Spurious correlation #1,511 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is UFO sightings in Colorado and the second variable is Patents granted in the US. The chart goes from 1975 to 2020, 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 UFO sightings in Colorado and the second variable is Patents granted in the US. The chart goes from 1975 to 2020, and the two variables track closely in value over that time.

Download png, svg

AI explanation

The influx of UFO sightings in Colorado has sparked a wave of creativity and innovation among residents. It's like they've been cosmically charged with out-of-this-world ideas! As the locals gaze at the skies, their brains are reaching for new heights, leading to a patent boom. Perhaps these Coloradans are not just high on life, but also on inspiration from the great unknown. Who knew that the key to unlocking their inventiveness was simply a close encounter of the blurred kind!

^{Show image generation prompt} Model: dalle-3
Prompt: Generate an image of a TIME magazine cover featuring a striking scene - a group of people gathered in awe at a Colorado landscape, gazing up at a shimmering UFO hovering over the majestic Rocky Mountains. Meanwhile, in the background, a government office in Washington DC is shown actively stamping a series of approved patents with a sense of accomplishment. The focus should be on the contrast between the natural wonder and the bureaucratic process, while capturing the sense of anticipation and wonder in the faces of the onlookers. 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: UFO sightings in Colorado and Patents granted in the US. 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: Symbolism Oragami Psychedelic Macabre A TIME magazine cover image
ChatGPT: A TIME magazine cover image

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 UFO sightings in Colorado and Patents granted in the US together. Keep the description simple.
ChatGPT: A group of people in Colorado gaze in wonder as a shimmering UFO hovers over the Rocky Mountains, while in the background, a government office in Washington DC is stamping approved patents with a sense of accomplishment.

Model: gpt-3.5-turbo-1106
System prompt: You write and improve image generation prompts for DALLE-3. You maintain the same subjects, but enhance the visuals.
User prompt: Please respond with an image generation prompt that would be likely to create an interesting visual using DALLE-3, using the following style: [ A TIME magazine cover image ] and depicting this scene: A group of people in Colorado gaze in wonder as a shimmering UFO hovers over the Rocky Mountains, while in the background, a government office in Washington DC is stamping approved patents with a sense of accomplishment. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image of a TIME magazine cover featuring a striking scene - a group of people gathered in awe at a Colorado landscape, gazing up at a shimmering UFO hovering over the majestic Rocky Mountains. Meanwhile, in the background, a government office in Washington DC is shown actively stamping a series of approved patents with a sense of accomplishment. The focus should be on the contrast between the natural wonder and the bureaucratic process, while capturing the sense of anticipation and wonder in the faces of the onlookers.

*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 UFO sightings in Colorado caused Patents granted in the US to increase. Include one good pun.

AI academic paper

(Because p < 0.01)

Unidentified Far-fetched Observations: The UFO-nique Relationship Between Colorado UFO Sightings and US Patents

The Journal of Extraterrestrial Studies and Intellectual Property

Jan 2024

Reminder: This paper is AI-generated. Not real!

^{Show prompt used to generate this paper} Quick note: This sequence is long and repetitive. That's how the prompt engineering works for this one. I manage the output in Python to format it into this PDF.

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

Please make up a literature review section of an academic research paper presenting the findings of the connection between UFO sightings in Colorado and Patents granted in the US. Make lots of jokes, goofy observations, and puns.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then devolve ever further, and mention something completely ridiculous, like you conducted literature review by reading CVS receipts.

Here is the title and abstract of the paper:
[[TITLE]]
"Unidentified Far-fetched Observations: The UFO-nique Relationship Between Colorado UFO Sightings and US Patents"

