected correlation beckons for a closer examination, delving into potential factors that might underpin such a peculiar association. While we remain cautious in drawing premature conclusions, we interpret these findings with a measure of playful curiosity, akin to unraveling a mystery novel with an unconventional plot twist. As we embark on this scholarly odyssey, we encourage our readers to adopt a lighthearted disposition, embracing this unorthodox exploration with open-mindedness and a hint of jest.
In the subsequent sections of this paper, we will discuss our methodology, present our empirical findings, and engage in a speculative discourse on the potential mechanisms that could engender such an improbable relationship. Brace yourselves for a journey that blends the solemnity of academic inquiry with the intrigue of uncovering an unexpected intersection between environmental factors and the realm of sports. Let us proceed with the gravity of scholarly rigor and the levity of inquisitive amusement as we unpick this most peculiar puzzle.

-------

Your response should start like this:

[[LITERATURE REVIEW]]



ChatGPT:
[[LITERATURE REVIEW]]

The relationship between air pollution and its multifaceted impacts has been extensively documented in academic literature. Smith et al. (2015) underscore the detrimental health effects of prolonged exposure to particulate matter and airborne toxins, shedding light on the pernicious ramifications of environmental pollution on respiratory and cardiovascular well-being. Doe and Jones (2018) illuminate the intricate interplay between industrial emissions and ambient air quality, elucidating the nuances of pollution dispersion patterns in urban settings.

Furthermore, the influence of environmental factors on human performance and societal phenomena has been a subject of scholarly intrigue. In "Breathe: The New Science of a Lost Art" by James Nestor, the author expounds upon the profound impact of breathing and oxygen intake on physical prowess and cognitive function. Likewise, "The Air We Breathe" by Andrea Barrett delves into the multifaceted narratives intertwined with air quality, weaving a tapestry of human experiences shaped by atmospheric conditions.

On a more tangential note, fictional literature also offers allegorical insights into the intersection of environmental dynamics and unexpected outcomes. Works such as "The Air He Breathes" by Brittainy C. Cherry and "The Wind-Up Bird Chronicle" by Haruki Murakami beckon readers into surreal realms, where serendipitous connections and enigmatic relationships unfurl amidst atmospheric backdrops.

While our research journey involved delving into scholarly texts and scientific journals, it would be remiss not to acknowledge auxiliary sources that have inadvertently contributed to our intellectual inquiry. In the spirit of unearthing unconventional revelations, we confess to perusing the backs of shampoo bottles, seeking elusive epiphanies amidst the mundane musings on fragrant essences and hair care instructions.

In the ensuing sections, we will expound upon our empirical findings and unfurl the cloak of mystery veiling the improbable correlation between air pollution levels in Decatur, Illinois, and the total points accrued by the New England Patriots in the NFL season. Prepare to embark on a whimsical odyssey that traverses the frontiers of scholarly inquiry and whimsy, as we navigate the uncharted terrain of this improbable nexus.


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.You draft the methodology 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 methodology section of an academic research paper presenting the findings of the connection between Air pollution in Decatur, Illinois and Total Points scored by the New England Patriots in the NFL season. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and Pro-football-reference . You used data from 1980 to 2022

Make up the research methods you don't know. Make them a bit goofy and convoluted.

Here is the title, abstract, and introduction of the paper:
[[TITLE]]
A Breath of Fresh Air: Uncovering the Air Pollution versus Football Points Paradox

[[ABSTRACT]]
In this paper, we delve into an unconventional analysis of the relationship between air pollution levels in Decatur, Illinois, and the total points scored by the New England Patriots in the NFL season. Leveraging EPA data on air quality and Pro-football-reference statistics, our research team has unearthed a startling correlation between these seemingly disparate phenomena. The correlation coefficient of 0.6471551 and p < 0.01 from 1980 to 2022 indicates a significant relationship that warrants further inquiry.

While the causal mechanisms underlying this connection remain enshrouded in mystery, our findings raise intriguing implications for both environmental science and sports analytics. We urge readers to inhale this research with cautious skepticism and an air of whimsy, as we leave no stone unturned in unraveling this offbeat enigma. Through this study, we aim to inject a breath of fresh air into the dry sphere of scholarly research, sparking laughter and curiosity in equal measure.

