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Spurious correlation #1,091 · View random

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air quality in Crescent City, California and the second variable is NCAA Men's Skiing champion's points.  The chart goes from 1988 to 2022, and the two variables track closely in value over that time. Small Image
Download png
, svg

AI explanation

As air quality improved, local squirrels became more efficient at sharpening their teeth on ski poles, leading to a boost in the performance of the ski champions. The cleaner air also inspired the athletes to do more celebratory backflips and snow angels, adding to their overall points.

Model: dalle-3
Prompt: Create an image that looks like it is a scene from 'Star Wars', depicting the intersection of a small, picturesque town and a nearby ski resort. In the foreground, a small, charming town exudes an old-world charm with quaint cottages and cobblestone streets. The sky is tinted with elements of a distant galaxy, hinting at the presence of a larger universe beyond. Meanwhile, in the background, a towering ski resort serves as a hub of activity, with skiers gearing up for their race. The entire scene is bathed in a warm glow, and the aroma of sizzling barbecue smoke wafts from the town's barbecue competition, mingling with the crisp mountain air. At the center of the composition, the NCAA Men's Skiing champion, flanked by fellow skiers, stands before a sumptuous breakfast spread. The champion is eyeing a plate of crispy bacon with intent, contemplating its potential to fuel his upcoming race. 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 situation described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here is a situation: "Smoke from local barbecue competition led to NCAA Men's Skiing champion's strategic bacon intake, affecting performance". Given that situation, which of the following image descriptions seems most appropriate? Pick the one that seems to be related to one of the variables at hand and the tone of the explanation. Please respond with only one of the following potential descriptions: Cyberpunk An image that looks like it is a scene from 'Star Wars' Psychedelic Psychedelic Surrealism
ChatGPT: An image that looks like it is a scene from 'Star Wars'

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated and the explanation described. Do not reference graphs or charts; describe physical objects.
User prompt: Please describe a visual scene that depicts the following situation. Keep the description simple. "Smoke from local barbecue competition led to NCAA Men's Skiing champion's strategic bacon intake, affecting performance"
ChatGPT: In a small, picturesque town, the aroma of sizzling barbecue smoke fills the air as a local barbecue competition gets underway. Meanwhile, at the nearby ski resort, a group of skiers, including the NCAA Men's Skiing champion, enjoy a hearty breakfast before their race. Among the spread of delicious breakfast foods, a plate of crispy bacon catches the champion's eye, prompting him to strategically load up on it to fuel his performance.

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: [ An image that looks like it is a scene from 'Star Wars' ] and depicting this scene: In a small, picturesque town, the aroma of sizzling barbecue smoke fills the air as a local barbecue competition gets underway. Meanwhile, at the nearby ski resort, a group of skiers, including the NCAA Men's Skiing champion, enjoy a hearty breakfast before their race. Among the spread of delicious breakfast foods, a plate of crispy bacon catches the champion's eye, prompting him to strategically load up on it to fuel his performance. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Create an image that looks like it is a scene from 'Star Wars', depicting the intersection of a small, picturesque town and a nearby ski resort. In the foreground, a small, charming town exudes an old-world charm with quaint cottages and cobblestone streets. The sky is tinted with elements of a distant galaxy, hinting at the presence of a larger universe beyond. Meanwhile, in the background, a towering ski resort serves as a hub of activity, with skiers gearing up for their race. The entire scene is bathed in a warm glow, and the aroma of sizzling barbecue smoke wafts from the town's barbecue competition, mingling with the crisp mountain air. At the center of the composition, the NCAA Men's Skiing champion, flanked by fellow skiers, stands before a sumptuous breakfast spread. The champion is eyeing a plate of crispy bacon with intent, contemplating its potential to fuel his upcoming race.

*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 quality in Crescent City, California positively influenced NCAA Men's Skiing champion's points.

AI academic paper

(Because p < 0.01)
Sloping Down: The Downhill Connection between Air Quality in Crescent City, California and NCAA Men's Skiing Champion's Points

The Journal of Environmental Dynamics and Extreme Sports Sociology

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 witty academic researcher. Your writing sounds like it belongs in a statistics journal.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 quality in Crescent City, California and NCAA Men's Skiing champion's points. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

Make the title seem clever.

Your research team used data from Environmental Protection Agency and NCAA to assess this nagging question. You found a correlation coefficient of 0.8120015 and p < 0.01 for 1988 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]]
"Sloping Down: The Downhill Connection between Air Quality in Crescent City, California and NCAA Men's Skiing Champion's Points"

[[ABSTRACT]]
In this study, we embarked on a ski-entific quest to explore the unexpected relationship between air quality in Crescent City, California and the performance of NCAA Men's Skiing champions. Utilizing data from the Environmental Protection Agency to gauge air quality and NCAA records to tally the skiing champion's points, we set out to uncover if there is a breath-taking correlation between these seemingly unrelated factors. Our efforts led to the unearthing of a correlation coefficient of 0.8120015 and a p-value less than 0.01 for the years spanning from 1988 to 2022.

Our findings reveal an intriguing relationship that might just leave you breathless—much like skiing down a treacherous slope. It appears that the air quality in Crescent City may exert an unexpected influence on the performance of NCAA Men's Skiing champions. We speculate that perhaps the fresh, crisp air may propel these athletes to new heights, or perhaps a dip in air quality may lead to a slope in their points.

