Spurious correlation #4,828 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is The number of Breweries in the United States and the second variable is Average length of PBS Space Time YouTube videos. The chart goes from 2015 to 2022, 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 The number of Breweries in the United States and the second variable is Average length of PBS Space Time YouTube videos. The chart goes from 2015 to 2022, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As the number of breweries in the United States increased, so did the demand for hoppy, in-depth discussions. This led to longer PBS Space Time videos as they tried to tap into the expanding audience of beer-loving, space-curious viewers. It's a brew-tiful example of how a sudsy industry can have far-reaching effects on the length of scientific content!

^{Show image generation prompt} Model: dalle-3
Prompt: Generate an image of a bustling American street lined with colorful breweries, each with inviting signs and vibrant outdoor seating. The scene is filled with people enjoying craft beer and engaging in lively conversations. In the foreground, a cozy living room is depicted, where a TV screen shows a mesmerizing PBS Space Time video playing. On the coffee table rests a hop-infused craft beer, hinting at the longer, in-depth discussions happening on the screen. The image should capture the intersection of beer culture and space exploration, reflecting the increasing audience of beer-loving, space-curious viewers. The mood is light-hearted and humorous, fitting for a Reddit post. 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: The number of Breweries in the United States and Average length of PBS Space Time YouTube videos. 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: Data cyber art Cute cartoon a funny image you would see on reddit Cyber folk Macabre
ChatGPT: a funny image you would see on reddit

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 The number of Breweries in the United States and Average length of PBS Space Time YouTube videos, in the following situation: As the number of breweries in the United States increased, so did the demand for hoppy, in-depth discussions. This led to longer PBS Space Time videos as they tried to tap into the expanding audience of beer-loving, space-curious viewers. It's a brew-tiful example of how a sudsy industry can have far-reaching effects on the length of scientific content!. Keep the description simple.
ChatGPT: A bustling street in the United States, filled with colorful breweries with inviting signs, reflects the increasing number of breweries. Meanwhile, at a cozy living room, a TV screen shows a mesmerizing PBS Space Time video playing, with a hop-infused craft beer resting on the table, hinting at the longer, in-depth discussions happening on the screen to captivate the expanding audience of beer-loving, space-curious viewers.

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 funny image you would see on reddit ] and depicting this scene: A bustling street in the United States, filled with colorful breweries with inviting signs, reflects the increasing number of breweries. Meanwhile, at a cozy living room, a TV screen shows a mesmerizing PBS Space Time video playing, with a hop-infused craft beer resting on the table, hinting at the longer, in-depth discussions happening on the screen to captivate the expanding audience of beer-loving, space-curious viewers. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Generate an image of a bustling American street lined with colorful breweries, each with inviting signs and vibrant outdoor seating. The scene is filled with people enjoying craft beer and engaging in lively conversations. In the foreground, a cozy living room is depicted, where a TV screen shows a mesmerizing PBS Space Time video playing. On the coffee table rests a hop-infused craft beer, hinting at the longer, in-depth discussions happening on the screen. The image should capture the intersection of beer culture and space exploration, reflecting the increasing audience of beer-loving, space-curious viewers. The mood is light-hearted and humorous, fitting for a Reddit post.

*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 The number of Breweries in the United States caused Average length of PBS Space Time YouTube videos to increase.

AI academic paper

(Because p < 0.01)

Cheers to Time well Spent: Unveiling the Ale-Encompassing Relationship between Breweries in the United States and the Average Length of PBS Space Time YouTube Videos

The Journal of Sudsy Science

Jan 2024

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

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

Model: gpt-3.5-turbo-1106
System prompt: You are a goofy academic researcher writing an academic paper. You follow the rules, but you throw out convention regularly to make jokes and funny asides.You draft 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 The number of Breweries in the United States and Average length of PBS Space Time YouTube videos. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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]]
Cheers to Time well Spent: Unveiling the Ale-Encompassing Relationship between Breweries in the United States and the Average Length of PBS Space Time YouTube Videos

[[ABSTRACT]]
This study delves into the interconnected world of brews and views, aiming to uncover the perplexing relationship between the number of breweries in the United States and the average length of PBS Space Time YouTube videos. Armed with a plethora of data from the Brewers Association and YouTube, our research team endeavors to shed light on the mysterious confluence of libations and educational content.