[[INTRODUCTION]]
The relationship between air pollution and human health has long been a topic of concern and scholarly investigation. Decatur, Illinois, known for its industrial activity, has been a focal point for air quality studies. Conversely, in the realm of sports, the New England Patriots have garnered attention for their consistent performance in the NFL. These two seemingly unrelated domains converge in our research, as we embark on unraveling the enigmatic connection between air pollution in Decatur and the total points scored by the New England Patriots in the NFL season.
The city of Decatur, situated in Macon County, Illinois, has witnessed fluctuations in air quality over the years, primarily due to industrial emissions and vehicular activities. Meanwhile, the New England Patriots, based in the bustling metropolis of Foxborough, Massachusetts, have etched their name in NFL history with impressive offensive displays. Surprisingly, our preliminary analysis has uncovered a statistically significant correlation between air pollution levels in Decatur and the points amassed by the Patriots on the gridiron. The correlation coefficient of 0.6471551 and p < 0.01 from 1980 to 2022 has left our research team both captivated and perplexed.
This unexpected correlation beckons for a closer examination, delving into potential factors that might underpin such a peculiar association. While we remain cautious in drawing premature conclusions, we interpret these findings with a measure of playful curiosity, akin to unraveling a mystery novel with an unconventional plot twist. As we embark on this scholarly odyssey, we encourage our readers to adopt a lighthearted disposition, embracing this unorthodox exploration with open-mindedness and a hint of jest.
In the subsequent sections of this paper, we will discuss our methodology, present our empirical findings, and engage in a speculative discourse on the potential mechanisms that could engender such an improbable relationship. Brace yourselves for a journey that blends the solemnity of academic inquiry with the intrigue of uncovering an unexpected intersection between environmental factors and the realm of sports. Let us proceed with the gravity of scholarly rigor and the levity of inquisitive amusement as we unpick this most peculiar puzzle.

-------

Your response should start like this:

[[METHODOLOGY]]



ChatGPT:

[[METHODOLOGY]]

To untangle the enigmatic web of connections between air pollution in Decatur, Illinois, and the total points scored by the New England Patriots in the NFL season, our research team employed a multifaceted and undeniably whimsical approach. We embarked on this scholarly escapade with a mixture of scholarly rigor and a hint of playful exuberance, recognizing that the essence of academic inquiry often resides in the unlikeliest of places.

The first step in our convoluted, yet surprisingly effective, methodology was to gather air quality data from the Environmental Protection Agency (EPA). Our researchers scoured the virtual expanse of the internet, navigating through labyrinthine databases and tangled web pages with the dexterity of seasoned explorers. After momentous efforts and persistent keystrokes, a treasure trove of air quality measurements in Decatur, Illinois, spanning the years 1980 to 2022, was finally unearthed.

Simultaneously, our intrepid band of researchers delved into the hallowed archives of Pro-football-reference, where the statistical riches of the New England Patriots' performances awaited. Armed with spreadsheets and algorithms, we meticulously documented the total points amassed by the Patriots in each NFL season during the same time span, carefully distinguishing between touchdowns, field goals, and the occasional safety. As we waded through countless grids of numerical data, our fervor for uncovering the unusual link between air pollution and football points remained undaunted.

With these treasure troves of data in hand, we proceeded to conduct a series of statistical analyses that would make even the most seasoned mathematicians nod in approval. Our calculations involved complex algorithms and mathematical machinations that, in the spirit of full disclosure, may have elicited a few bemused glances from our more traditionally minded colleagues. Nonetheless, the results of our statistical acrobatics yielded a correlation coefficient of 0.6471551 and a p-value of less than 0.01, unveiling a significant relationship between air pollution in Decatur and the Patriots' points scored.

In addition to these quantitative escapades, we ventured into the realm of qualitative analysis, engaging in probing discussions and spirited debates to discern the potential mechanisms underpinning this unexpected correlation. With a pinch of scholarly skepticism and a dollop of imaginative speculation, we explored various hypothetical scenarios, contemplating the enthralling possibility of pollutants sparking a gust of inspiration in the Patriots' offensive strategies.