Furthermore, our results beg the question: could the high-ozone days in Crescent City be a breath of fresh air for the skiing champions, or do they find themselves breathless in the low-quality air? These tongue-in-cheek musings aside, our research sheds light on an unexpected correlation and paves the way for further investigation into the curious alliance between air quality and skiing prowess.


Model: gpt-3.5-turbo-1106
System prompt: You are a witty academic researcher. Your writing sounds like it belongs in a statistics journal.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 quality in Crescent City, California and NCAA Men's Skiing champion's points. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Here is the title and abstract of the paper:
[[TITLE]]
"Sloping Down: The Downhill Connection between Air Quality in Crescent City, California and NCAA Men's Skiing Champion's Points"

[[ABSTRACT]]
In this study, we embarked on a ski-entific quest to explore the unexpected relationship between air quality in Crescent City, California and the performance of NCAA Men's Skiing champions. Utilizing data from the Environmental Protection Agency to gauge air quality and NCAA records to tally the skiing champion's points, we set out to uncover if there is a breath-taking correlation between these seemingly unrelated factors. Our efforts led to the unearthing of a correlation coefficient of 0.8120015 and a p-value less than 0.01 for the years spanning from 1988 to 2022.

Our findings reveal an intriguing relationship that might just leave you breathless—much like skiing down a treacherous slope. It appears that the air quality in Crescent City may exert an unexpected influence on the performance of NCAA Men's Skiing champions. We speculate that perhaps the fresh, crisp air may propel these athletes to new heights, or perhaps a dip in air quality may lead to a slope in their points.

Furthermore, our results beg the question: could the high-ozone days in Crescent City be a breath of fresh air for the skiing champions, or do they find themselves breathless in the low-quality air? These tongue-in-cheek musings aside, our research sheds light on an unexpected correlation and paves the way for further investigation into the curious alliance between air quality and skiing prowess.

-------

Your response should start like this:

[[INTRODUCTION]]



ChatGPT:
[[INTRODUCTION]]

The intersection of environmental factors and athletic performance has long been an area of interest in the realm of sports science. While much attention has been paid to the impact of altitude, temperature, and humidity on athletic outcomes, the relationship between air quality and athletic performance remains relatively unexplored. In this study, we sought to uncover the correlation between the air quality in Crescent City, California, and the points accrued by NCAA Men's Skiing champions. This off-piste investigation offers an exciting opportunity to traverse uncharted territory in the realm of sports science and environmental research.

Dad Joke: What does a skier say when they finally reach the bottom of the mountain? "I've peaked."

Our study took advantage of the vast and meticulously collected data on air quality maintained by the Environmental Protection Agency. Utilizing air quality index readings, we were able to gauge the concentration of pollutants such as ozone, particulate matter, and carbon monoxide in the atmospheric milieu of Crescent City. On the other hand, NCAA Men's Skiing championship records provided a comprehensive archive of the points accrued by skiing champions over the years—a treasure trove for our analytical pursuits.

Dad Joke: Why do skiers make terrible spies? Because they're always going downhill.


Model: gpt-3.5-turbo-1106
System prompt: You are a witty academic researcher. Your writing sounds like it belongs in a statistics journal.You draft a literature review section of an academic research paper, that starts out dry for the first few sentences but then becomes hilarious and goofy.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up a literature review section of an academic research paper presenting the findings of the connection between Air quality in Crescent City, California and NCAA Men's Skiing champion's points. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then name some movies that you watched that are tangentially related to the topic.

Here is the title and abstract of the paper:
[[TITLE]]
"Sloping Down: The Downhill Connection between Air Quality in Crescent City, California and NCAA Men's Skiing Champion's Points"

[[ABSTRACT]]
In this study, we embarked on a ski-entific quest to explore the unexpected relationship between air quality in Crescent City, California and the performance of NCAA Men's Skiing champions. Utilizing data from the Environmental Protection Agency to gauge air quality and NCAA records to tally the skiing champion's points, we set out to uncover if there is a breath-taking correlation between these seemingly unrelated factors. Our efforts led to the unearthing of a correlation coefficient of 0.8120015 and a p-value less than 0.01 for the years spanning from 1988 to 2022.

Our findings reveal an intriguing relationship that might just leave you breathless—much like skiing down a treacherous slope. It appears that the air quality in Crescent City may exert an unexpected influence on the performance of NCAA Men's Skiing champions. We speculate that perhaps the fresh, crisp air may propel these athletes to new heights, or perhaps a dip in air quality may lead to a slope in their points.

Furthermore, our results beg the question: could the high-ozone days in Crescent City be a breath of fresh air for the skiing champions, or do they find themselves breathless in the low-quality air? These tongue-in-cheek musings aside, our research sheds light on an unexpected correlation and paves the way for further investigation into the curious alliance between air quality and skiing prowess.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The intersection of environmental factors and athletic performance has long been an area of interest in the realm of sports science. While much attention has been paid to the impact of altitude, temperature, and humidity on athletic outcomes, the relationship between air quality and athletic performance remains relatively unexplored. In this study, we sought to uncover the correlation between the air quality in Crescent City, California, and the points accrued by NCAA Men's Skiing champions. This off-piste investigation offers an exciting opportunity to traverse uncharted territory in the realm of sports science and environmental research.
Dad Joke: What does a skier say when they finally reach the bottom of the mountain? "I've peaked."
Our study took advantage of the vast and meticulously collected data on air quality maintained by the Environmental Protection Agency. Utilizing air quality index readings, we were able to gauge the concentration of pollutants such as ozone, particulate matter, and carbon monoxide in the atmospheric milieu of Crescent City. On the other hand, NCAA Men's Skiing championship records provided a comprehensive archive of the points accrued by skiing champions over the years—a treasure trove for our analytical pursuits.
Dad Joke: Why do skiers make terrible spies? Because they're always going downhill.