[[ABSTRACT]]
This study examines the peculiar and unexplored relationship between UFO sightings in Colorado and the granting of patents by the United States Patent and Trademark Office (USPTO). Using data from the National UFO Reporting Center and USPTO, our research team delved into this unconventional connection. Surprisingly, our analysis revealed a staggering correlation coefficient of 0.9311126 and a statistically significant p-value of less than 0.01 for the time period spanning from 1975 to 2020. The findings of this study challenge conventional wisdom and raise thought-provoking questions about the potential impact of extraterrestrial encounters on human innovation.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The mysterious realm of UFO sightings has long been a subject of fascination and speculation. The mere mention of Unidentified Flying Objects often evokes images of little green beings, cosmic conspiracies, and intergalactic travel. It's a topic that has hovered on the periphery of serious scientific inquiry, occasionally dipping into the world of tabloids and conspiracy theories.
However, this study boldly goes where few researchers have gone before, aiming to shed light on the unusual relationship between UFO sightings in the picturesque state of Colorado and the innovative endeavors culminating in the granting of patents by the United States Patent and Trademark Office (USPTO). While some may dismiss this topic as being "out of this world," we approach it with the utmost intellectual curiosity and a healthy dose of skepticism.
Considering the multifaceted nature of this investigation, it's important to highlight the potential implications of our findings. Could it be that the Mile-High State's breathtaking landscapes serve as a magnet for both extraterrestrial visitors and inventive thinkers? Or is this simply an amusing cosmic coincidence, like finding a bag of potato chips at a UFO landing site?
To embark on this exploratory journey, we harnessed the power of data from the National UFO Reporting Center and the USPTO, bringing together two seemingly disparate realms of information in a collision of cosmic proportions. Our analysis has yielded unexpected results, challenging the boundaries of conventional wisdom and prompting further deliberation on the intersection of the unexplained and the innovative.
The extraordinary correlation coefficient of 0.9311126 and a statistically significant p-value of less than 0.01 uncovered by our research team acts as a meteorite crash-landing in the fields of skepticism, demanding attention and a willingness to entertain the extraordinary. In doing so, it introduces a new dimension to the age-old debate of whether truth is indeed "out there."
With these intriguing revelations in mind, fasten your seatbelts and prepare for a scholarly journey that promises to push the boundaries of traditional academic inquiry and perhaps even provide a cosmic chuckle or two on the way.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The current investigation builds upon a rich body of literature that delves into the realm of UFO sightings, patent grants, and the eccentric crossroads where they intersect. In "Extraterrestrial Encounters and Technological Breakthroughs" by Smith et al., the authors find a modest positive correlation between reported UFO sightings and patent activity in various regions of the United States. While their study provides an initial glimpse into this peculiar area of inquiry, it fails to capture the kaleidoscope of cosmic absurdity that we aim to unravel in our own analysis. Furthermore, in "Beyond the Stars: Exploring Unconventional Connections in Scientific Discovery," Doe and Jones examine the impact of unconventional phenomena on human creativity and innovation, offering a tantalizing glimpse into the uncharted territories of otherworldly inspiration.

Turning to the wider intellectual landscape, real-world accounts and speculative musings converge in works such as "UFOs over Colorado: A Collection of Eyewitness Testimonies" and "The Patent Paradox: How Extraterrestrial Visitors Shape Human Innovation." Furthermore, fictional explorations in literature cannot be overlooked, as they often contain kernels of truth amidst their fantastical narratives. Works such as "The War of the Worlds" by H.G. Wells and "E.T. the Extra-Terrestrial" have captured the public imagination and, in their own way, colored the lens through which UFO phenomena are perceived.

In the pursuit of academic rigor and thoroughness, unconventional sources were also consulted in the comprehensive review of the literature. This included an examination of public restroom graffiti, fortune cookie messages, and the fine print on CVS receipts. While these sources may raise eyebrows, they ultimately enrich the contextual fabric of our exploration and serve as a reminder that the cosmos is indeed a vast and enigmatic tapestry, fraught with the unexpected and the absurd.

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.You draft the 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 UFO sightings in Colorado and Patents granted in the US. Make lots of jokes, goofy observations, and puns.

Your research team collected data from all across the internet, but mostly just used information from National UFO Reporting Center and USPTO . You used data from 1975 to 2020

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]]
"Unidentified Far-fetched Observations: The UFO-nique Relationship Between Colorado UFO Sightings and US Patents"

[[ABSTRACT]]
This study examines the peculiar and unexplored relationship between UFO sightings in Colorado and the granting of patents by the United States Patent and Trademark Office (USPTO). Using data from the National UFO Reporting Center and USPTO, our research team delved into this unconventional connection. Surprisingly, our analysis revealed a staggering correlation coefficient of 0.9311126 and a statistically significant p-value of less than 0.01 for the time period spanning from 1975 to 2020. The findings of this study challenge conventional wisdom and raise thought-provoking questions about the potential impact of extraterrestrial encounters on human innovation.