Ultimately, our methodology was a tapestry of data gathering, computational wizardry, and fervent discourse, woven together by the spirit of curiosity and a dash of unconventional zeal. As we tread further into our empirical findings and speculative musings, we invite our readers to embrace this outlandish journey with an open mind and a glint of amusement, for it is in the unexpected and the whimsical that scholarly discoveries often flourish.


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.You draft the results section of an academic research paper. You speak in the past tense (you found...).
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 results section of an academic research paper presenting the findings of the connection between Air pollution in Decatur, Illinois and Total Points scored by the New England Patriots in the NFL season. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and Pro-football-reference .

For the time period 1980 to 2022, you found a correlation 0.6471551, r-squared of 0.4188097, and p < 0.01.

One figure will be included. The figure (Fig. 1) is a scatterplot showing the strong correlation between the two variables. You don't need to specify where; I will add the figure.

Here is the title and abstract of the paper:
[[TITLE]]
A Breath of Fresh Air: Uncovering the Air Pollution versus Football Points Paradox

[[ABSTRACT]]
In this paper, we delve into an unconventional analysis of the relationship between air pollution levels in Decatur, Illinois, and the total points scored by the New England Patriots in the NFL season. Leveraging EPA data on air quality and Pro-football-reference statistics, our research team has unearthed a startling correlation between these seemingly disparate phenomena. The correlation coefficient of 0.6471551 and p < 0.01 from 1980 to 2022 indicates a significant relationship that warrants further inquiry.

While the causal mechanisms underlying this connection remain enshrouded in mystery, our findings raise intriguing implications for both environmental science and sports analytics. We urge readers to inhale this research with cautious skepticism and an air of whimsy, as we leave no stone unturned in unraveling this offbeat enigma. Through this study, we aim to inject a breath of fresh air into the dry sphere of scholarly research, sparking laughter and curiosity in equal measure.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The relationship between air pollution and human health has long been a topic of concern and scholarly investigation. Decatur, Illinois, known for its industrial activity, has been a focal point for air quality studies. Conversely, in the realm of sports, the New England Patriots have garnered attention for their consistent performance in the NFL. These two seemingly unrelated domains converge in our research, as we embark on unraveling the enigmatic connection between air pollution in Decatur and the total points scored by the New England Patriots in the NFL season.
The city of Decatur, situated in Macon County, Illinois, has witnessed fluctuations in air quality over the years, primarily due to industrial emissions and vehicular activities. Meanwhile, the New England Patriots, based in the bustling metropolis of Foxborough, Massachusetts, have etched their name in NFL history with impressive offensive displays. Surprisingly, our preliminary analysis has uncovered a statistically significant correlation between air pollution levels in Decatur and the points amassed by the Patriots on the gridiron. The correlation coefficient of 0.6471551 and p < 0.01 from 1980 to 2022 has left our research team both captivated and perplexed.
This unexpected correlation beckons for a closer examination, delving into potential factors that might underpin such a peculiar association. While we remain cautious in drawing premature conclusions, we interpret these findings with a measure of playful curiosity, akin to unraveling a mystery novel with an unconventional plot twist. As we embark on this scholarly odyssey, we encourage our readers to adopt a lighthearted disposition, embracing this unorthodox exploration with open-mindedness and a hint of jest.
In the subsequent sections of this paper, we will discuss our methodology, present our empirical findings, and engage in a speculative discourse on the potential mechanisms that could engender such an improbable relationship. Brace yourselves for a journey that blends the solemnity of academic inquiry with the intrigue of uncovering an unexpected intersection between environmental factors and the realm of sports. Let us proceed with the gravity of scholarly rigor and the levity of inquisitive amusement as we unpick this most peculiar puzzle.

-------

Your response should start like this:

[[RESULTS]]



ChatGPT:

[[RESULTS]]

The statistical analysis of the data revealed a correlation coefficient (r) of 0.6471551 between air pollution levels in Decatur, Illinois, and the total points scored by the New England Patriots in the NFL season from 1980 to 2022. Additionally, the coefficient of determination (r-squared) was calculated to be 0.4188097, indicating that approximately 42% of the variability in the Patriots' total points can be explained by the fluctuations in air pollution levels in Decatur. The p-value of less than 0.01 suggests a strong significance, further bolstering the robustness of this surprising relationship.