-------

Your response should start like this:

[[LITERATURE REVIEW]]



ChatGPT:
[[LITERATURE REVIEW]]

Numerous studies have explored the impact of environmental factors on athletic performance, with a focus on altitude, temperature, and humidity. However, the relationship between air quality and athletic prowess remains an understudied area. In "Smith et al.'s investigation," the authors find a compelling correlation between air quality in urban areas and aerobic endurance among athletes, shedding light on the potential influence of air pollution on athletic performance.

Dad Joke: Why don't skiers ever tell secrets while on the chairlift? Because they might blurt out things that are quite slippery.

Moving forward, "Doe and Jones' research" delves into the effects of air quality on cognitive function and reaction times, raising the intriguing possibility that air quality may also impact physical performance in athletes. This line of inquiry paves the way for our investigation into the association between air quality in Crescent City, California, and the performance of NCAA Men's Skiing champions.

In addition, "Book's analysis of environmental factors in sports performance" offers valuable insights into the role of air quality in determining athletic outcomes, providing a theoretical framework for our study.

Dad Joke: What did the ski instructor say to the lawnmower? "Cut it out!"

Extending our purview beyond scholarly articles, the works of "Fresh Air and Athletic Achievement" by Lungs Galore and "The Thin Air Advantage" by Breezy Breaths disgorge the philosophical, yet zephyr-like, musings on the interplay between air quality and athletic excellence. These texts, while not grounded in rigorous empirical evidence, offer a gust of inspiration for our investigation.

Furthermore, works of fiction such as "Snowy Peaks and Clear Skies" by Cliff Hanger and "Alpine Ambitions" by Slope Soarer skulk in the periphery of relevant literature, invoking the thrill of skiing and the allure of pristine air in the mountainous terrain. While not academic in nature, these narratives impart a sense of whimsy to our serious inquiry.

Dad Joke: What do you call a group of skiers waiting in line for the ski lift? A ski queue!

Additionally, cinematic references to the world of skiing, such as "Downhill Dreams" and "Slope Seekers," punctuate the cultural backdrop against which our research unfolds. While not directly related to air quality and skiing performance, these movies evoke the adrenaline rush and competitive fervor intrinsic to the sport of skiing.

In sum, the literature encompasses a wide spectrum of scholarly, fictional, and cinematic works, all of which converge to frame our investigation into the unexpected relationship between air quality in Crescent City, California, and the performance of NCAA Men's Skiing champions.



Model: gpt-3.5-turbo-1106
System prompt: You are a witty academic researcher. Your writing sounds like it belongs in a statistics journal.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 quality in Crescent City, California and NCAA Men's Skiing champion's points. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Your research team collected data from all across the internet, but mostly just used information from Environmental Protection Agency and NCAA . You used data from 1988 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]]
"Sloping Down: The Downhill Connection between Air Quality in Crescent City, California and NCAA Men's Skiing Champion's Points"

[[ABSTRACT]]
In this study, we embarked on a ski-entific quest to explore the unexpected relationship between air quality in Crescent City, California and the performance of NCAA Men's Skiing champions. Utilizing data from the Environmental Protection Agency to gauge air quality and NCAA records to tally the skiing champion's points, we set out to uncover if there is a breath-taking correlation between these seemingly unrelated factors. Our efforts led to the unearthing of a correlation coefficient of 0.8120015 and a p-value less than 0.01 for the years spanning from 1988 to 2022.

Our findings reveal an intriguing relationship that might just leave you breathless—much like skiing down a treacherous slope. It appears that the air quality in Crescent City may exert an unexpected influence on the performance of NCAA Men's Skiing champions. We speculate that perhaps the fresh, crisp air may propel these athletes to new heights, or perhaps a dip in air quality may lead to a slope in their points.

Furthermore, our results beg the question: could the high-ozone days in Crescent City be a breath of fresh air for the skiing champions, or do they find themselves breathless in the low-quality air? These tongue-in-cheek musings aside, our research sheds light on an unexpected correlation and paves the way for further investigation into the curious alliance between air quality and skiing prowess.

[[INTRODUCTION]]
The intersection of environmental factors and athletic performance has long been an area of interest in the realm of sports science. While much attention has been paid to the impact of altitude, temperature, and humidity on athletic outcomes, the relationship between air quality and athletic performance remains relatively unexplored. In this study, we sought to uncover the correlation between the air quality in Crescent City, California, and the points accrued by NCAA Men's Skiing champions. This off-piste investigation offers an exciting opportunity to traverse uncharted territory in the realm of sports science and environmental research.
Dad Joke: What does a skier say when they finally reach the bottom of the mountain? "I've peaked."
Our study took advantage of the vast and meticulously collected data on air quality maintained by the Environmental Protection Agency. Utilizing air quality index readings, we were able to gauge the concentration of pollutants such as ozone, particulate matter, and carbon monoxide in the atmospheric milieu of Crescent City. On the other hand, NCAA Men's Skiing championship records provided a comprehensive archive of the points accrued by skiing champions over the years—a treasure trove for our analytical pursuits.
Dad Joke: Why do skiers make terrible spies? Because they're always going downhill.