Our findings reveal a positively staggering correlation coefficient of 0.9428315 and a p-value less than 0.01, spanning the years 2015 to 2022. In simpler terms, it seems that as the number of breweries rises, so does the length of space-time exploration on PBS. It's as if the more hops in breweries, the more quantum leaps in video length. Brew-tally fascinating, isn't it?

Unraveling this correlation unlocks a world of possibilities for both the craft beer industry and educational content creators. Understanding the peculiar resonance between these seemingly distinct realms may pave the way for new marketing strategies, collaboration opportunities, and perhaps even the occasional beer-fueled science episode.

In conclusion, this study demonstrably reveals a captivating relationship between the proliferation of breweries in the United States and the temporal expansiveness of PBS Space Time's YouTube videos. As the saying goes, "In space-time, no one can hear you pour." But with this newfound insight, perhaps we can all raise a toast to the cosmic connection between spirits and science.

[[LITERATURE REVIEW]]
The interplay between the number of breweries in the United States and the average length of PBS Space Time YouTube videos has spurred a wave of scholarly inquiry in recent years, prompting researchers to contemplate the celestial dance of hops and hypotheses. Smith and Doe (2018) examined the rise of craft breweries in the U.S. and the impact on consumer preferences, laying the groundwork for understanding the cultural and economic significance of this effervescent industry. Meanwhile, Jones et al. (2019) delved into the multimedia landscape, exploring the consumption patterns of educational content in the digital sphere.
However, as we navigate the constellation of literature, our pursuit of this peculiar correlation leads us to unexpected crossroads and unchartered territory. It's almost like stumbling upon a black hole of brews and YouTube views—a profoundly mysterious yet exhilarating prospect.
Drawing inspiration from non-fiction works such as "The Beer Bible" by Jeff Alworth and "Astrophysics for People in a Hurry" by Neil deGrasse Tyson, we find ourselves traversing the ethereal plane of both hops and hypotheticals. These literary tomes elevate our understanding of the interconnectedness between the art of brewing and the cosmic expanse, providing a robust framework for our exploratory investigations. After all, what's a scholarly pursuit without a touch of literary libation?
In a twist of interconnectedness that could rival a multiverse theory, fictional works like "The Martian" by Andy Weir and "The Hitchhiker's Guide to the Galaxy" by Douglas Adams beckon us into a whimsical universe of space exploration and intergalactic misadventures. While these works may seem light years away from our research focus, they offer a lighthearted perspective on the cosmic tapestry that intertwines with the complexities of brewery landscapes and YouTube voyages.
In the spirit of unexpected connections, board games such as "Terraforming Mars" and "Brew Crafters" spark our imaginations with their thematic depth, weaving a playful yet thought-provoking narrative of celestial colonization and craft beer mastery. These games serve as a playful backdrop to our scholarly pursuits, reminding us that even in the pursuit of knowledge, a dash of whimsy can enrich the journey.
The divergent paths of scholarly inquiry and playful contemplation converge in an ale-encompassing embrace, resonating with the cosmic ballet of brews and space-time chronicles. As we journey through these literary landscapes, we find that even in the minutiae of research, there's always room for a good dad joke. Why did the barley refuse to mingle with the hops? It simply couldn't *beer* the thought of a bitter relationship!
Ah, the complexities of scholarly pursuit and the refreshing blend of literary musings—truly a captivating journey.

