Spurious correlation #4,309 · 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 Pocatello, Idaho and the second variable is Google searches for 'ice bath'. The chart goes from 2004 to 2023, 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 Pocatello, Idaho and the second variable is Google searches for 'ice bath'. The chart goes from 2004 to 2023, and the two variables track closely in value over that time.

Download png, svg

AI explanation

The increase in air pollution led to a higher demand for ice baths as the citizens of Pocatello sought refuge from the smog in their own homes. As the air quality decreased, the appeal of submerging oneself in a chilly tub of water became a more attractive way to escape the pollution and breathe in some metaphorical 'fresh' air.

^{Show image generation prompt} Model: dalle-3
Prompt: [Whimsical illustration] Create an image of a quaint neighborhood street in Pocatello, Idaho, with tiny houses nestled amongst towering mountains. A thick, colorful haze looms over the houses, illustrating the smog that fills the air. Residents are depicted outside their homes, filling bathtubs with ice, their expressions portraying a mix of determination and relief. The scene is whimsical, with exaggerated features and vivid colors, showcasing the unique and peculiar solution to the pollution problem. 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 Pocatello, Idaho and Google searches for 'ice bath'. 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: Glitch art Cute 2D animation Hyper-realistic Cute cartoon Whimsical illustration
ChatGPT: Whimsical illustration

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 Pocatello, Idaho and Google searches for 'ice bath', in the following situation: The increase in air pollution led to a higher demand for ice baths as the citizens of Pocatello sought refuge from the smog in their own homes. As the air quality decreased, the appeal of submerging oneself in a chilly tub of water became a more attractive way to escape the pollution and breathe in some metaphorical 'fresh' air.. Keep the description simple.
ChatGPT: In Pocatello, Idaho, a thick haze of smog hangs in the air, obscuring the usually clear view of the surrounding mountains. Amidst the pollution, residents hastily fill their bathtubs with ice, seeking solace from the gray atmosphere. The sound of running water and the clinking of ice cubes echo through the neighborhood as people turn to homemade ice baths to escape the air pollution outside.

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: [ Whimsical illustration ] and depicting this scene: In Pocatello, Idaho, a thick haze of smog hangs in the air, obscuring the usually clear view of the surrounding mountains. Amidst the pollution, residents hastily fill their bathtubs with ice, seeking solace from the gray atmosphere. The sound of running water and the clinking of ice cubes echo through the neighborhood as people turn to homemade ice baths to escape the air pollution outside. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: [Whimsical illustration] Create an image of a quaint neighborhood street in Pocatello, Idaho, with tiny houses nestled amongst towering mountains. A thick, colorful haze looms over the houses, illustrating the smog that fills the air. Residents are depicted outside their homes, filling bathtubs with ice, their expressions portraying a mix of determination and relief. The scene is whimsical, with exaggerated features and vivid colors, showcasing the unique and peculiar solution to the pollution problem.

*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 Pocatello, Idaho caused ice bath (Google searches for 'ice bath') to increase.

AI academic paper

(Because p < 0.01)

Choking on Smoke, Taking an Ice Bath and Doesn't Choke

The Journal of Eccentric Medical Case Reports

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 goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.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 Pocatello, Idaho and Google searches for 'ice bath'. Make lots of jokes, goofy observations, and puns.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Perhaps you also got inspiration from some board games that are vaugely related.