-------

Your response should start like this:

[[METHODOLOGY]]



ChatGPT:

[[METHODOLOGY]]

Our research team embarked on this lofty endeavor by collating data from the Environmental Protection Agency's Air Quality System and the NCAA records for Men's Skiing championships. We gathered air quality index readings from Crescent City, California, covering the years from 1988 to 2022, encompassing a spectrum of atmospheric conditions from the high peaks to the low valleys. Similarly, we assembled the points accumulated by the skiing champions, showcasing their remarkable feats of athleticism on the powdery slopes of the NCAA circuit.

To enhance the robustness of our analysis, we employed a multi-step, snowball sampling technique to ensure that our data collection process covered a wide array of atmospheric conditions and skiing performances. Through careful sifting and sorting of the data like an Alpine skier maneuvering through gates, we aimed to capture the nuanced interplay between air quality and skiing prowess.

Dad Joke: How do you become a better skier? Just chill, it'll all snowball from there.

Having amassed our data, we performed a series of statistical analyses to unveil the potential association between air quality in Crescent City and the performance of NCAA Men's Skiing champions. Employing a series of regression models, we sought to tease out the intricate relationship between various pollutants and the skiing champions' points, akin to navigating the twists and turns of a slalom course.

Furthermore, we utilized sophisticated time-series analysis techniques to decipher the temporal patterns underlying air quality fluctuations and skiing champion performances. This involved unraveling the seasonal variations in air quality and their potential impact on the skiing results, akin to decoding the subtle shifts in snow conditions that can affect a skier's trajectory down the mountain.

Dad Joke: What kind of exercise do skiers do in the summer? Downhill mountain biking—because every season is ski-son.

Lastly, we conducted a sensitivity analysis to ensure the robustness of our findings, accounting for various confounding factors such as weather conditions, altitude, and the skiers' training regimens. This allowed us to gauge the specific influence of air quality on skiing performance, shedding light on whether these athletes truly take a breath of fresh air or find themselves navigating a downhill battle in the face of air pollution.

In summary, our methodology encapsulated a comprehensive approach to unveil the hidden connections between air quality in Crescent City, California, and the remarkable performances of NCAA Men's Skiing champions. Through the careful assembly and analysis of data, we sought to carve a path through the snowy landscape of sports science and environmental research, ultimately shedding light on this unexpected, yet captivating, correlation.


Model: gpt-3.5-turbo-1106
System prompt: You are a witty academic researcher. Your writing sounds like it belongs in a statistics journal.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 quality in Crescent City, California and NCAA Men's Skiing champion's points. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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

For the time period 1988 to 2022, you found a correlation 0.8120015, r-squared of 0.6593464, 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]]
"Sloping Down: The Downhill Connection between Air Quality in Crescent City, California and NCAA Men's Skiing Champion's Points"

[[ABSTRACT]]
In this study, we embarked on a ski-entific quest to explore the unexpected relationship between air quality in Crescent City, California and the performance of NCAA Men's Skiing champions. Utilizing data from the Environmental Protection Agency to gauge air quality and NCAA records to tally the skiing champion's points, we set out to uncover if there is a breath-taking correlation between these seemingly unrelated factors. Our efforts led to the unearthing of a correlation coefficient of 0.8120015 and a p-value less than 0.01 for the years spanning from 1988 to 2022.

Our findings reveal an intriguing relationship that might just leave you breathless—much like skiing down a treacherous slope. It appears that the air quality in Crescent City may exert an unexpected influence on the performance of NCAA Men's Skiing champions. We speculate that perhaps the fresh, crisp air may propel these athletes to new heights, or perhaps a dip in air quality may lead to a slope in their points.

Furthermore, our results beg the question: could the high-ozone days in Crescent City be a breath of fresh air for the skiing champions, or do they find themselves breathless in the low-quality air? These tongue-in-cheek musings aside, our research sheds light on an unexpected correlation and paves the way for further investigation into the curious alliance between air quality and skiing prowess.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The intersection of environmental factors and athletic performance has long been an area of interest in the realm of sports science. While much attention has been paid to the impact of altitude, temperature, and humidity on athletic outcomes, the relationship between air quality and athletic performance remains relatively unexplored. In this study, we sought to uncover the correlation between the air quality in Crescent City, California, and the points accrued by NCAA Men's Skiing champions. This off-piste investigation offers an exciting opportunity to traverse uncharted territory in the realm of sports science and environmental research.
Dad Joke: What does a skier say when they finally reach the bottom of the mountain? "I've peaked."
Our study took advantage of the vast and meticulously collected data on air quality maintained by the Environmental Protection Agency. Utilizing air quality index readings, we were able to gauge the concentration of pollutants such as ozone, particulate matter, and carbon monoxide in the atmospheric milieu of Crescent City. On the other hand, NCAA Men's Skiing championship records provided a comprehensive archive of the points accrued by skiing champions over the years—a treasure trove for our analytical pursuits.
Dad Joke: Why do skiers make terrible spies? Because they're always going downhill.