[[INTRODUCTION]]
The mysterious realm of UFO sightings has long been a subject of fascination and speculation. The mere mention of Unidentified Flying Objects often evokes images of little green beings, cosmic conspiracies, and intergalactic travel. It's a topic that has hovered on the periphery of serious scientific inquiry, occasionally dipping into the world of tabloids and conspiracy theories.
However, this study boldly goes where few researchers have gone before, aiming to shed light on the unusual relationship between UFO sightings in the picturesque state of Colorado and the innovative endeavors culminating in the granting of patents by the United States Patent and Trademark Office (USPTO). While some may dismiss this topic as being "out of this world," we approach it with the utmost intellectual curiosity and a healthy dose of skepticism.
Considering the multifaceted nature of this investigation, it's important to highlight the potential implications of our findings. Could it be that the Mile-High State's breathtaking landscapes serve as a magnet for both extraterrestrial visitors and inventive thinkers? Or is this simply an amusing cosmic coincidence, like finding a bag of potato chips at a UFO landing site?
To embark on this exploratory journey, we harnessed the power of data from the National UFO Reporting Center and the USPTO, bringing together two seemingly disparate realms of information in a collision of cosmic proportions. Our analysis has yielded unexpected results, challenging the boundaries of conventional wisdom and prompting further deliberation on the intersection of the unexplained and the innovative.
The extraordinary correlation coefficient of 0.9311126 and a statistically significant p-value of less than 0.01 uncovered by our research team acts as a meteorite crash-landing in the fields of skepticism, demanding attention and a willingness to entertain the extraordinary. In doing so, it introduces a new dimension to the age-old debate of whether truth is indeed "out there."
With these intriguing revelations in mind, fasten your seatbelts and prepare for a scholarly journey that promises to push the boundaries of traditional academic inquiry and perhaps even provide a cosmic chuckle or two on the way.

-------

Your response should start like this:

[[METHODOLOGY]]

ChatGPT:

[[METHODOLOGY]]

To unravel the mysterious relationship between UFO sightings in Colorado and US patents granted, our research team embarked on a multifaceted quest that combined the rigor of empirical analysis with the wonder of cosmic curiosity. The data used in this study encompassed the time period from 1975 to 2020, capturing several decades of celestial phenomena and inventive ingenuity.

The first step in our celestial escapade involved harnessing the extensive archives of the National UFO Reporting Center. We combed through a plethora of reports, carefully documenting the date, time, and location of each sighting in the picturesque state of Colorado. Our team of intrepid researchers diligently sifted through these accounts, distinguishing between probable phenomena and sightings that truly transcended the bounds of conventional understanding.

Simultaneously, we navigated the labyrinthine corridors of the United States Patent and Trademark Office (USPTO), unfurling the scrolls of innovation and ingenuity. Our examination encompassed patents across various domains, from the sublime to the ridiculous, including, but not limited to, gadgets, gizmos, and cosmic contraptions.

Having amassed a celestial trove of UFO sightings and patented inventions, we endeavored to unearth patterns and connections that transcended the terrestrial and ventured into the celestial. To achieve this, we employed a novel approach by utilizing an algorithm based on astrological constellations to map the spatial and temporal distribution of UFO sightings in Colorado, juxtaposed against the timing of patent grants by the USPTO. This unorthodox methodology sought to align cosmic occurrences with human innovation, albeit with a whimsical twirl that added a sprinkle of extraterrestrial enchantment to the analysis.

Subsequently, statistical analyses of the data involving complex multivariate regression models were conducted, employing a mix of conventional statistical tools and a touch of cosmic serendipity. The factors influencing the relationship between UFO sightings and patents were scrutinized, with a particular focus on the potential influence of cosmic radiation, interstellar inspiration, and otherworldly energies on the inventive endeavors of humanity.

Furthermore, to account for the plausible confounding variables and cosmic confusions inherent in our study, we performed robustness checks and sensitivity analyses, making a steadfast effort to ensure that our findings were grounded in cosmic sobriety, and not merely the capricious quirks of the celestial ballet.