Here is the title and abstract of the paper:
[[TITLE]]
"Choking on Smoke, Taking an Ice Bath and Doesn't Choke"

[[ABSTRACT]]
Air pollution is no joke, but the correlation between air quality and the urge to take an ice bath in Pocatello, Idaho might just make you chuckle. In this study, we delved into the peculiar relationship between particulate matter, ozone, and the Google searches for 'ice bath'. With data sourced from the Environmental Protection Agency and Google Trends, we uncovered a startlingly strong link that's as clear as a breath of fresh air. Our findings reveal a correlation coefficient of 0.8945527, indicating a robust connection between deteriorating air quality and a surge in virtual quests for the chilling respite of an ice bath. The p-value, standing at less than 0.01, affirms the statistical significance of this unexpected yet intriguing relationship. While Pocatello's air quality may leave one breathless, it seems residents are turning to an icy solution. This research not only sheds light on the whimsical side of public behavior in response to environmental stressors but also underscores the need to cool off in the face of air pollution.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
As the old adage goes, "When the going gets tough, the tough take ice baths." Okay, maybe that's not quite how it goes, but in the context of air pollution in Pocatello, Idaho, it seems that the urge to plunge into an ice bath becomes increasingly prevalent. It's like a real-life game of "Chilling Adventures of Sabrina," except it's not witches seeking respite, but rather residents amidst a haze of smoke and particles.
Air pollution, a formidable foe to both human health and environmental well-being, has been the subject of countless studies and initiatives aimed at mitigating its effects. However, while many have focused on the respiratory and cardiovascular impacts of polluted air, few have ventured into the realm of seemingly unrelated behaviors, like the sudden craving for a bone-chilling ice bath.
In this study, we set out to explore the hitherto uncharted territory of the correlation between air pollution and Google searches for 'ice bath' in Pocatello, Idaho. While one might expect the populace to seek refuge indoors or perhaps indulge in meditation or yoga to combat the noxious air, it turns out that icy dips may be the unexpected coping mechanism of choice.
As researchers, we continually find ourselves confronted with unexpected turns and surprises in the data. Just when you think you've got it all figured out, along comes a correlation that's as eyebrow-raising as it is eyebrow-sweat-inducing in the face of polluted air. The intersection of science and society often presents us with these delightful head-scratchers, and it's in this spirit that we embarked on this peculiar investigation.
You might say we were "cool under pressure" as we dug into the data, endeavoring to unearth any chilling insights about the community's response to the less-than-pristine air quality. So, without further ado, let's plunge into the heart of this curious correlation and see if we can't "clear the air" about the connection between air pollution and the unyielding allure of an ice bath.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The relationship between air pollution and public behavior has been a topic of interest for researchers across various disciplines. Smith et al. (2018) studied the psychological effects of air pollution on urban populations, highlighting the impact on stress levels and coping mechanisms. Similarly, Doe and Jones (2016) explored the behavioral responses to environmental stressors, emphasizing the need for adaptive strategies in the face of deteriorating air quality.

In "Airborne Particles: A Toxic Tale" by Environmental Scientist, the authors delve into the composition and health effects of particulate matter, shedding light on its pervasive impact on human well-being. Furthermore, "The Ozone Conundrum" by Climatologist Expert provides a comprehensive overview of ozone pollution and its implications for public health.

Turning to fictional works, the stark imagery of polluted skies and the quest for unconventional solace can be found in Margaret Atwood's "Oryx and Crake," where the protagonist seeks refuge in icy waters amidst a dystopian backdrop of environmental degradation. Additionally, the popular board game "Smoggy City Escape" imparts a playful yet relevant narrative of air pollution and the whimsical measures individuals might resort to in seeking respite.

However, amid these scholarly and imaginative explorations, the connection between air pollution in Pocatello, Idaho, and the Google searches for 'ice bath' introduces a whimsical twist to the prevailing discourse. While the literature offers insights into the physiological and psychological impacts of air pollution, the unexpected correlation uncovered in this study adds a quirky dimension to the nuanced interplay between environmental stressors and human responses.

As we embark on this unconventional journey, it's essential to not only consider the serious implications of air pollution but also to embrace the lighthearted nature of human behavior in the face of adversity. With this in mind, we delve into the peculiar correlation with open minds and a readiness to uncover the unexpected quirks of communal coping mechanisms in the presence of polluted air.

Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.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 Pocatello, Idaho and Google searches for 'ice bath'. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and Google Trends .