-------

Your response should start like this:

[[RESULTS]]



ChatGPT:

[[RESULTS]]

The statistical analysis of the relationship between air quality in Crescent City, California and the performance of NCAA Men's Skiing champions resulted in a noteworthy correlation coefficient of 0.8120015. This finding indicates a strong positive linear relationship between the two variables, suggesting that as air quality improves, the points accrued by skiing champions also tend to increase. It seems that cleaner air may indeed be a breath of fresh air for these athletes, both figuratively and literally.

The coefficient of determination (r-squared) was calculated to be 0.6593464, indicating that approximately 65.93% of the variability in the skiing champions' points can be explained by the variation in air quality. This substantial proportion further underscores the influential role of air quality in shaping the performance of these elite athletes, adding an unexpected twist to the typical factors considered in athletic success.

Of course, as any statistician worth their salt knows, a low p-value is the cherry on top of the correlation sundae. In our analysis, the p-value was found to be less than 0.01, providing strong evidence against the null hypothesis and affirming the presence of a significant relationship between air quality and NCAA Men's Skiing champion's points. This result underscores the robustness of the observed correlation and supports the notion that air quality may indeed play a pivotal role in the performance of skiing champions.

Figure 1 depicts the scatterplot illustrating the striking correlation between air quality and NCAA Men's Skiing champion's points. As air quality improves, there is a clear trend of an increase in skiing champion's points, affirming the positive association uncovered through our analysis.

In conclusion, our study has unearthed a slope-tacular relationship, demonstrating the unexpected influence of air quality in Crescent City, California on the performance of NCAA Men's Skiing champions. These findings not only add a breath of fresh air to the field of sports science but also open up new avenues for exploration into the interplay between environmental factors and athletic success.


Model: gpt-3.5-turbo-1106
System prompt: You are a witty academic researcher. Your writing sounds like it belongs in a statistics journal.You draft the discussion section of an academic research paper.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up the discussion section of an academic research paper presenting the findings of the connection between Air quality in Crescent City, California and NCAA Men's Skiing champion's points. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Limit your response to 500 tokens.

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

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

[[TITLE]]
"Sloping Down: The Downhill Connection between Air Quality in Crescent City, California and NCAA Men's Skiing Champion's Points"

[[ABSTRACT]]
In this study, we embarked on a ski-entific quest to explore the unexpected relationship between air quality in Crescent City, California and the performance of NCAA Men's Skiing champions. Utilizing data from the Environmental Protection Agency to gauge air quality and NCAA records to tally the skiing champion's points, we set out to uncover if there is a breath-taking correlation between these seemingly unrelated factors. Our efforts led to the unearthing of a correlation coefficient of 0.8120015 and a p-value less than 0.01 for the years spanning from 1988 to 2022.

Our findings reveal an intriguing relationship that might just leave you breathless—much like skiing down a treacherous slope. It appears that the air quality in Crescent City may exert an unexpected influence on the performance of NCAA Men's Skiing champions. We speculate that perhaps the fresh, crisp air may propel these athletes to new heights, or perhaps a dip in air quality may lead to a slope in their points.

Furthermore, our results beg the question: could the high-ozone days in Crescent City be a breath of fresh air for the skiing champions, or do they find themselves breathless in the low-quality air? These tongue-in-cheek musings aside, our research sheds light on an unexpected correlation and paves the way for further investigation into the curious alliance between air quality and skiing prowess.

[[LITERATURE REVIEW]]
Numerous studies have explored the impact of environmental factors on athletic performance, with a focus on altitude, temperature, and humidity. However, the relationship between air quality and athletic prowess remains an understudied area. In "Smith et al.'s investigation," the authors find a compelling correlation between air quality in urban areas and aerobic endurance among athletes, shedding light on the potential influence of air pollution on athletic performance.
Dad Joke: Why don't skiers ever tell secrets while on the chairlift? Because they might blurt out things that are quite slippery.
Moving forward, "Doe and Jones' research" delves into the effects of air quality on cognitive function and reaction times, raising the intriguing possibility that air quality may also impact physical performance in athletes. This line of inquiry paves the way for our investigation into the association between air quality in Crescent City, California, and the performance of NCAA Men's Skiing champions.
In addition, "Book's analysis of environmental factors in sports performance" offers valuable insights into the role of air quality in determining athletic outcomes, providing a theoretical framework for our study.
Dad Joke: What did the ski instructor say to the lawnmower? "Cut it out!"
Extending our purview beyond scholarly articles, the works of "Fresh Air and Athletic Achievement" by Lungs Galore and "The Thin Air Advantage" by Breezy Breaths disgorge the philosophical, yet zephyr-like, musings on the interplay between air quality and athletic excellence. These texts, while not grounded in rigorous empirical evidence, offer a gust of inspiration for our investigation.
Furthermore, works of fiction such as "Snowy Peaks and Clear Skies" by Cliff Hanger and "Alpine Ambitions" by Slope Soarer skulk in the periphery of relevant literature, invoking the thrill of skiing and the allure of pristine air in the mountainous terrain. While not academic in nature, these narratives impart a sense of whimsy to our serious inquiry.
Dad Joke: What do you call a group of skiers waiting in line for the ski lift? A ski queue!
Additionally, cinematic references to the world of skiing, such as "Downhill Dreams" and "Slope Seekers," punctuate the cultural backdrop against which our research unfolds. While not directly related to air quality and skiing performance, these movies evoke the adrenaline rush and competitive fervor intrinsic to the sport of skiing.
In sum, the literature encompasses a wide spectrum of scholarly, fictional, and cinematic works, all of which converge to frame our investigation into the unexpected relationship between air quality in Crescent City, California, and the performance of NCAA Men's Skiing champions.


