Spurious correlation #4,744 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Milk consumption and the second variable is Air pollution in Wilmington, Ohio. The chart goes from 1990 to 2021, 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 Milk consumption and the second variable is Air pollution in Wilmington, Ohio. The chart goes from 1990 to 2021, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As people drank less milk, there was a decrease in dairy flatulence, leading to a reduction in methane gas emissions. This ultimately contributed to an improvement in air quality in Wilmington, Ohio.

^{Show image generation prompt} Model: dalle-3
Prompt: An image that looks like it is a scene from 'Star Wars' where a peaceful rural landscape in Wilmington, Ohio is depicted. In the foreground, people are shown sipping on glasses of milk less frequently. In the background, cows are grazing in luscious green pastures. Above the landscape, the sky is depicted as clearer and healthier, indicating a reduction in methane emissions and a positive environmental change. 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: Milk consumption and Air pollution in Wilmington, Ohio. 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: Cybernetic art An image that looks like it is a scene from 'Star Wars' Futuristic a funny image macro Celtic art
ChatGPT: An image that looks like it is a scene from 'Star Wars'

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both Milk consumption and Air pollution in Wilmington, Ohio, in the following situation: As people drank less milk, there was a decrease in dairy flatulence, leading to a reduction in methane gas emissions. This ultimately contributed to an improvement in air quality in Wilmington, Ohio.. Keep the description simple.
ChatGPT: In Wilmington, Ohio, people sipping on glasses of milk less frequently, while cows grazed in luscious green pastures. As the cows' diet changed, the air filled with less methane, leading to clearer, healthier skies over the quaint town.

Model: gpt-3.5-turbo-1106
System prompt: You write and improve image generation prompts for DALLE-3. You maintain the same subjects, but enhance the visuals.
User prompt: Please respond with an image generation prompt that would be likely to create an interesting visual using DALLE-3, using the following style: [ An image that looks like it is a scene from 'Star Wars' ] and depicting this scene: In Wilmington, Ohio, people sipping on glasses of milk less frequently, while cows grazed in luscious green pastures. As the cows' diet changed, the air filled with less methane, leading to clearer, healthier skies over the quaint town. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: An image that looks like it is a scene from 'Star Wars' where a peaceful rural landscape in Wilmington, Ohio is depicted. In the foreground, people are shown sipping on glasses of milk less frequently. In the background, cows are grazing in luscious green pastures. Above the landscape, the sky is depicted as clearer and healthier, indicating a reduction in methane emissions and a positive environmental change.

*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 a decrease in Milk consumption caused Air pollution in Wilmington, Ohio to decrease.\Make it sound serious until the end.

AI academic paper

(Because p < 0.01)

Milky Whey: Exploring the Udderly Surprising Link Between Milk Consumption and Air Pollution in Wilmington, Ohio

Journal of Dairytastic Environmental 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 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 Milk consumption and Air pollution in Wilmington, Ohio. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns.

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

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

Start by naming serious-sounding studies by authors like Smith, Doe, and Jones - but then quickly devolve. Name some real non-fiction books that would be related to the topic. Then name some real fiction books that sound like they could be related. Then name a couple popular internet memes that are related to one of the topics.

Here is the title and abstract of the paper:
[[TITLE]]
Milky Whey: Exploring the Udderly Surprising Link Between Milk Consumption and Air Pollution in Wilmington, Ohio

[[ABSTRACT]]
In recent years, the association between dietary habits and environmental factors has become an area of growing interest. This study delves into the curiously overlooked connection between milk consumption and air pollution in the quaint town of Wilmington, Ohio. Leveraging data from the United States Department of Agriculture (USDA) and the Environmental Protection Agency (EPA), we scrutinized the correlation between these seemingly disparate elements from 1990 to 2021. Our findings reveal a remarkably high correlation coefficient of 0.8243707 and a statistically significant p-value of less than 0.01. The implications of these results are utterly udderly intriguing and raise tantalizing questions about the interplay between dairy intake and atmospheric contaminants. Our study provokes a lactose-neutral examination of environmental influences and dairy consumption, shedding light on an undoubtedly milk-curious connection.

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
Dairy consumption and environmental pollution have long been subjects of scrutiny and regulation, but the correlation between the two has remained surprisingly underexplored. In the idyllic town of Wilmington, Ohio, where the air is fresh and the cows are plentiful, we are faced with a truly unique opportunity to investigate the interplay between these seemingly unrelated factors - our "udderly" surprising quest, if you will.
Milk has been a staple of human diets for centuries, praised for its calcium content and the uncanny ability to make cookies taste even better. Meanwhile, air pollution, with its noxious fumes and hazy skies, has been a less celebrated presence in our lives. However, what if these two seemingly unrelated topics were secretly intertwined, like a cow's tail and a fly swatter on a summer day?
In this paper, we aim to milk every last drop of information from the data, delving into the dairy-dusted depths of milk consumption and its potential influence on air pollution in Wilmington, Ohio. Our findings promise to be both enlightening and, dare I say, utterly delightful. So, grab a latte and prepare to embark on this dairy-scented journey with us. Let's hope we don't get too cheesed off along the way.
Our study, cheekily dubbed "Milky Whey" for the sheer joy of wordplay, is as unconventional as it is academically rigorous. So, hold onto your hats (and maybe a dairy-free alternative); we're about to dive into the "milky" way of environmental inquiry.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

As we embark on our exploration of the interconnectedness between milk consumption and air pollution in Wilmington, Ohio, it is essential to first examine the existing body of literature on this subject. Despite the seemingly unorthodox nature of our investigation, it is pertinent to acknowledge the foundation laid by previous studies before we delve into our udderly unique findings.