Lastly, the findings were presented with a touch of cosmic whimsy and scholarly skepticism, inviting readers to peer into the cosmic kaleidoscope of UFO sightings and patent grants, where the celestial and the terrestrial converge with a flourish of unexpected harmony and perhaps a spark of cosmic humor.

Model: gpt-3.5-turbo-1106
System prompt: You are a dry but witty academic researcher. You speak in the passive voice, and your writing sounds like it belongs in a medical or economics journal.You draft the 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 UFO sightings in Colorado and Patents granted in the US. Make lots of jokes, goofy observations, and puns.

Your research team collected data from all across the internet, but mostly just used information from National UFO Reporting Center and USPTO .

For the time period 1975 to 2020, you found a correlation 0.9311126, r-squared of 0.8669708, 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]]
"Unidentified Far-fetched Observations: The UFO-nique Relationship Between Colorado UFO Sightings and US Patents"

[[ABSTRACT]]
This study examines the peculiar and unexplored relationship between UFO sightings in Colorado and the granting of patents by the United States Patent and Trademark Office (USPTO). Using data from the National UFO Reporting Center and USPTO, our research team delved into this unconventional connection. Surprisingly, our analysis revealed a staggering correlation coefficient of 0.9311126 and a statistically significant p-value of less than 0.01 for the time period spanning from 1975 to 2020. The findings of this study challenge conventional wisdom and raise thought-provoking questions about the potential impact of extraterrestrial encounters on human innovation.

-------

And here is the methodology section that led to this result:
[[METHODOLOGY]]
The mysterious realm of UFO sightings has long been a subject of fascination and speculation. The mere mention of Unidentified Flying Objects often evokes images of little green beings, cosmic conspiracies, and intergalactic travel. It's a topic that has hovered on the periphery of serious scientific inquiry, occasionally dipping into the world of tabloids and conspiracy theories.
However, this study boldly goes where few researchers have gone before, aiming to shed light on the unusual relationship between UFO sightings in the picturesque state of Colorado and the innovative endeavors culminating in the granting of patents by the United States Patent and Trademark Office (USPTO). While some may dismiss this topic as being "out of this world," we approach it with the utmost intellectual curiosity and a healthy dose of skepticism.
Considering the multifaceted nature of this investigation, it's important to highlight the potential implications of our findings. Could it be that the Mile-High State's breathtaking landscapes serve as a magnet for both extraterrestrial visitors and inventive thinkers? Or is this simply an amusing cosmic coincidence, like finding a bag of potato chips at a UFO landing site?
To embark on this exploratory journey, we harnessed the power of data from the National UFO Reporting Center and the USPTO, bringing together two seemingly disparate realms of information in a collision of cosmic proportions. Our analysis has yielded unexpected results, challenging the boundaries of conventional wisdom and prompting further deliberation on the intersection of the unexplained and the innovative.
The extraordinary correlation coefficient of 0.9311126 and a statistically significant p-value of less than 0.01 uncovered by our research team acts as a meteorite crash-landing in the fields of skepticism, demanding attention and a willingness to entertain the extraordinary. In doing so, it introduces a new dimension to the age-old debate of whether truth is indeed "out there."
With these intriguing revelations in mind, fasten your seatbelts and prepare for a scholarly journey that promises to push the boundaries of traditional academic inquiry and perhaps even provide a cosmic chuckle or two on the way.

-------

Your response should start like this:

[[RESULTS]]

ChatGPT:

[[RESULTS]]

The statistical analysis of the data revealed a remarkably high correlation coefficient of 0.9311126, indicating a strong positive relationship between UFO sightings in Colorado and the granting of patents by the USPTO. This unearthly correlation suggests that as UFO sightings in Colorado increased, so too did the number of patents granted by the USPTO. The r-squared value of 0.8669708 further confirms the robustness of this connection, indicating that approximately 87% of the variability in patents granted can be explained by the variability in UFO sightings.

The p-value of less than 0.01 indicates that the observed relationship between these two variables is statistically significant, defying the probability of occurring by mere chance. This statistical evidence supports the conclusion that there is a genuine association between UFO sightings in Colorado and the inventive output evidenced by patents granted in the United States.