In Figure 1, which depicts the scatterplot of the two variables, one can discern a discernible trend, underscoring the consistent nature of the correlation. However, as always, correlation does not imply causation, so we resist the temptation to jump to hasty conclusions. Yet, it is undeniably intriguing that the Patriots' scoring seems to mirror the ebb and flow of air pollution levels in Decatur over the years.

The strength of this correlation certainly gives one pause, prompting contemplation about the potential mechanisms at play. The idea that the Patriots' offensive prowess might somehow be influenced by the air quality over 1,000 miles away is both perplexing and, dare I say, comedic. It seems the Patriots' performance truly takes our breath away, albeit in a metaphorical sense.

This serendipitous link between environmental factors and athletic achievements adds an unexpected layer of whimsy to the otherwise solemn arena of scholarly research. As we continue to unravel this strange and stupendous association, we caution readers to approach our findings with a sprinkling of skepticism and a hearty dash of humor. After all, we wouldn't want to pollute the scholarly atmosphere with overly serious dispositions.

Stay tuned for the ensuing sections, where we will delve deeper into this wholesale peculiarity and speculate on the underlying dynamics that may account for this improbable link. Brace yourselves for a journey that marries the solidity of empirical inquiry with the enthrallment of deciphering an improbable conundrum.


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.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 Decatur, Illinois and Total Points scored by the New England Patriots in the NFL season. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. 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]]
A Breath of Fresh Air: Uncovering the Air Pollution versus Football Points Paradox

[[ABSTRACT]]
In this paper, we delve into an unconventional analysis of the relationship between air pollution levels in Decatur, Illinois, and the total points scored by the New England Patriots in the NFL season. Leveraging EPA data on air quality and Pro-football-reference statistics, our research team has unearthed a startling correlation between these seemingly disparate phenomena. The correlation coefficient of 0.6471551 and p < 0.01 from 1980 to 2022 indicates a significant relationship that warrants further inquiry.

While the causal mechanisms underlying this connection remain enshrouded in mystery, our findings raise intriguing implications for both environmental science and sports analytics. We urge readers to inhale this research with cautious skepticism and an air of whimsy, as we leave no stone unturned in unraveling this offbeat enigma. Through this study, we aim to inject a breath of fresh air into the dry sphere of scholarly research, sparking laughter and curiosity in equal measure.

[[LITERATURE REVIEW]]
The relationship between air pollution and its multifaceted impacts has been extensively documented in academic literature. Smith et al. (2015) underscore the detrimental health effects of prolonged exposure to particulate matter and airborne toxins, shedding light on the pernicious ramifications of environmental pollution on respiratory and cardiovascular well-being. Doe and Jones (2018) illuminate the intricate interplay between industrial emissions and ambient air quality, elucidating the nuances of pollution dispersion patterns in urban settings.
Furthermore, the influence of environmental factors on human performance and societal phenomena has been a subject of scholarly intrigue. In "Breathe: The New Science of a Lost Art" by James Nestor, the author expounds upon the profound impact of breathing and oxygen intake on physical prowess and cognitive function. Likewise, "The Air We Breathe" by Andrea Barrett delves into the multifaceted narratives intertwined with air quality, weaving a tapestry of human experiences shaped by atmospheric conditions.
On a more tangential note, fictional literature also offers allegorical insights into the intersection of environmental dynamics and unexpected outcomes. Works such as "The Air He Breathes" by Brittainy C. Cherry and "The Wind-Up Bird Chronicle" by Haruki Murakami beckon readers into surreal realms, where serendipitous connections and enigmatic relationships unfurl amidst atmospheric backdrops.
While our research journey involved delving into scholarly texts and scientific journals, it would be remiss not to acknowledge auxiliary sources that have inadvertently contributed to our intellectual inquiry. In the spirit of unearthing unconventional revelations, we confess to perusing the backs of shampoo bottles, seeking elusive epiphanies amidst the mundane musings on fragrant essences and hair care instructions.
In the ensuing sections, we will expound upon our empirical findings and unfurl the cloak of mystery veiling the improbable correlation between air pollution levels in Decatur, Illinois, and the total points accrued by the New England Patriots in the NFL season. Prepare to embark on a whimsical odyssey that traverses the frontiers of scholarly inquiry and whimsy, as we navigate the uncharted terrain of this improbable nexus.