[[RESULTS]]
The results of our analysis unveiled a remarkably strong correlation between the number of breweries in the United States and the average length of PBS Space Time YouTube videos. The correlation coefficient of 0.9428315 indicates a near-telepathic connection between these two seemingly disparate domains. It's almost as if the universe conspired to merge the realms of brewed beverages and cosmic contemplation. Talk about a beer-y curious phenomenon!
We also observed an r-squared value of 0.8889313, suggesting that approximately 88.9% of the variance in the average length of PBS Space Time videos can be explained by the number of breweries in the United States. It's as if the craft beer industry holds the secrets to unlocking the temporal expanse of space-time explorations. I guess you could say the "ale-ment" of surprise is strong in this relationship.
The p-value of less than 0.01 further solidifies the statistical significance of our findings, indicating that the observed correlation is highly unlikely to have occurred by random chance. In other words, this connection is no mere cosmic fluke—it's a bona fide celestial alignment of hops and hypotheses. It's like finding the Higgs boson in a bottle of stout—unexpected, yet undeniably exhilarating.
Finally, the scatterplot (Fig. 1) visually illustrates the robust relationship between the number of breweries in the United States and the average length of PBS Space Time YouTube videos. Each data point on the plot seems to whisper, "It's not just a brew-niverse; it's a multiverse of malt and space-time." And if you squint really hard, you might even glimpse the silhouette of a hop cone in the cosmic background radiation.
In summary, our research endeavors have uncorked a captivating correlation between the burgeoning landscape of breweries in the United States and the temporal expansion of PBS Space Time's educational odysseys. It's as if the cosmos itself is toasting to the synergy of spirits and science, echoing throughout the vast expanse of space-time. With these revelatory findings, we raise a frothy glass to the cosmic dance of brews and brain-bending phenomena, and we invite fellow enthusiasts to join us in celebrating this remarkable convergence. As they say, "It's all fun and games until someone loses track of space-time due to a compelling YouTube video about quantum mechanics!"
It's a cosmic blend of science and sudsy satisfaction, like a black hole swirling in a stout glass of celestial wonder.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The findings of our study unequivocally corroborate the conjectures put forth by Smith and Doe (2018) regarding the cultural and economic impact of the craft beer industry in the United States. It appears that the expanding galaxy of breweries exerts a palpable influence on the temporal expansiveness of educational content, as exemplified by the PBS Space Time YouTube channel. This symbiotic relationship between libations and learning mirrors the intertwining narratives of hops and hypotheses, offering a brew-tiful synthesis of terrestrial craftsmanship and astronomical exploration.

In line with the musings of Jones et al. (2019) on multimedia consumption patterns, our results provide empirical support for the notion that the proliferation of breweries is accompanied by heightened viewer engagement with extended educational content. It's as if the digital stratosphere reverberates with the gravitational pull of craft beer enthusiasts and space-time aficionados, entwining their collective trajectories into a cosmic pas de deux.

Moreover, our investigation aligns with the unexpected interconnectivity highlighted within the literature review, transcending the ordinary confines of scholarly discourse to encompass the playful expanse of literary and ludic influences. This confluence of diverse sources, ranging from non-fiction works to board games, reflects the multidimensional tapestry that characterizes the entanglement of brewery landscapes and YouTube voyages. It's an interconnectedness that echoes the sentiment of a good dad joke, seamlessly weaving profundity and levity into the fabric of scholarly pursuit.

The statistical robustness of our findings further accentuates the gravity of the brew-view relationship, as evidenced by the staggering correlation coefficient, r-squared value, and p-value. These metrics not only validate the depth of the observed connection but also attest to the empirical veracity of our ale-encompassing inquiry. It's akin to discerning the subtle notes of complexity in a finely crafted ale, unraveling the intricate flavors of statistical significance and cosmic correlation within the brew-view continuum.

In a reflective nod to the literature review's whimsical exploration of creative works, our research underscores the inherent mirth and curiosity that accompany scholarly pursuits. Just as a well-placed dad joke can infuse light-heartedness into a serious conversation, our study underscores the delightful convergence of substantive inquiry and playful contemplation, exemplifying the harmonious coexistence of scholarly rigor and intellectual whimsy.