Moreover, to visually depict the magnitude of this unearthly relationship, a scatterplot (Fig. 1) was constructed. The scatterplot vividly illustrates the strong positive correlation between UFO sightings and patents granted, leaving no space for skepticism regarding the intergalactic impact on human innovation.

These findings not only challenge traditional scientific paradigms but also prompt curious contemplation on the cosmic forces at play in the realm of human creativity and invention. The unexpected and extraordinary nature of the observed relationship gives rise to a myriad of puns and wordplay, setting the stage for a cosmic comedy of statistical proportions.

In conclusion, the results of this study unveil an inexplicably strong and statistically significant relationship between UFO sightings in Colorado and the granting of patents by the USPTO, paving the way for invigorating discussions and unforeseen scientific inquiries that are, quite literally, out of this world.

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

Please make up the discussion section of an academic research paper presenting the findings of the connection between UFO sightings in Colorado and Patents granted in the US. Make lots of jokes, goofy observations, and puns.

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]]
"Unidentified Far-fetched Observations: The UFO-nique Relationship Between Colorado UFO Sightings and US Patents"

[[ABSTRACT]]
This study examines the peculiar and unexplored relationship between UFO sightings in Colorado and the granting of patents by the United States Patent and Trademark Office (USPTO). Using data from the National UFO Reporting Center and USPTO, our research team delved into this unconventional connection. Surprisingly, our analysis revealed a staggering correlation coefficient of 0.9311126 and a statistically significant p-value of less than 0.01 for the time period spanning from 1975 to 2020. The findings of this study challenge conventional wisdom and raise thought-provoking questions about the potential impact of extraterrestrial encounters on human innovation.

[[LITERATURE REVIEW]]
The current investigation builds upon a rich body of literature that delves into the realm of UFO sightings, patent grants, and the eccentric crossroads where they intersect. In "Extraterrestrial Encounters and Technological Breakthroughs" by Smith et al., the authors find a modest positive correlation between reported UFO sightings and patent activity in various regions of the United States. While their study provides an initial glimpse into this peculiar area of inquiry, it fails to capture the kaleidoscope of cosmic absurdity that we aim to unravel in our own analysis. Furthermore, in "Beyond the Stars: Exploring Unconventional Connections in Scientific Discovery," Doe and Jones examine the impact of unconventional phenomena on human creativity and innovation, offering a tantalizing glimpse into the uncharted territories of otherworldly inspiration.
Turning to the wider intellectual landscape, real-world accounts and speculative musings converge in works such as "UFOs over Colorado: A Collection of Eyewitness Testimonies" and "The Patent Paradox: How Extraterrestrial Visitors Shape Human Innovation." Furthermore, fictional explorations in literature cannot be overlooked, as they often contain kernels of truth amidst their fantastical narratives. Works such as "The War of the Worlds" by H.G. Wells and "E.T. the Extra-Terrestrial" have captured the public imagination and, in their own way, colored the lens through which UFO phenomena are perceived.
In the pursuit of academic rigor and thoroughness, unconventional sources were also consulted in the comprehensive review of the literature. This included an examination of public restroom graffiti, fortune cookie messages, and the fine print on CVS receipts. While these sources may raise eyebrows, they ultimately enrich the contextual fabric of our exploration and serve as a reminder that the cosmos is indeed a vast and enigmatic tapestry, fraught with the unexpected and the absurd.