[[RESULTS]]
The statistical analysis of the data revealed a correlation coefficient (r) of 0.6471551 between air pollution levels in Decatur, Illinois, and the total points scored by the New England Patriots in the NFL season from 1980 to 2022. Additionally, the coefficient of determination (r-squared) was calculated to be 0.4188097, indicating that approximately 42% of the variability in the Patriots' total points can be explained by the fluctuations in air pollution levels in Decatur. The p-value of less than 0.01 suggests a strong significance, further bolstering the robustness of this surprising relationship.
In Figure 1, which depicts the scatterplot of the two variables, one can discern a discernible trend, underscoring the consistent nature of the correlation. However, as always, correlation does not imply causation, so we resist the temptation to jump to hasty conclusions. Yet, it is undeniably intriguing that the Patriots' scoring seems to mirror the ebb and flow of air pollution levels in Decatur over the years.
The strength of this correlation certainly gives one pause, prompting contemplation about the potential mechanisms at play. The idea that the Patriots' offensive prowess might somehow be influenced by the air quality over 1,000 miles away is both perplexing and, dare I say, comedic. It seems the Patriots' performance truly takes our breath away, albeit in a metaphorical sense.
This serendipitous link between environmental factors and athletic achievements adds an unexpected layer of whimsy to the otherwise solemn arena of scholarly research. As we continue to unravel this strange and stupendous association, we caution readers to approach our findings with a sprinkling of skepticism and a hearty dash of humor. After all, we wouldn't want to pollute the scholarly atmosphere with overly serious dispositions.
Stay tuned for the ensuing sections, where we will delve deeper into this wholesale peculiarity and speculate on the underlying dynamics that may account for this improbable link. Brace yourselves for a journey that marries the solidity of empirical inquiry with the enthrallment of deciphering an improbable conundrum.

-------

Your response should start like this:

[[DISCUSSION]]



ChatGPT:

[[DISCUSSION]]

The discovery of a statistically significant correlation between air pollution levels in Decatur, Illinois, and the total points scored by the New England Patriots in the NFL season is a momentous anomaly that requires introspection and, dare I say, a healthy dose of amusement. This finding is no mere puff of smoke; rather, it represents a breath of fresh air in the realm of empirical inquiry, exuding a whimsical aura that piques the curiosity of researchers and sports enthusiasts alike.

Harking back to the tangential references in the literature review, we cannot overlook the allegorical insights woven into fiction that explore the enigmatic nexus between atmospheric elements and unforeseen outcomes. These tangential musings, though initially dismissed as whimsy, have in fact uncannily resonated with the findings of our empirical investigation. Perhaps, just perhaps, within the annals of literary figments lies a kernel of inadvertent truth, awaiting recognition in the scientific domain.

The robustness of the correlation coefficient, underscored by the significance and explanatory power of the relationship, reinforces and extends the prior research on the multifaceted impacts of environmental variables on human performance and societal phenomena. The work of Nestor on the profound impact of breathing and oxygen intake on physical prowess resonates humorously with this research, evoking the notion that the Patriots' offensive prowess truly takes one’s breath away, though not in a literal sense. Could it be that their scoring capacity is somehow buoyed by the proverbial winds of change blowing from Decatur?

While the exploration of an improbable correlation between air quality and sports may seem farcical at first blush, our study staunchly maintains an air of objectivity and scholarly rigor. The unexpected nature of this connection should not mask the underlying profundity that erects a sturdy pillar of scientific inquiry. As we continue to analyze the underlying mechanisms that may account for this improbable link, we implore fellow scholars to approach our findings with an inquisitive glint in their eyes and an appreciation for the whimsical intricacies of both nature and human endeavors. The quest to decode this paradox is no mere flight of fancy, but a voyage suffused with lighthearted curiosity and scholarly gravitas.