For the time period 2004 to 2023, you found a correlation 0.8945527, r-squared of 0.8002245, 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]]
"Choking on Smoke, Taking an Ice Bath and Doesn't Choke"

[[ABSTRACT]]
Air pollution is no joke, but the correlation between air quality and the urge to take an ice bath in Pocatello, Idaho might just make you chuckle. In this study, we delved into the peculiar relationship between particulate matter, ozone, and the Google searches for 'ice bath'. With data sourced from the Environmental Protection Agency and Google Trends, we uncovered a startlingly strong link that's as clear as a breath of fresh air. Our findings reveal a correlation coefficient of 0.8945527, indicating a robust connection between deteriorating air quality and a surge in virtual quests for the chilling respite of an ice bath. The p-value, standing at less than 0.01, affirms the statistical significance of this unexpected yet intriguing relationship. While Pocatello's air quality may leave one breathless, it seems residents are turning to an icy solution. This research not only sheds light on the whimsical side of public behavior in response to environmental stressors but also underscores the need to cool off in the face of air pollution.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
As the old adage goes, "When the going gets tough, the tough take ice baths." Okay, maybe that's not quite how it goes, but in the context of air pollution in Pocatello, Idaho, it seems that the urge to plunge into an ice bath becomes increasingly prevalent. It's like a real-life game of "Chilling Adventures of Sabrina," except it's not witches seeking respite, but rather residents amidst a haze of smoke and particles.
Air pollution, a formidable foe to both human health and environmental well-being, has been the subject of countless studies and initiatives aimed at mitigating its effects. However, while many have focused on the respiratory and cardiovascular impacts of polluted air, few have ventured into the realm of seemingly unrelated behaviors, like the sudden craving for a bone-chilling ice bath.
In this study, we set out to explore the hitherto uncharted territory of the correlation between air pollution and Google searches for 'ice bath' in Pocatello, Idaho. While one might expect the populace to seek refuge indoors or perhaps indulge in meditation or yoga to combat the noxious air, it turns out that icy dips may be the unexpected coping mechanism of choice.
As researchers, we continually find ourselves confronted with unexpected turns and surprises in the data. Just when you think you've got it all figured out, along comes a correlation that's as eyebrow-raising as it is eyebrow-sweat-inducing in the face of polluted air. The intersection of science and society often presents us with these delightful head-scratchers, and it's in this spirit that we embarked on this peculiar investigation.
You might say we were "cool under pressure" as we dug into the data, endeavoring to unearth any chilling insights about the community's response to the less-than-pristine air quality. So, without further ado, let's plunge into the heart of this curious correlation and see if we can't "clear the air" about the connection between air pollution and the unyielding allure of an ice bath.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

The results of our investigation into the correlation between air pollution in Pocatello, Idaho and Google searches for 'ice bath' left us feeling like we were walking on thin ice—surprised, a little slippery, and definitely in need of some solid ground to stand on. But fear not, for we braved this frosty frontier armed with statistical tools and a healthy appreciation for the unexpected.

First and foremost, the correlation coefficient between air pollution and 'ice bath' searches clocked in at a frosty 0.8945527. To put it simply, there's a strong relationship between the two variables, much like the unbreakable bond between salt and snow on a winter's day. This coefficient indicates that as the air quality took a nosedive, the interest in ice baths soared to new heights, leaving us pondering the depths of human ingenuity in the face of environmental adversity.

The r-squared value of 0.8002245 added another layer of ice to the cake, signifying that a staggering 80% of the variation in 'ice bath' searches can be explained by changes in air pollution. It's as if the air pollution was whispering, "Hey there, feeling a bit choked up? Why not take a refreshing dip in some frosty water?" This high r-squared value hinted at a robust relationship, making it clear that this correlation was not just a fluke, but a frozen fact.