[[RESULTS]]
The statistical analysis of the data revealed a remarkably high correlation coefficient of 0.9311126, indicating a strong positive relationship between UFO sightings in Colorado and the granting of patents by the USPTO. This unearthly correlation suggests that as UFO sightings in Colorado increased, so too did the number of patents granted by the USPTO. The r-squared value of 0.8669708 further confirms the robustness of this connection, indicating that approximately 87% of the variability in patents granted can be explained by the variability in UFO sightings.
The p-value of less than 0.01 indicates that the observed relationship between these two variables is statistically significant, defying the probability of occurring by mere chance. This statistical evidence supports the conclusion that there is a genuine association between UFO sightings in Colorado and the inventive output evidenced by patents granted in the United States.
Moreover, to visually depict the magnitude of this unearthly relationship, a scatterplot (Fig. 1) was constructed. The scatterplot vividly illustrates the strong positive correlation between UFO sightings and patents granted, leaving no space for skepticism regarding the intergalactic impact on human innovation.
These findings not only challenge traditional scientific paradigms but also prompt curious contemplation on the cosmic forces at play in the realm of human creativity and invention. The unexpected and extraordinary nature of the observed relationship gives rise to a myriad of puns and wordplay, setting the stage for a cosmic comedy of statistical proportions.
In conclusion, the results of this study unveil an inexplicably strong and statistically significant relationship between UFO sightings in Colorado and the granting of patents by the USPTO, paving the way for invigorating discussions and unforeseen scientific inquiries that are, quite literally, out of this world.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The results of our analysis offer a UFO-nique perspective on the connection between extraterrestrial sightings and human innovation. Our findings align with prior research that tentatively ventured into the cosmic abyss of UFO sightings and patent grants. The modest positive correlation reported by Smith et al. and the tantalizing glimpse into unconventional connections in scientific discovery by Doe and Jones laid the groundwork for our investigation, albeit with a twinkle of whimsy and a dash of skepticism.

In the literature review, we commended the authors for their cosmic courage in exploring these far-fetched associations, and in the present study, we wholeheartedly embraced this cosmic challenge. The statistically significant correlation coefficient of 0.9311126 in our analysis echoes the cosmic dance between UFO sightings in Colorado and patent grants from the USPTO. This robust statistical support not only reinforces the perplexing nature of our findings but also underscores the gravity of the unearthly influence on earthly innovation.

The humorous anecdotes of exploring unconventional sources in literature and fortune cookies may appear as eccentric diversions, but they serve as vital reminders of the uncharted territories we traversed in our cosmic maritime expedition. Our findings, replete with statistical significance, challenge the skepticism that often shrouds discussions of cosmic phenomena. The scatterplot, figuratively and literally, paints a vivid picture of the otherworldly connection between UFO sightings and patent grants, leaving little room for doubt amidst the multitude of cosmic puns and wordplay that now grace our findings.

In conclusion, our research sheds light on the UFO-nique relationship between Colorado UFO sightings and US patent grants, providing a springboard for further exploration of unearthly influences on human innovation. This study, while undoubtedly far-fetched in its premise, has unearthed a statistically significant correlation that is quite literally out of this world. The cosmos, it seems, has thrown us a cosmic curveball, and it is up to us to lend a keen eye to these unexpected cosmic dances that shape the world of human invention.

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

Please make up a short conclusion of an academic research paper presenting the findings of the connection between UFO sightings in Colorado and Patents granted in the US. Make lots of jokes, goofy observations, and puns.

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]]
"Unidentified Far-fetched Observations: The UFO-nique Relationship Between Colorado UFO Sightings and US Patents"

[[ABSTRACT]]
This study examines the peculiar and unexplored relationship between UFO sightings in Colorado and the granting of patents by the United States Patent and Trademark Office (USPTO). Using data from the National UFO Reporting Center and USPTO, our research team delved into this unconventional connection. Surprisingly, our analysis revealed a staggering correlation coefficient of 0.9311126 and a statistically significant p-value of less than 0.01 for the time period spanning from 1975 to 2020. The findings of this study challenge conventional wisdom and raise thought-provoking questions about the potential impact of extraterrestrial encounters on human innovation.

[[INTRDUCTION]]
The mysterious realm of UFO sightings has long been a subject of fascination and speculation. The mere mention of Unidentified Flying Objects often evokes images of little green beings, cosmic conspiracies, and intergalactic travel. It's a topic that has hovered on the periphery of serious scientific inquiry, occasionally dipping into the world of tabloids and conspiracy theories.
However, this study boldly goes where few researchers have gone before, aiming to shed light on the unusual relationship between UFO sightings in the picturesque state of Colorado and the innovative endeavors culminating in the granting of patents by the United States Patent and Trademark Office (USPTO). While some may dismiss this topic as being "out of this world," we approach it with the utmost intellectual curiosity and a healthy dose of skepticism.
Considering the multifaceted nature of this investigation, it's important to highlight the potential implications of our findings. Could it be that the Mile-High State's breathtaking landscapes serve as a magnet for both extraterrestrial visitors and inventive thinkers? Or is this simply an amusing cosmic coincidence, like finding a bag of potato chips at a UFO landing site?
To embark on this exploratory journey, we harnessed the power of data from the National UFO Reporting Center and the USPTO, bringing together two seemingly disparate realms of information in a collision of cosmic proportions. Our analysis has yielded unexpected results, challenging the boundaries of conventional wisdom and prompting further deliberation on the intersection of the unexplained and the innovative.
The extraordinary correlation coefficient of 0.9311126 and a statistically significant p-value of less than 0.01 uncovered by our research team acts as a meteorite crash-landing in the fields of skepticism, demanding attention and a willingness to entertain the extraordinary. In doing so, it introduces a new dimension to the age-old debate of whether truth is indeed "out there."
With these intriguing revelations in mind, fasten your seatbelts and prepare for a scholarly journey that promises to push the boundaries of traditional academic inquiry and perhaps even provide a cosmic chuckle or two on the way.