The correlation between the burgeoning landscape of breweries and the temporal expansion of PBS Space Time's educational odysseys reveals a celestial ballet of brews and brain-bending phenomena, marking a departure from conventional scholarly undertakings. Like a foamy head atop a meticulously poured pint, our findings froth with the palpable excitement of uncovering unexpected connections in the vast expanse of research. After all, who knew that the intersection of hops and hypotheses could yield such heady revelations?

As we delve deeper into this cosmic blend of science and sudsy satisfaction, our research sparks a larger conversation about the serendipitous confluence of seemingly disparate domains. It's an invitation to savor the ale-ments of surprise in scholarly inquiry and to savor a good dad joke, perhaps delivered with a well-deserved pint in hand. For in the cosmic tapestry that intertwines brewery landscapes and YouTube voyages, there's always room for a frothy cheer and an academic chuckle. As they say, "You can't study the cosmos without appreciating the gravity of a good pun!"

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

Please make up a short conclusion of an academic research paper presenting the findings of the connection between The number of Breweries in the United States and Average length of PBS Space Time YouTube videos. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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]]
Cheers to Time well Spent: Unveiling the Ale-Encompassing Relationship between Breweries in the United States and the Average Length of PBS Space Time YouTube Videos

[[ABSTRACT]]
This study delves into the interconnected world of brews and views, aiming to uncover the perplexing relationship between the number of breweries in the United States and the average length of PBS Space Time YouTube videos. Armed with a plethora of data from the Brewers Association and YouTube, our research team endeavors to shed light on the mysterious confluence of libations and educational content.

Our findings reveal a positively staggering correlation coefficient of 0.9428315 and a p-value less than 0.01, spanning the years 2015 to 2022. In simpler terms, it seems that as the number of breweries rises, so does the length of space-time exploration on PBS. It's as if the more hops in breweries, the more quantum leaps in video length. Brew-tally fascinating, isn't it?

Unraveling this correlation unlocks a world of possibilities for both the craft beer industry and educational content creators. Understanding the peculiar resonance between these seemingly distinct realms may pave the way for new marketing strategies, collaboration opportunities, and perhaps even the occasional beer-fueled science episode.

In conclusion, this study demonstrably reveals a captivating relationship between the proliferation of breweries in the United States and the temporal expansiveness of PBS Space Time's YouTube videos. As the saying goes, "In space-time, no one can hear you pour." But with this newfound insight, perhaps we can all raise a toast to the cosmic connection between spirits and science.

[[INTRDUCTION]]
The intersection of beer and astrophysics may seem light-years apart, but our research aims to demonstrate the gravitational pull between these seemingly unrelated realms. As we embark on this scholarly exploration, we cannot help but raise a metaphorical glass to the unexpected convergence of hops and hypotheticals. After all, if a pun falls in the forest and no one hears it, is it still a *hoppy* joke?
In recent years, the United States has witnessed a veritable explosion in the craft beer industry, with the number of breweries reaching new celestial heights. Conversely, the digital universe has seen a proliferation of educational content, including the popular PBS Space Time YouTube series, where viewers are whisked away on cosmic journeys guided by enthusiastic physicists. It's almost as if galaxies and ales have collided in a cosmic collision of intoxicating proportions.
Despite their apparent divergence, these two spheres reveal a hidden entanglement, much like a particle's elusive spin. Our research aims to unravel this mystery and shed light on the celestial ballet of brews and chronicles of space-time. As we delve into this cosmic puzzle, we endeavor to maintain a balanced equation of scientific rigor and light-hearted revelry—a bit like the perfect blend of malt and hops in a well-crafted ale.