And as if that wasn't enough, the p-value graced us with its presence, twinkling like freshly fallen snow with a value of less than 0.01. This means that the connection we stumbled upon is no statistical fluke—it's as real as a snowdrift in December. In other words, it's highly unlikely that this correlation is due to random chance, affirming the significance of the relationship between air pollution and the desire to take an icy plunge.

To encapsulate these findings in a visually appealing manner, we present Figure 1—a scatterplot that visually captures the chill-inducing correlation between air pollution and the virtual quest for an 'ice bath'. As the air quality worsened, the frequency of 'ice bath' searches danced in tandem, painting a picture as mesmerizing as a snow globe in the midst of a blizzard.

In conclusion, our results provide compelling evidence of a remarkable link between air pollution and the appeal of taking a bracing, bone-chilling ice bath. While the icy allure of this correlation may seem like the tip of the iceberg, it serves as a reminder that in the frosty face of adversity, the human propensity for unexpected solutions can be as refreshing as an unexpected snow day.

Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.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 Pocatello, Idaho and Google searches for 'ice bath'. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Limit your response to 500 tokens.

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

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

[[TITLE]]
"Choking on Smoke, Taking an Ice Bath and Doesn't Choke"

[[ABSTRACT]]
Air pollution is no joke, but the correlation between air quality and the urge to take an ice bath in Pocatello, Idaho might just make you chuckle. In this study, we delved into the peculiar relationship between particulate matter, ozone, and the Google searches for 'ice bath'. With data sourced from the Environmental Protection Agency and Google Trends, we uncovered a startlingly strong link that's as clear as a breath of fresh air. Our findings reveal a correlation coefficient of 0.8945527, indicating a robust connection between deteriorating air quality and a surge in virtual quests for the chilling respite of an ice bath. The p-value, standing at less than 0.01, affirms the statistical significance of this unexpected yet intriguing relationship. While Pocatello's air quality may leave one breathless, it seems residents are turning to an icy solution. This research not only sheds light on the whimsical side of public behavior in response to environmental stressors but also underscores the need to cool off in the face of air pollution.

[[LITERATURE REVIEW]]
The relationship between air pollution and public behavior has been a topic of interest for researchers across various disciplines. Smith et al. (2018) studied the psychological effects of air pollution on urban populations, highlighting the impact on stress levels and coping mechanisms. Similarly, Doe and Jones (2016) explored the behavioral responses to environmental stressors, emphasizing the need for adaptive strategies in the face of deteriorating air quality.
In "Airborne Particles: A Toxic Tale" by Environmental Scientist, the authors delve into the composition and health effects of particulate matter, shedding light on its pervasive impact on human well-being. Furthermore, "The Ozone Conundrum" by Climatologist Expert provides a comprehensive overview of ozone pollution and its implications for public health.
Turning to fictional works, the stark imagery of polluted skies and the quest for unconventional solace can be found in Margaret Atwood's "Oryx and Crake," where the protagonist seeks refuge in icy waters amidst a dystopian backdrop of environmental degradation. Additionally, the popular board game "Smoggy City Escape" imparts a playful yet relevant narrative of air pollution and the whimsical measures individuals might resort to in seeking respite.
However, amid these scholarly and imaginative explorations, the connection between air pollution in Pocatello, Idaho, and the Google searches for 'ice bath' introduces a whimsical twist to the prevailing discourse. While the literature offers insights into the physiological and psychological impacts of air pollution, the unexpected correlation uncovered in this study adds a quirky dimension to the nuanced interplay between environmental stressors and human responses.
As we embark on this unconventional journey, it's essential to not only consider the serious implications of air pollution but also to embrace the lighthearted nature of human behavior in the face of adversity. With this in mind, we delve into the peculiar correlation with open minds and a readiness to uncover the unexpected quirks of communal coping mechanisms in the presence of polluted air.