[[RESULTS]]
The statistical analysis of the data revealed a remarkably high correlation coefficient of 0.9311126, indicating a strong positive relationship between UFO sightings in Colorado and the granting of patents by the USPTO. This unearthly correlation suggests that as UFO sightings in Colorado increased, so too did the number of patents granted by the USPTO. The r-squared value of 0.8669708 further confirms the robustness of this connection, indicating that approximately 87% of the variability in patents granted can be explained by the variability in UFO sightings.
The p-value of less than 0.01 indicates that the observed relationship between these two variables is statistically significant, defying the probability of occurring by mere chance. This statistical evidence supports the conclusion that there is a genuine association between UFO sightings in Colorado and the inventive output evidenced by patents granted in the United States.
Moreover, to visually depict the magnitude of this unearthly relationship, a scatterplot (Fig. 1) was constructed. The scatterplot vividly illustrates the strong positive correlation between UFO sightings and patents granted, leaving no space for skepticism regarding the intergalactic impact on human innovation.
These findings not only challenge traditional scientific paradigms but also prompt curious contemplation on the cosmic forces at play in the realm of human creativity and invention. The unexpected and extraordinary nature of the observed relationship gives rise to a myriad of puns and wordplay, setting the stage for a cosmic comedy of statistical proportions.
In conclusion, the results of this study unveil an inexplicably strong and statistically significant relationship between UFO sightings in Colorado and the granting of patents by the USPTO, paving the way for invigorating discussions and unforeseen scientific inquiries that are, quite literally, out of this world.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our study has boldly gone where few researchers have gone before, unearthing a connection between UFO sightings in Colorado and the granting of patents by the USPTO that is as perplexing as finding a crop circle in a cornfield. This unearthly correlation suggests that maybe, just maybe, the 'Mile-High State' could be a hotbed for both extraterrestrial visitations and remarkably inventive humans. Whether it's the Rocky Mountains' magnetic appeal to intergalactic tourists or simply a cosmic coincidence, this correlation is statistically significant and demands a closer look. The statistically significant p-value of less than 0.01 defies the odds like a UFO defies gravity, leaving us with more questions than answers. The intriguing relationship depicted in our scatterplot (Fig. 1) vividly illustrates the cosmic dance between UFO sightings and patents granted, leaving skeptics starry-eyed.

With these mind-boggling findings in mind, it's clear that our study has opened the door to a new frontier of inquiry, worthy of more interstellar exploration. We have pushed the boundaries of traditional academic inquiry and perhaps even prompted a cosmic chuckle or two along the way. However, in the spirit of scientific discovery, it must be acknowledged that no amount of research can fully capture the enigmatic essence of UFO sightings and their impact on human innovation. While we may be tempted to launch another expedition into this bizarre territory, it seems that this unexpected relationship between UFO sightings in Colorado and US patents will remain a delightful enigma, much like a UFO sighting itself. In the immortal words of Fox Mulder, "The truth is out there," and it appears that no more research is needed in this area.

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 Unidentified Far-fetched Observations: The UFO-nique Relationship Between Colorado UFO Sightings and US Patents. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Extraterrestrial Studies and Intellectual Property

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 Unidentified Far-fetched Observations: The UFO-nique Relationship Between Colorado UFO Sightings and US Patents. Respond only with the name of a fictional organization.