The ensuing sections will unfurl an expedition into the heart of this uncharted terrain, seeking to explicate the underlying dynamics that engender this captivating paradox. Join us as we embark on a journey that traverses the frontiers of scholarly inquiry and whimsy, transcending the mundane to unlock the hidden truths that underpin this improbable nexus between air pollution and football scores.


Model: gpt-3.5-turbo-1106
System prompt: You are a researcher writing an academic paper.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 Decatur, Illinois and Total Points scored by the New England Patriots in the NFL season. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. 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]]
A Breath of Fresh Air: Uncovering the Air Pollution versus Football Points Paradox

[[ABSTRACT]]
In this paper, we delve into an unconventional analysis of the relationship between air pollution levels in Decatur, Illinois, and the total points scored by the New England Patriots in the NFL season. Leveraging EPA data on air quality and Pro-football-reference statistics, our research team has unearthed a startling correlation between these seemingly disparate phenomena. The correlation coefficient of 0.6471551 and p < 0.01 from 1980 to 2022 indicates a significant relationship that warrants further inquiry.

While the causal mechanisms underlying this connection remain enshrouded in mystery, our findings raise intriguing implications for both environmental science and sports analytics. We urge readers to inhale this research with cautious skepticism and an air of whimsy, as we leave no stone unturned in unraveling this offbeat enigma. Through this study, we aim to inject a breath of fresh air into the dry sphere of scholarly research, sparking laughter and curiosity in equal measure.

[[INTRDUCTION]]
The relationship between air pollution and human health has long been a topic of concern and scholarly investigation. Decatur, Illinois, known for its industrial activity, has been a focal point for air quality studies. Conversely, in the realm of sports, the New England Patriots have garnered attention for their consistent performance in the NFL. These two seemingly unrelated domains converge in our research, as we embark on unraveling the enigmatic connection between air pollution in Decatur and the total points scored by the New England Patriots in the NFL season.
The city of Decatur, situated in Macon County, Illinois, has witnessed fluctuations in air quality over the years, primarily due to industrial emissions and vehicular activities. Meanwhile, the New England Patriots, based in the bustling metropolis of Foxborough, Massachusetts, have etched their name in NFL history with impressive offensive displays. Surprisingly, our preliminary analysis has uncovered a statistically significant correlation between air pollution levels in Decatur and the points amassed by the Patriots on the gridiron. The correlation coefficient of 0.6471551 and p < 0.01 from 1980 to 2022 has left our research team both captivated and perplexed.
This unexpected correlation beckons for a closer examination, delving into potential factors that might underpin such a peculiar association. While we remain cautious in drawing premature conclusions, we interpret these findings with a measure of playful curiosity, akin to unraveling a mystery novel with an unconventional plot twist. As we embark on this scholarly odyssey, we encourage our readers to adopt a lighthearted disposition, embracing this unorthodox exploration with open-mindedness and a hint of jest.
In the subsequent sections of this paper, we will discuss our methodology, present our empirical findings, and engage in a speculative discourse on the potential mechanisms that could engender such an improbable relationship. Brace yourselves for a journey that blends the solemnity of academic inquiry with the intrigue of uncovering an unexpected intersection between environmental factors and the realm of sports. Let us proceed with the gravity of scholarly rigor and the levity of inquisitive amusement as we unpick this most peculiar puzzle.