[[RESULTS]]
The statistical analysis of the relationship between air quality in Crescent City, California and the performance of NCAA Men's Skiing champions resulted in a noteworthy correlation coefficient of 0.8120015. This finding indicates a strong positive linear relationship between the two variables, suggesting that as air quality improves, the points accrued by skiing champions also tend to increase. It seems that cleaner air may indeed be a breath of fresh air for these athletes, both figuratively and literally.
The coefficient of determination (r-squared) was calculated to be 0.6593464, indicating that approximately 65.93% of the variability in the skiing champions' points can be explained by the variation in air quality. This substantial proportion further underscores the influential role of air quality in shaping the performance of these elite athletes, adding an unexpected twist to the typical factors considered in athletic success.
Of course, as any statistician worth their salt knows, a low p-value is the cherry on top of the correlation sundae. In our analysis, the p-value was found to be less than 0.01, providing strong evidence against the null hypothesis and affirming the presence of a significant relationship between air quality and NCAA Men's Skiing champion's points. This result underscores the robustness of the observed correlation and supports the notion that air quality may indeed play a pivotal role in the performance of skiing champions.
Figure 1 depicts the scatterplot illustrating the striking correlation between air quality and NCAA Men's Skiing champion's points. As air quality improves, there is a clear trend of an increase in skiing champion's points, affirming the positive association uncovered through our analysis.
In conclusion, our study has unearthed a slope-tacular relationship, demonstrating the unexpected influence of air quality in Crescent City, California on the performance of NCAA Men's Skiing champions. These findings not only add a breath of fresh air to the field of sports science but also open up new avenues for exploration into the interplay between environmental factors and athletic success.

-------

Your response should start like this:

[[DISCUSSION]]



ChatGPT:

[[DISCUSSION]]

Our findings have unveiled a remarkable connection between the air quality in Crescent City, California and the performance of NCAA Men's Skiing champions, echoing the prior research that hinted at the influence of air quality on athletic prowess. The correlation coefficient of 0.8120015, coupled with a p-value less than 0.01, aligns with previous studies that have posited the impact of environmental factors, including air quality, on athletic performance. It appears that the proverbial adage, "the air quality's the limit," holds a grain of truth in the world of competitive skiing.

The observed link between air quality and skiing champions' points may be reminiscent of that familiar feeling of serenity experienced when gliding down fresh powder—both the skier and the ski slope are seeking the breath of fresh air. This finding not only provides a breath-taking twist to the existing literature but also elevates the discourse on environmental influences in sports performance to new heights.

The tangible correlation identified in our study aligns with "Smith et al.'s investigation" into the impact of air quality on aerobic endurance among athletes. Just as the clean air in Crescent City may invigorate the skiing champions, enhancing their performance, Smith and colleagues' work underscores the broader implications of air quality on athletes' physical capacity. It seems that breathing in the pristine air of Crescent City may impart these skiing champions with a gust of energy, propelling them further down the slope to victory.

Likewise, "Doe and Jones' research" on the effects of air quality on cognitive function unveils the interconnectedness between air quality and physical performance. While their study primarily focused on reaction times, the notion that air quality can influence cognitive function resonates with our findings, hinting at the multifaceted impact of air quality on athletes' overall performance. Indeed, our study adds another layer to this airily intricate tapestry of research, painting a picture of the pervasive influence of air quality on athletic achievement.

The high coefficient of determination (r-squared) of 0.6593464 further accentuates the influence of air quality on the prowess of NCAA Men's Skiing champions, aligning with previous work that has emphasized the substantial role of environmental factors in shaping athletic outcomes. It appears that the air quality in Crescent City may wield a defining influence, much like a seasoned skier maneuvering through a treacherous slalom course.

As we navigate through the unexpected twists and turns of our research, it's important to note the limitations and opportunities that lay ahead. While our study has established a robust correlation between air quality and skiing champion's points, further investigations into the specific mechanisms through which air quality impacts skiing performance are warranted. Additionally, exploring the generalizability of our findings to other geographical locations and athletic disciplines could pave the way for a comprehensive understanding of the interplay between air quality and athletic achievement.

Our study stands as a beacon of fresh inspiration in the realm of sports science, illuminating the uncharted terrain of environmental influences on athletic success. By uncovering the unexpected relationship between air quality in Crescent City, California and the performance of NCAA Men's Skiing champions, we hope to sow the seeds for future research endeavors that will continue to carve through unexplored slopes, ultimately enriching our understanding of the intricate dance between the environment and athletic proficiency.


Model: gpt-3.5-turbo-1106
System prompt: You are a witty academic researcher. Your writing sounds like it belongs in a statistics journal.You draft the discussion section of goofy academic research papers that sounds like it belongs based on the title and abstract provided.
User prompt:
Pretend you are an academic researcher. Your writing sounds like it belongs in a medical or economics journal. However, you frequently crack jokes, make puns, or add unexpected twists in your writing.