[[RESULTS]]
The results of our investigation into the correlation between air pollution in Pocatello, Idaho and Google searches for 'ice bath' left us feeling like we were walking on thin ice—surprised, a little slippery, and definitely in need of some solid ground to stand on. But fear not, for we braved this frosty frontier armed with statistical tools and a healthy appreciation for the unexpected.
First and foremost, the correlation coefficient between air pollution and 'ice bath' searches clocked in at a frosty 0.8945527. To put it simply, there's a strong relationship between the two variables, much like the unbreakable bond between salt and snow on a winter's day. This coefficient indicates that as the air quality took a nosedive, the interest in ice baths soared to new heights, leaving us pondering the depths of human ingenuity in the face of environmental adversity.
The r-squared value of 0.8002245 added another layer of ice to the cake, signifying that a staggering 80% of the variation in 'ice bath' searches can be explained by changes in air pollution. It's as if the air pollution was whispering, "Hey there, feeling a bit choked up? Why not take a refreshing dip in some frosty water?" This high r-squared value hinted at a robust relationship, making it clear that this correlation was not just a fluke, but a frozen fact.
And as if that wasn't enough, the p-value graced us with its presence, twinkling like freshly fallen snow with a value of less than 0.01. This means that the connection we stumbled upon is no statistical fluke—it's as real as a snowdrift in December. In other words, it's highly unlikely that this correlation is due to random chance, affirming the significance of the relationship between air pollution and the desire to take an icy plunge.
To encapsulate these findings in a visually appealing manner, we present Figure 1—a scatterplot that visually captures the chill-inducing correlation between air pollution and the virtual quest for an 'ice bath'. As the air quality worsened, the frequency of 'ice bath' searches danced in tandem, painting a picture as mesmerizing as a snow globe in the midst of a blizzard.
In conclusion, our results provide compelling evidence of a remarkable link between air pollution and the appeal of taking a bracing, bone-chilling ice bath. While the icy allure of this correlation may seem like the tip of the iceberg, it serves as a reminder that in the frosty face of adversity, the human propensity for unexpected solutions can be as refreshing as an unexpected snow day.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

Now, onto the chilly chatter and frosty banter about our findings! The results of our study not only thawed out the curious conundrum of the correlation between air pollution and 'ice bath' searches but also revealed a captivating connection that packs a polar punch. Our findings align with previous research, skating smoothly alongside the existing literature on the influence of environmental stressors on human behavior.

Smith et al. (2018) emphasized the psychological effects of air pollution on coping mechanisms, and lo and behold, our study uncovers a tangible behavioral response—cue the surge in 'ice bath' queries. It seems that when the going gets tough, the tough get Googling for cold comfort! Similarly, Doe and Jones (2016) underscored the need for adaptive strategies in the face of deteriorating air quality, and our results serve as a frigid testament to the inventive ways individuals adapt to environmental stressors, proving that when life gives you polluted air, you Google ice baths.

Of course, we can't overlook the frosty fictional inspirations that led us to this unexpectedly icy endeavor. Margaret Atwood's "Oryx and Crake" painted a stark picture of seeking solace in icy waters, and here we are, unraveling the frosty fascination with simulated dips into frigid relief. As for "Smoggy City Escape," it turns out that while it's just a game, the quest for respite from pollution resonates with real-world behavior—albeit in a whimsically unexpected form. It seems that reality can be stranger than fiction, especially when it involves chilly dips in response to filthy air.

Our results underscore the serious implications of air pollution on public behavior while adding a dash of whimsy to the scholarly discourse. The robust correlation coefficient and the high r-squared value validate the statistical significance of this connection, painting a picture as clear as a pristine snowfield. While our findings may have initially seemed as improbable as a snowball in summer, they stand as a testament to the unexpected yet undeniable ties between air quality and the allure of a bone-chilling ice bath.

So, as we navigate this frosty frontier, let's not forget that amidst the serious discussions of environmental stressors, there's room for a lighthearted look at human responses. Our study not only reflects the tangible impact of air pollution but also highlights the whimsical nature of human behavior in the face of adversity. And who knows, our findings might just inspire an 'ice bath' trend in the scientific community—a chilling way to cool off after those heated debates on statistical analyses and variable manipulation!

Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.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 Pocatello, Idaho and Google searches for 'ice bath'. Make lots of jokes, goofy observations, and puns. Sneak in some jokes and clever puns about science, research, statistics, and the variables.

Limit your response to 300 tokens. At the very end, assert that no more research is needed in this area.

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
"Choking on Smoke, Taking an Ice Bath and Doesn't Choke"

[[ABSTRACT]]
Air pollution is no joke, but the correlation between air quality and the urge to take an ice bath in Pocatello, Idaho might just make you chuckle. In this study, we delved into the peculiar relationship between particulate matter, ozone, and the Google searches for 'ice bath'. With data sourced from the Environmental Protection Agency and Google Trends, we uncovered a startlingly strong link that's as clear as a breath of fresh air. Our findings reveal a correlation coefficient of 0.8945527, indicating a robust connection between deteriorating air quality and a surge in virtual quests for the chilling respite of an ice bath. The p-value, standing at less than 0.01, affirms the statistical significance of this unexpected yet intriguing relationship. While Pocatello's air quality may leave one breathless, it seems residents are turning to an icy solution. This research not only sheds light on the whimsical side of public behavior in response to environmental stressors but also underscores the need to cool off in the face of air pollution.

[[INTRDUCTION]]
As the old adage goes, "When the going gets tough, the tough take ice baths." Okay, maybe that's not quite how it goes, but in the context of air pollution in Pocatello, Idaho, it seems that the urge to plunge into an ice bath becomes increasingly prevalent. It's like a real-life game of "Chilling Adventures of Sabrina," except it's not witches seeking respite, but rather residents amidst a haze of smoke and particles.
Air pollution, a formidable foe to both human health and environmental well-being, has been the subject of countless studies and initiatives aimed at mitigating its effects. However, while many have focused on the respiratory and cardiovascular impacts of polluted air, few have ventured into the realm of seemingly unrelated behaviors, like the sudden craving for a bone-chilling ice bath.
In this study, we set out to explore the hitherto uncharted territory of the correlation between air pollution and Google searches for 'ice bath' in Pocatello, Idaho. While one might expect the populace to seek refuge indoors or perhaps indulge in meditation or yoga to combat the noxious air, it turns out that icy dips may be the unexpected coping mechanism of choice.
As researchers, we continually find ourselves confronted with unexpected turns and surprises in the data. Just when you think you've got it all figured out, along comes a correlation that's as eyebrow-raising as it is eyebrow-sweat-inducing in the face of polluted air. The intersection of science and society often presents us with these delightful head-scratchers, and it's in this spirit that we embarked on this peculiar investigation.
You might say we were "cool under pressure" as we dug into the data, endeavoring to unearth any chilling insights about the community's response to the less-than-pristine air quality. So, without further ado, let's plunge into the heart of this curious correlation and see if we can't "clear the air" about the connection between air pollution and the unyielding allure of an ice bath.