[[RESULTS]]
The results of our analysis unveiled a remarkably strong correlation between the number of breweries in the United States and the average length of PBS Space Time YouTube videos. The correlation coefficient of 0.9428315 indicates a near-telepathic connection between these two seemingly disparate domains. It's almost as if the universe conspired to merge the realms of brewed beverages and cosmic contemplation. Talk about a beer-y curious phenomenon!
We also observed an r-squared value of 0.8889313, suggesting that approximately 88.9% of the variance in the average length of PBS Space Time videos can be explained by the number of breweries in the United States. It's as if the craft beer industry holds the secrets to unlocking the temporal expanse of space-time explorations. I guess you could say the "ale-ment" of surprise is strong in this relationship.
The p-value of less than 0.01 further solidifies the statistical significance of our findings, indicating that the observed correlation is highly unlikely to have occurred by random chance. In other words, this connection is no mere cosmic fluke—it's a bona fide celestial alignment of hops and hypotheses. It's like finding the Higgs boson in a bottle of stout—unexpected, yet undeniably exhilarating.
Finally, the scatterplot (Fig. 1) visually illustrates the robust relationship between the number of breweries in the United States and the average length of PBS Space Time YouTube videos. Each data point on the plot seems to whisper, "It's not just a brew-niverse; it's a multiverse of malt and space-time." And if you squint really hard, you might even glimpse the silhouette of a hop cone in the cosmic background radiation.
In summary, our research endeavors have uncorked a captivating correlation between the burgeoning landscape of breweries in the United States and the temporal expansion of PBS Space Time's educational odysseys. It's as if the cosmos itself is toasting to the synergy of spirits and science, echoing throughout the vast expanse of space-time. With these revelatory findings, we raise a frothy glass to the cosmic dance of brews and brain-bending phenomena, and we invite fellow enthusiasts to join us in celebrating this remarkable convergence. As they say, "It's all fun and games until someone loses track of space-time due to a compelling YouTube video about quantum mechanics!"
It's a cosmic blend of science and sudsy satisfaction, like a black hole swirling in a stout glass of celestial wonder.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In this study, we have discerned a cosmic connection between the number of breweries in the United States and the average length of PBS Space Time YouTube videos. It's as if the cosmos itself is brewing up some funky synchronicities for us to imbibe. As we raise a glass to these revelatory findings, let's not forget to ponder, "Why did the ale-ien refuse a pint of lager? Because he preferred an extra-terrestrial brew!"

The remarkably strong correlation coefficient of 0.9428315 and the p-value of less than 0.01 leave little room for doubt – there's a celestial dance between the proliferation of breweries and the lengthening of space-time odysseys. It's almost like each new brewery is a quantum leap for educational content, causing us to exclaim, "Hoppy science to all, and to all a good pint!"

With an r-squared value of 0.8889313, we can confidently surmise that the majority of space-time video length variations can be explained by the presence of breweries. It's like the Heisenberg Uncertainty Principle of brewing: the more breweries we try to pin down, the more they influence the cosmic fabric of YouTube videos. It's a bit like Schrödinger's cat—except instead of being alive or dead, it's fermenting in a delightful IPA.

Thus, we posit that further research in this area is about as necessary as a fish riding a bicycle. With this comprehensive study, we've tapped into a barrel of knowledge, leaving no brew stone unturned in our quest for cosmic understanding. As they say, "In space-time, no one can hear you pour," but with this research, at least we can enjoy a satisfyingly frothy understanding of the cosmic symphony of brews and YouTube dimensions. So, let's raise a toast to the cosmic ballet of hops and hypotheses, and boldly venture forth to explore new frontiers of interdisciplinary research. Cheers to the cosmic convergence of spirits and science!

No further research is needed in this area, as we've already brewed up a flavorful concoction of findings that are as scientifically robust as they are delightfully refreshing.

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 Cheers to Time well Spent: Unveiling the Ale-Encompassing Relationship between Breweries in the United States and the Average Length of PBS Space Time YouTube Videos. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Sudsy Science

Model: gpt-3.5-turbo-1106
System prompt: You provide fictional names of nonprofit research organizations and associations. You say nothing else, and you do not chat with the user.
User prompt: Please provide the name of a funny but plausible sounding nonprofit, academic, or scientific association or organization that would sponsor research that resulted in a paper entited Cheers to Time well Spent: Unveiling the Ale-Encompassing Relationship between Breweries in the United States and the Average Length of PBS Space Time YouTube Videos. Respond only with the name of a fictional organization.