Please make up a short conclusion of an academic research paper presenting the findings of the connection between Air quality in Crescent City, California and NCAA Men's Skiing champion's points. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
"Sloping Down: The Downhill Connection between Air Quality in Crescent City, California and NCAA Men's Skiing Champion's Points"

[[ABSTRACT]]
In this study, we embarked on a ski-entific quest to explore the unexpected relationship between air quality in Crescent City, California and the performance of NCAA Men's Skiing champions. Utilizing data from the Environmental Protection Agency to gauge air quality and NCAA records to tally the skiing champion's points, we set out to uncover if there is a breath-taking correlation between these seemingly unrelated factors. Our efforts led to the unearthing of a correlation coefficient of 0.8120015 and a p-value less than 0.01 for the years spanning from 1988 to 2022.

Our findings reveal an intriguing relationship that might just leave you breathless—much like skiing down a treacherous slope. It appears that the air quality in Crescent City may exert an unexpected influence on the performance of NCAA Men's Skiing champions. We speculate that perhaps the fresh, crisp air may propel these athletes to new heights, or perhaps a dip in air quality may lead to a slope in their points.

Furthermore, our results beg the question: could the high-ozone days in Crescent City be a breath of fresh air for the skiing champions, or do they find themselves breathless in the low-quality air? These tongue-in-cheek musings aside, our research sheds light on an unexpected correlation and paves the way for further investigation into the curious alliance between air quality and skiing prowess.

[[INTRDUCTION]]
The intersection of environmental factors and athletic performance has long been an area of interest in the realm of sports science. While much attention has been paid to the impact of altitude, temperature, and humidity on athletic outcomes, the relationship between air quality and athletic performance remains relatively unexplored. In this study, we sought to uncover the correlation between the air quality in Crescent City, California, and the points accrued by NCAA Men's Skiing champions. This off-piste investigation offers an exciting opportunity to traverse uncharted territory in the realm of sports science and environmental research.
Dad Joke: What does a skier say when they finally reach the bottom of the mountain? "I've peaked."
Our study took advantage of the vast and meticulously collected data on air quality maintained by the Environmental Protection Agency. Utilizing air quality index readings, we were able to gauge the concentration of pollutants such as ozone, particulate matter, and carbon monoxide in the atmospheric milieu of Crescent City. On the other hand, NCAA Men's Skiing championship records provided a comprehensive archive of the points accrued by skiing champions over the years—a treasure trove for our analytical pursuits.
Dad Joke: Why do skiers make terrible spies? Because they're always going downhill.

[[RESULTS]]
The statistical analysis of the relationship between air quality in Crescent City, California and the performance of NCAA Men's Skiing champions resulted in a noteworthy correlation coefficient of 0.8120015. This finding indicates a strong positive linear relationship between the two variables, suggesting that as air quality improves, the points accrued by skiing champions also tend to increase. It seems that cleaner air may indeed be a breath of fresh air for these athletes, both figuratively and literally.
The coefficient of determination (r-squared) was calculated to be 0.6593464, indicating that approximately 65.93% of the variability in the skiing champions' points can be explained by the variation in air quality. This substantial proportion further underscores the influential role of air quality in shaping the performance of these elite athletes, adding an unexpected twist to the typical factors considered in athletic success.
Of course, as any statistician worth their salt knows, a low p-value is the cherry on top of the correlation sundae. In our analysis, the p-value was found to be less than 0.01, providing strong evidence against the null hypothesis and affirming the presence of a significant relationship between air quality and NCAA Men's Skiing champion's points. This result underscores the robustness of the observed correlation and supports the notion that air quality may indeed play a pivotal role in the performance of skiing champions.
Figure 1 depicts the scatterplot illustrating the striking correlation between air quality and NCAA Men's Skiing champion's points. As air quality improves, there is a clear trend of an increase in skiing champion's points, affirming the positive association uncovered through our analysis.
In conclusion, our study has unearthed a slope-tacular relationship, demonstrating the unexpected influence of air quality in Crescent City, California on the performance of NCAA Men's Skiing champions. These findings not only add a breath of fresh air to the field of sports science but also open up new avenues for exploration into the interplay between environmental factors and athletic success.

-------

Your response should start like this:

[[CONCLUSION]]



ChatGPT:

[[CONCLUSION]]

In summation, our ski-entific expedition has illuminated a striking correlation between air quality in Crescent City, California and the performance of NCAA Men's Skiing champions. The robust correlation coefficient of 0.8120015 and the minuscule p-value of less than 0.01 lend undeniable credence to the existence of a breath-taking link between these seemingly unrelated variables. Our findings not only ski-daddle into uncharted territory but also carve out a new trail in the domain of sports science and environmental research.

While our results offer a slope-tacular revelation, it's crucial to acknowledge the limitations of our study. Factors such as individual athlete characteristics, training regimens, and specific competition conditions were not fully accounted for, leaving room for further exploration into the nuanced interplay between air quality and skiing prowess. However, the substantial coefficient of determination of 0.6593464 underscores the substantial impact of air quality on skiing champions' points, pointing to a compelling association ripe for additional investigation.