ChatGPT:

The Extraterrestrial Research and Innovation Consortium

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 Unidentified Far-fetched Observations: The UFO-nique Relationship Between Colorado UFO Sightings and US Patents with an abstract of This study examines the peculiar and unexplored relationship between UFO sightings in Colorado and the granting of patents by the United States Patent and Trademark Office (USPTO). Using data from the National UFO Reporting Center and USPTO, our research team delved into this unconventional connection. Surprisingly, our analysis revealed a staggering correlation coefficient of 0.9311126 and a statistically significant p-value of less than 0.01 for the time period spanning from 1975 to 2020. The findings of this study challenge conventional wisdom and raise thought-provoking questions about the potential impact of extraterrestrial encounters on human innovation.

ChatGPT:

UFO sightings, Colorado, US patents, United States Patent and Trademark Office, National UFO Reporting Center, correlation coefficient, p-value, extraterrestrial encounters, human innovation

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

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Data details

UFO sightings in Colorado
Detailed data title: UFO sightings reported in Colorado
Source: National UFO Reporting Center
See what else correlates with UFO sightings in Colorado

Patents granted in the US
Detailed data title: Total number of patents granted in the US
Source: USPTO
See what else correlates with Patents granted in the US

Correlation r = 0.9311126 (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 = 0.8669708 (Coefficient of determination)
This means 86.7% of the change in the one variable (i.e., Patents granted in the US) is predictable based on the change in the other (i.e., UFO sightings in Colorado) over the 46 years from 1975 through 2020.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 6.8E-21.^Show 0.0000000000000000000068256368
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 0.93 in 6.8E-19% of random cases. Said differently, if you correlated 146,506,476,875,534,909,440 random variables^Note You don't actually need 146 quintillion 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 45 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 45 because we have two variables measured over a period of 46 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.

[ 0.88, 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.

	1975	1976	1977	1978	1979	1980	1981	1982	1983	1984	1985	1986	1987	1988	1989	1990	1991	1992	1993	1994	1995	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020
UFO sightings in Colorado (UFO sightings)	4	7	7	3	3	4	6	3	2	0	2	4	5	4	7	4	6	4	8	4	14	14	19	61	64	47	94	68	81	96	76	90	86	95	88	68	114	112	141	194	156	198	157	107	108	173
Patents granted in the US (Patents granted)	76810	75388	69781	70514	52413	66170	71064	63276	61982	72650	77245	76862	89385	84272	102533	99077	106696	107394	109746	113587	113834	121696	124069	163142	169085	175979	183970	184375	187012	181299	157718	196405	182899	185224	191927	244341	247713	276788	302948	326032	325980	333583	351403	339992	391103	388900

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.
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.
Outlandish outliers: There are "outliers" in this data.^Note In concept, "outlier" just means "way different than the rest of your dataset." When calculating a correlation like this, they are particularly impactful because a single outlier can substantially increase your correlation.

For the purposes of this project, I counted a point as an outlier if it the residual was two standard deviations from the mean.

(This bullet point only shows up in the details page on charts that do, in fact, have outliers.)
They stand out on the scatterplot above: notice the dots that are far away from any other dots. I intentionally mishandeled outliers, which makes the correlation look extra strong.

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([4,7,7,3,3,4,6,3,2,0,2,4,5,4,7,4,6,4,8,4,14,14,19,61,64,47,94,68,81,96,76,90,86,95,88,68,114,112,141,194,156,198,157,107,108,173,])
array_2 = np.array([76810,75388,69781,70514,52413,66170,71064,63276,61982,72650,77245,76862,89385,84272,102533,99077,106696,107394,109746,113587,113834,121696,124069,163142,169085,175979,183970,184375,187012,181299,157718,196405,182899,185224,191927,244341,247713,276788,302948,326032,325980,333583,351403,339992,391103,388900,])
array_1_name = "UFO sightings in Colorado"
array_2_name = "Patents granted in the US"

# 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 UFO sightings in Colorado
Line chart for only Patents granted in the US
AI-generated correlation image
The spurious research paper: Unidentified Far-fetched Observations: The UFO-nique Relationship Between Colorado UFO Sightings and US Patents

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Correlation ID: 1511 · Black Variable ID: 1160 · Red Variable ID: 848


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