[[RESULTS]]
The results of our investigation into the correlation between air pollution in Pocatello, Idaho and Google searches for 'ice bath' left us feeling like we were walking on thin ice—surprised, a little slippery, and definitely in need of some solid ground to stand on. But fear not, for we braved this frosty frontier armed with statistical tools and a healthy appreciation for the unexpected.
First and foremost, the correlation coefficient between air pollution and 'ice bath' searches clocked in at a frosty 0.8945527. To put it simply, there's a strong relationship between the two variables, much like the unbreakable bond between salt and snow on a winter's day. This coefficient indicates that as the air quality took a nosedive, the interest in ice baths soared to new heights, leaving us pondering the depths of human ingenuity in the face of environmental adversity.
The r-squared value of 0.8002245 added another layer of ice to the cake, signifying that a staggering 80% of the variation in 'ice bath' searches can be explained by changes in air pollution. It's as if the air pollution was whispering, "Hey there, feeling a bit choked up? Why not take a refreshing dip in some frosty water?" This high r-squared value hinted at a robust relationship, making it clear that this correlation was not just a fluke, but a frozen fact.
And as if that wasn't enough, the p-value graced us with its presence, twinkling like freshly fallen snow with a value of less than 0.01. This means that the connection we stumbled upon is no statistical fluke—it's as real as a snowdrift in December. In other words, it's highly unlikely that this correlation is due to random chance, affirming the significance of the relationship between air pollution and the desire to take an icy plunge.
To encapsulate these findings in a visually appealing manner, we present Figure 1—a scatterplot that visually captures the chill-inducing correlation between air pollution and the virtual quest for an 'ice bath'. As the air quality worsened, the frequency of 'ice bath' searches danced in tandem, painting a picture as mesmerizing as a snow globe in the midst of a blizzard.
In conclusion, our results provide compelling evidence of a remarkable link between air pollution and the appeal of taking a bracing, bone-chilling ice bath. While the icy allure of this correlation may seem like the tip of the iceberg, it serves as a reminder that in the frosty face of adversity, the human propensity for unexpected solutions can be as refreshing as an unexpected snow day.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, it seems that the people of Pocatello, Idaho have found themselves in a frosty conundrum, with air pollution sparking a seemingly arctic attraction to ice baths. Our research has uncovered a correlation so strong, it's colder than a polar bear's toenails. The statistical evidence leaves little room for doubt – it's as clear as ice that when the air quality goes downhill, the search for a chilly soak goes uphill. This correlation is as solid as, well, ice – and it's no mere fluke, but a bona fide snowball effect.

We've unraveled a snowstorm of statistical significance, with a correlation coefficient so robust, you'd think it had been bench pressing glaciers. The r-squared value adds another layer of frost to the findings, suggesting that around 80% of the variation in 'ice bath' searches can be explained by changes in air pollution. It's like the air pollution is whispering, "Hey there, feeling a bit choked up? Why not take a refreshing dip in some frosty water?" And don't even get me started on the p-value – it's rarer than a snow leopard in the Sahara.

We present these findings with a mixture of bewilderment and delight, much like stumbling upon a yeti in a snowstorm. It's a reminder that in the face of environmental adversity, the human propensity for unexpected solutions can be as refreshing as an unexpected snow day. But fear not, we've cracked this icy case wide open, and it's time to let it go – no need for further research in this area. We've frozen this correlation in time, and it's as clear as an ice castle on a winter's day.

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 Choking on Smoke, Taking an Ice Bath and Doesn't Choke. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Eccentric Medical Case Reports

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 Choking on Smoke, Taking an Ice Bath and Doesn't Choke. Respond only with the name of a fictional organization.

ChatGPT:

The Society for Quirky Research 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 Choking on Smoke, Taking an Ice Bath and Doesn't Choke with an abstract of Air pollution is no joke, but the correlation between air quality and the urge to take an ice bath in Pocatello, Idaho might just make you chuckle. In this study, we delved into the peculiar relationship between particulate matter, ozone, and the Google searches for 'ice bath'. With data sourced from the Environmental Protection Agency and Google Trends, we uncovered a startlingly strong link that's as clear as a breath of fresh air. Our findings reveal a correlation coefficient of 0.8945527, indicating a robust connection between deteriorating air quality and a surge in virtual quests for the chilling respite of an ice bath. The p-value, standing at less than 0.01, affirms the statistical significance of this unexpected yet intriguing relationship. While Pocatello's air quality may leave one breathless, it seems residents are turning to an icy solution. This research not only sheds light on the whimsical side of public behavior in response to environmental stressors but also underscores the need to cool off in the face of air pollution.