In the realm of sports science, this unexpected connection offers a panoramic view of the multifaceted influences shaping athletic achievement. Our study's findings not only elevate the importance of air quality but also remind us that sometimes, the most surprising relationships are hiding in plain sight, much like an elusive powder stash waiting to be discovered by a intrepid skier.

In the spirit of good humor and scholarly rigor, we submit that no further exploration is needed in this area. Our results have carved a slalom-like path, shedding light on a correlation that is sure to leave both athletes and researchers breathless.

With our findings, we invite the scientific community to embrace this slope-tacular association and perhaps ponder the question: if air quality impacts skiing performance, does a good pun improve statistical analysis?


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 Sloping Down: The Downhill Connection between Air Quality in Crescent City, California and NCAA Men's Skiing Champion's Points. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Environmental Dynamics and Extreme Sports Sociology


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 Sloping Down: The Downhill Connection between Air Quality in Crescent City, California and NCAA Men's Skiing Champion's Points. Respond only with the name of a fictional organization.

ChatGPT:

The Center for Alpine Environmental Research and Sport Science


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 Sloping Down: The Downhill Connection between Air Quality in Crescent City, California and NCAA Men's Skiing Champion's Points with an abstract of In this study, we embarked on a ski-entific quest to explore the unexpected relationship between air quality in Crescent City, California and the performance of NCAA Men's Skiing champions. Utilizing data from the Environmental Protection Agency to gauge air quality and NCAA records to tally the skiing champion's points, we set out to uncover if there is a breath-taking correlation between these seemingly unrelated factors. Our efforts led to the unearthing of a correlation coefficient of 0.8120015 and a p-value less than 0.01 for the years spanning from 1988 to 2022.
Our findings reveal an intriguing relationship that might just leave you breathless—much like skiing down a treacherous slope. It appears that the air quality in Crescent City may exert an unexpected influence on the performance of NCAA Men's Skiing champions. We speculate that perhaps the fresh, crisp air may propel these athletes to new heights, or perhaps a dip in air quality may lead to a slope in their points.
Furthermore, our results beg the question: could the high-ozone days in Crescent City be a breath of fresh air for the skiing champions, or do they find themselves breathless in the low-quality air? These tongue-in-cheek musings aside, our research sheds light on an unexpected correlation and paves the way for further investigation into the curious alliance between air quality and skiing prowess.

ChatGPT:

air quality, Crescent City California, NCAA Men's Skiing, champion's points, environmental protection agency, correlation coefficient, p-value, skiing performance, skiing champions, ozone levels, air pollution, atmospheric conditions

*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 quality in Crescent City, California
Detailed data title: Percentage of days with good or moderate air quality in Crescent City, CA
Source: Environmental Protection Agency
See what else correlates with Air quality in Crescent City, California

NCAA Men's Skiing champion's points
Source: NCAA
See what else correlates with NCAA Men's Skiing champion's points

Correlation r = 0.8120015 (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 = 0.6593464 (Coefficient of determination)
This means 65.9% of the change in the one variable (i.e., NCAA Men's Skiing champion's points) is predictable based on the change in the other (i.e., Air quality in Crescent City, California) over the 35 years from 1988 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 3.2E-9. 0.0000000032121690651697225000
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 0.81 in 3.2E-7% of random cases. Said differently, if you correlated 311,316,117 random variables You don't actually need 311 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 34 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 34 because we have two variables measured over a period of 35 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.

[ 0.66, 0.9 ] 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.
19881989199019911992199319941995199619971998199920002001200220032004200520062007200820092010201120122013201420152016201720182019202020212022
Air quality in Crescent City, California (Good air quality)11110.9972221111110.992908111111111111111110.993289110.96917811
NCAA Men's Skiing champion's points (Points)651672671713683.5783688720.5719686654650720649656682623622.5654698649.6659785.5831832708556505567.5541.5603530.50554578




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.
  4. Confounding variable: 2020 is particularly different from the other years on this graph. Confounding variables (like global pandemics) will cause two variables to look connected when in fact a "sneaky third" variable is influencing both of them behind the scenes.
  5. Y-axis doesn't start at zero: I truncated the Y-axes of the graph above. I also used a line graph, which makes the visual connection stand out more than it deserves. Nothing against line graphs. They are great at telling a story when you have linear data! But visually it is deceptive because the only data is at the points on the graph, not the lines on the graph. In between each point, the data could have been doing anything. Like going for a random walk by itself!
    Mathematically what I showed is true, but it is intentionally misleading. Below is the same chart but with both Y-axes starting at zero.




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([1,1,1,1,0.997222,1,1,1,1,1,1,0.992908,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0.993289,1,1,0.969178,1,1,])
array_2 = np.array([651,672,671,713,683.5,783,688,720.5,719,686,654,650,720,649,656,682,623,622.5,654,698,649.6,659,785.5,831,832,708,556,505,567.5,541.5,603,530.5,0,554,578,])
array_1_name = "Air quality in Crescent City, California"
array_2_name = "NCAA Men's Skiing champion's points"

# Perform the calculation
print(f"Calculating the correlation between {array_1_name} and {array_2_name}...")
correlation, r_squared, p_value = calculate_correlation(array_1, array_2)

# Print the results
print("Correlation Coefficient:", correlation)
print("R-squared:", r_squared)
print("P-value:", p_value)



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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."

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Correlation ID: 1091 · Black Variable ID: 21993 · Red Variable ID: 241
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