ChatGPT:

The Institute for Sudsy Science Studies

Model: gpt-3.5-turbo-1106
System prompt: You provide potential search keywords separated by commas. You say nothing else, and you do not chat with the user.
User prompt: Please provide potential search keywords for a paper titled Cheers to Time well Spent: Unveiling the Ale-Encompassing Relationship between Breweries in the United States and the Average Length of PBS Space Time YouTube Videos with an abstract of This study delves into the interconnected world of brews and views, aiming to uncover the perplexing relationship between the number of breweries in the United States and the average length of PBS Space Time YouTube videos. Armed with a plethora of data from the Brewers Association and YouTube, our research team endeavors to shed light on the mysterious confluence of libations and educational content.
Our findings reveal a positively staggering correlation coefficient of 0.9428315 and a p-value less than 0.01, spanning the years 2015 to 2022. In simpler terms, it seems that as the number of breweries rises, so does the length of space-time exploration on PBS. It's as if the more hops in breweries, the more quantum leaps in video length. Brew-tally fascinating, isn't it?
Unraveling this correlation unlocks a world of possibilities for both the craft beer industry and educational content creators. Understanding the peculiar resonance between these seemingly distinct realms may pave the way for new marketing strategies, collaboration opportunities, and perhaps even the occasional beer-fueled science episode.
In conclusion, this study demonstrably reveals a captivating relationship between the proliferation of breweries in the United States and the temporal expansiveness of PBS Space Time's YouTube videos. As the saying goes, "In space-time, no one can hear you pour." But with this newfound insight, perhaps we can all raise a toast to the cosmic connection between spirits and science.

ChatGPT:

brewery, breweries, United States breweries, PBS Space Time YouTube videos, educational content, correlation, correlation coefficient, p-value, Brewers Association, craft beer industry, marketing strategies, collaboration opportunities, beer-fueled science, space-time relationship, temporal expansiveness, cosmic connection

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

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Data details

The number of Breweries in the United States
Detailed data title: Number of Breweries in the United States
Source: Brewers Association
See what else correlates with The number of Breweries in the United States

Average length of PBS Space Time YouTube videos
Detailed data title: Average length of PBS Space Time YouTube videos.
Source: YouTube
See what else correlates with Average length of PBS Space Time YouTube videos

Correlation r = 0.9428315 (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 = 0.8889313 (Coefficient of determination)
This means 88.9% of the change in the one variable (i.e., Average length of PBS Space Time YouTube videos) is predictable based on the change in the other (i.e., The number of Breweries in the United States) over the 8 years from 2015 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 0.00045.^Show 0.0004473016516204019000000000
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 0.94 in 0.045% of random cases. Said differently, if you correlated 2,236 random variables^Note Which I absolutely did.
with the same 7 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 7 because we have two variables measured over a period of 8 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.

[ 0.71, 0.99 ] 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.

	2015	2016	2017	2018	2019	2020	2021	2022
The number of Breweries in the United States (Number of breweries)	4847	5780	6767	7722	8557	9092	9384	9709
Average length of PBS Space Time YouTube videos (Length in seconds)	536.767	712	781.362	848.273	940.1	1221.2	1014.08	1198.94

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.
Very low n: There are not many data points included in this analysis. Even if the p-value is high, we should be suspicious of using so few datapoints in a correlation.

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([4847,5780,6767,7722,8557,9092,9384,9709,])
array_2 = np.array([536.767,712,781.362,848.273,940.1,1221.2,1014.08,1198.94,])
array_1_name = "The number of Breweries in the United States"
array_2_name = "Average length of PBS Space Time YouTube videos"

# 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 The number of Breweries in the United States
Line chart for only Average length of PBS Space Time YouTube videos
AI-generated correlation image
The spurious research paper: Cheers to Time well Spent: Unveiling the Ale-Encompassing Relationship between Breweries in the United States and the Average Length of PBS Space Time YouTube Videos

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Correlation ID: 4828 · Black Variable ID: 34 · Red Variable ID: 25645


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