ChatGPT:

air pollution, ice bath, Pocatello, Idaho, particulate matter, ozone, Environmental Protection Agency, Google Trends, correlation coefficient, statistical significance, public behavior, environmental stressors

*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 Pocatello, Idaho
Detailed data title: Percentage of days 'unhealthy' or worse air quality in Pocatello, ID
Source: Environmental Protection Agency
See what else correlates with Air pollution in Pocatello, Idaho

Google searches for 'ice bath'
Detailed data title: Relative volume of Google searches for 'ice bath' (Worldwide, without quotes)
Source: Google Trends
Additional Info: ^{See full details} Relative search volume (not absolute numbers)

See what else correlates with Google searches for 'ice bath'

Correlation r = 0.8945527 (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 = 0.8002245 (Coefficient of determination)
This means 80% of the change in the one variable (i.e., Google searches for 'ice bath') is predictable based on the change in the other (i.e., Air pollution in Pocatello, Idaho) over the 20 years from 2004 through 2023.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 1.04E-7.^Show 0.0000001038177530912370200000
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 0.89 in 1.04E-5% of random cases. Said differently, if you correlated 9,632,264 random variables^Note You don't actually need 9 million 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 19 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 19 because we have two variables measured over a period of 20 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.

[ 0.75, 0.96 ] 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.

	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
Air pollution in Pocatello, Idaho (Bad air quality days)	0.00547945	0.00547945	0	0	0.0027933	0	0	0	0.00819672	0	0	0.00273973	0	0.00821918	0.00547945	0	0.0110497	0.00273973	0	0.171271
Google searches for 'ice bath' (Rel. search volume)	8.91667	8.75	8.08333	9	9.66667	9.83333	12.25	13.6667	17.1667	17.5	19	19.9167	20.3333	20.9167	21.8333	23.5	23.75	27.0833	38.3333	86.2

Why this works

Data dredging: I have 25,153 variables in my database. I compare all these variables against each other to find ones that randomly match up. That's 632,673,409 correlation calculations! This is called “data dredging.” Instead of starting with a hypothesis and testing it, I instead abused the data to see what correlations shake out. It’s a dangerous way to go about analysis, because any sufficiently large dataset will yield strong correlations completely at random.
Lack of causal connection: There is probably^Note Because these pages are automatically generated, it's possible that the two variables you are viewing are in fact causually related. I take steps to prevent the obvious ones from showing on the site (I don't let data about the weather in one city correlate with the weather in a neighboring city, for example), but sometimes they still pop up. If they are related, cool! You found a loophole.
no direct connection between these variables, despite what the AI says above. This is exacerbated by the fact that I used "Years" as the base variable. Lots of things happen in a year that are not related to each other! Most studies would use something like "one person" in stead of "one year" to be the "thing" studied.
Observations not independent: For many variables, sequential years are not independent of each other. If a population of people is continuously doing something every day, there is no reason to think they would suddenly change how they are doing that thing on January 1. A simple^Note Personally I don't find any p-value calculation to be 'simple,' but you know what I mean.
p-value calculation does not take this into account, so mathematically it appears less probable than it really is.

Try it yourself

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

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

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

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

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

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

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

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

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

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

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

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

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

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([0.00547945,0.00547945,0,0,0.0027933,0,0,0,0.00819672,0,0,0.00273973,0,0.00821918,0.00547945,0,0.0110497,0.00273973,0,0.171271,])
array_2 = np.array([8.91667,8.75,8.08333,9,9.66667,9.83333,12.25,13.6667,17.1667,17.5,19,19.9167,20.3333,20.9167,21.8333,23.5,23.75,27.0833,38.3333,86.2,])
array_1_name = "Air pollution in Pocatello, Idaho"
array_2_name = "Google searches for 'ice bath'"

# 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 Pocatello, Idaho
Line chart for only Google searches for 'ice bath'
AI-generated correlation image
The spurious research paper: Choking on Smoke, Taking an Ice Bath and Doesn't Choke

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Correlation ID: 4309 · Black Variable ID: 22029 · Red Variable ID: 1408


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