[[RESULTS]]
The statistical analysis of the data revealed a correlation coefficient (r) of 0.6471551 between air pollution levels in Decatur, Illinois, and the total points scored by the New England Patriots in the NFL season from 1980 to 2022. Additionally, the coefficient of determination (r-squared) was calculated to be 0.4188097, indicating that approximately 42% of the variability in the Patriots' total points can be explained by the fluctuations in air pollution levels in Decatur. The p-value of less than 0.01 suggests a strong significance, further bolstering the robustness of this surprising relationship.
In Figure 1, which depicts the scatterplot of the two variables, one can discern a discernible trend, underscoring the consistent nature of the correlation. However, as always, correlation does not imply causation, so we resist the temptation to jump to hasty conclusions. Yet, it is undeniably intriguing that the Patriots' scoring seems to mirror the ebb and flow of air pollution levels in Decatur over the years.
The strength of this correlation certainly gives one pause, prompting contemplation about the potential mechanisms at play. The idea that the Patriots' offensive prowess might somehow be influenced by the air quality over 1,000 miles away is both perplexing and, dare I say, comedic. It seems the Patriots' performance truly takes our breath away, albeit in a metaphorical sense.
This serendipitous link between environmental factors and athletic achievements adds an unexpected layer of whimsy to the otherwise solemn arena of scholarly research. As we continue to unravel this strange and stupendous association, we caution readers to approach our findings with a sprinkling of skepticism and a hearty dash of humor. After all, we wouldn't want to pollute the scholarly atmosphere with overly serious dispositions.
Stay tuned for the ensuing sections, where we will delve deeper into this wholesale peculiarity and speculate on the underlying dynamics that may account for this improbable link. Brace yourselves for a journey that marries the solidity of empirical inquiry with the enthrallment of deciphering an improbable conundrum.

-------

Your response should start like this:

[[CONCLUSION]]



ChatGPT:

[[CONCLUSION]]

In conclusion, our offbeat odyssey into the connection between air pollution levels in Decatur, Illinois, and the total points scored by the New England Patriots in the NFL season has yielded surprising revelations. The significant correlation coefficient and p-value below 0.01 have left us in a state of bemused astonishment. The whimsical notion that the Patriots' offensive prowess might be influenced by the air quality in a distant Midwestern city has undeniably enlivened our scholarly pursuits. However, we resist the urge to assert causality, as correlation does not equate to causation, and jumping to conclusions would be a flagrant foul. Nonetheless, the lighthearted nature of this correlation has injected an unexpected dose of mirth into the staid halls of empirical inquiry. We must admit, the idea that air pollution in Decatur has been secretly bolstering the Patriots' performance hovers in the realm of delightful absurdity. As we bid adieu to this peculiar correlation, we assert with earnest humor and a mirthful glint in our eyes that further research in this area is as needless as a football team's desire for more deflated balls.


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 A Breath of Fresh Air: Uncovering the Air Pollution versus Football Points Paradox. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Environmental Sports Science


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 A Breath of Fresh Air: Uncovering the Air Pollution versus Football Points Paradox. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Quirky Environmental 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 A Breath of Fresh Air: Uncovering the Air Pollution versus Football Points Paradox with an abstract of In this paper, we delve into an unconventional analysis of the relationship between air pollution levels in Decatur, Illinois, and the total points scored by the New England Patriots in the NFL season. Leveraging EPA data on air quality and Pro-football-reference statistics, our research team has unearthed a startling correlation between these seemingly disparate phenomena. The correlation coefficient of 0.6471551 and p < 0.01 from 1980 to 2022 indicates a significant relationship that warrants further inquiry.
While the causal mechanisms underlying this connection remain enshrouded in mystery, our findings raise intriguing implications for both environmental science and sports analytics. We urge readers to inhale this research with cautious skepticism and an air of whimsy, as we leave no stone unturned in unraveling this offbeat enigma. Through this study, we aim to inject a breath of fresh air into the dry sphere of scholarly research, sparking laughter and curiosity in equal measure.

ChatGPT:

air pollution, football points, correlation, EPA data, Decatur Illinois, New England Patriots, NFL season, environmental science, sports analytics

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



Random correlation

Discover a new correlation

View all correlations

View all research papers

Report an error


Data details

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

Total Points scored by the New England Patriots in the NFL season
Source: Pro-football-reference
See what else correlates with Total Points scored by the New England Patriots in the NFL season

Correlation r = 0.6471551 (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 = 0.4188097 (Coefficient of determination)
This means 41.9% of the change in the one variable (i.e., Total Points scored by the New England Patriots in the NFL season) is predictable based on the change in the other (i.e., Air pollution in Decatur, Illinois) over the 43 years from 1980 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 2.7E-6. 0.0000027374360935232476000000
The p-value is a measure of how probable it is that we would randomly find a result this extreme. More specifically the p-value is a measure of how probable it is that we would randomly find a result this extreme if we had only tested one pair of variables one time.

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

Who is going to stop me? p-value reporting doesn't require me to report how many calculations I had to go through in order to find a low p-value!
On average, you will find a correaltion as strong as 0.65 in 0.00027% of random cases. Said differently, if you correlated 365,305 random variables You don't actually need 365 thousand 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 42 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 42 because we have two variables measured over a period of 43 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.

[ 0.43, 0.79 ] 95% correlation confidence interval (using the Fisher z-transformation)
The confidence interval is an estimate the range of the value of the correlation coefficient, using the correlation itself as an input. The values are meant to be the low and high end of the correlation coefficient with 95% confidence.

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


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

Still, sometimes one of the variables has more years of data available than the other. This page only shows the overlapping years. To see all the years, click on "See what else correlates with..." link above.
1980198119821983198419851986198719881989199019911992199319941995199619971998199920002001200220032004200520062007200820092010201120122013201420152016201720182019202020212022
Air pollution in Decatur, Illinois (Bad air quality days)25.83338.974369.5522426.792520.797718.156426.099720.391126.592826.330519.667616.95417.22227.6056318.784517.630918.784516.483522.19182426.77628.02228.925625.753413.698629.86323.691549.58930.57854041.095941.095939.890719.72629.041124.931516.438418.457333.972628.571417.679628.808921.9178
Total Points scored by the New England Patriots in the NFL season (Points)441322143274362362412320250297181211205238351294418369337299276371381348437379385589410427518513557444468465441458436420326462364




Why this works

  1. 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.
  2. Lack of causal connection: There is probably Because these pages are automatically generated, it's possible that the two variables you are viewing are in fact causually related. I take steps to prevent the obvious ones from showing on the site (I don't let data about the weather in one city correlate with the weather in a neighboring city, for example), but sometimes they still pop up. If they are related, cool! You found a loophole.
    no direct connection between these variables, despite what the AI says above. This is exacerbated by the fact that I used "Years" as the base variable. Lots of things happen in a year that are not related to each other! Most studies would use something like "one person" in stead of "one year" to be the "thing" studied.
  3. Observations not independent: For many variables, sequential years are not independent of each other. If a population of people is continuously doing something every day, there is no reason to think they would suddenly change how they are doing that thing on January 1. A simple Personally I don't find any p-value calculation to be 'simple,' but you know what I mean.
    p-value calculation does not take this into account, so mathematically it appears less probable than it really is.




Try it yourself

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

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

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

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

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

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

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

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

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


# These modules make it easier to perform the calculation
import numpy as np
from scipy import stats

# We'll define a function that we can call to return the correlation calculations
def calculate_correlation(array1, array2):

    # Calculate Pearson correlation coefficient and p-value
    correlation, p_value = stats.pearsonr(array1, array2)

    # Calculate R-squared as the square of the correlation coefficient
    r_squared = correlation**2

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([25.8333,8.97436,9.55224,26.7925,20.7977,18.1564,26.0997,20.3911,26.5928,26.3305,19.6676,16.954,17.2222,7.60563,18.7845,17.6309,18.7845,16.4835,22.1918,24,26.776,28.022,28.9256,25.7534,13.6986,29.863,23.6915,49.589,30.5785,40,41.0959,41.0959,39.8907,19.726,29.0411,24.9315,16.4384,18.4573,33.9726,28.5714,17.6796,28.8089,21.9178,])
array_2 = np.array([441,322,143,274,362,362,412,320,250,297,181,211,205,238,351,294,418,369,337,299,276,371,381,348,437,379,385,589,410,427,518,513,557,444,468,465,441,458,436,420,326,462,364,])
array_1_name = "Air pollution in Decatur, Illinois"
array_2_name = "Total Points scored by the New England Patriots in the NFL season"

# 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. 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:


View another random correlation

How fun was this correlation?

Thanks for shining a light on this correlation!


Correlation ID: 3829 · Black Variable ID: 20535 · Red Variable ID: 330
about · subscribe · emailme@tylervigen.com · twitter

CC BY 4.0