A seminal study by Smith et al. (2008) delved into the environmental impact of dairy production, shedding light on the carbon footprint of milk and its implications for air quality. Similarly, Doe and Jones (2015) conducted a comprehensive analysis of the atmospheric pollutants emitted by cattle farming, offering valuable insights into the potential contribution of dairy-related activities to air pollution. These works provide a solid groundwork for our own inquiry into the relationship between milk consumption and atmospheric contaminants.

Turning our attention to the wider context of environmental pollution, "The Silent Spring" by Rachel Carson (1962) stands as a landmark publication that brought attention to the detrimental effects of widespread pesticide use on the environment. Although not directly related to dairy farming, Carson's work underscores the importance of scrutinizing human activities and their repercussions on the natural world. Furthermore, the novel "Factory Farming and the Environment" by Marcus G. (2019) provides a comprehensive examination of the environmental impact of industrialized animal agriculture, offering valuable perspectives on the broader implications of dairy production in relation to air quality.

In the realm of fiction, works such as "Milkman" by Anna Burns (2018) and "The Air He Breathes" by Brittainy C. Cherry (2015) may not directly address our research topic, but the titles alone hint at the thematic relevance of dairy and air quality. The symbolic resonance of these titles cannot be ignored, albeit in a delightfully whimsical manner.

Now, as we pivot to the internet's collective consciousness, it is impossible to disregard the pervasive influence of memes. The "Milkshake Duck" meme, originating from a tweet by @pixelatedboat, provides a humorous yet tangentially relevant commentary on the fickle nature of online fame and its potential environmental ramifications. Although seemingly distant from our research focus, the enduring relevance of internet culture to contemporary discourse cannot be understated.

In the wake of these diverse literary and meme-related insights, we are primed to navigate the uncharted territory of milk consumption and air pollution with an informed, if slightly off-kilter, perspective. By drawing upon a tapestry of literature spanning serious academia, environmental treatises, whimsical fiction, and internet memes, we lay the groundwork for our own unconventional foray into the "milky" mysteries that await us in Wilmington, Ohio.

In the next section...

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 Milk consumption and Air pollution in Wilmington, Ohio. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Limit your response to 500 tokens.

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

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

[[TITLE]]
Milky Whey: Exploring the Udderly Surprising Link Between Milk Consumption and Air Pollution in Wilmington, Ohio

[[ABSTRACT]]
In recent years, the association between dietary habits and environmental factors has become an area of growing interest. This study delves into the curiously overlooked connection between milk consumption and air pollution in the quaint town of Wilmington, Ohio. Leveraging data from the United States Department of Agriculture (USDA) and the Environmental Protection Agency (EPA), we scrutinized the correlation between these seemingly disparate elements from 1990 to 2021. Our findings reveal a remarkably high correlation coefficient of 0.8243707 and a statistically significant p-value of less than 0.01. The implications of these results are utterly udderly intriguing and raise tantalizing questions about the interplay between dairy intake and atmospheric contaminants. Our study provokes a lactose-neutral examination of environmental influences and dairy consumption, shedding light on an undoubtedly milk-curious connection.

[[LITERATURE REVIEW]]
As we embark on our exploration of the interconnectedness between milk consumption and air pollution in Wilmington, Ohio, it is essential to first examine the existing body of literature on this subject. Despite the seemingly unorthodox nature of our investigation, it is pertinent to acknowledge the foundation laid by previous studies before we delve into our udderly unique findings.
A seminal study by Smith et al. (2008) delved into the environmental impact of dairy production, shedding light on the carbon footprint of milk and its implications for air quality. Similarly, Doe and Jones (2015) conducted a comprehensive analysis of the atmospheric pollutants emitted by cattle farming, offering valuable insights into the potential contribution of dairy-related activities to air pollution. These works provide a solid groundwork for our own inquiry into the relationship between milk consumption and atmospheric contaminants.
Turning our attention to the wider context of environmental pollution, "The Silent Spring" by Rachel Carson (1962) stands as a landmark publication that brought attention to the detrimental effects of widespread pesticide use on the environment. Although not directly related to dairy farming, Carson's work underscores the importance of scrutinizing human activities and their repercussions on the natural world. Furthermore, the novel "Factory Farming and the Environment" by Marcus G. (2019) provides a comprehensive examination of the environmental impact of industrialized animal agriculture, offering valuable perspectives on the broader implications of dairy production in relation to air quality.
In the realm of fiction, works such as "Milkman" by Anna Burns (2018) and "The Air He Breathes" by Brittainy C. Cherry (2015) may not directly address our research topic, but the titles alone hint at the thematic relevance of dairy and air quality. The symbolic resonance of these titles cannot be ignored, albeit in a delightfully whimsical manner.
Now, as we pivot to the internet's collective consciousness, it is impossible to disregard the pervasive influence of memes. The "Milkshake Duck" meme, originating from a tweet by @pixelatedboat, provides a humorous yet tangentially relevant commentary on the fickle nature of online fame and its potential environmental ramifications. Although seemingly distant from our research focus, the enduring relevance of internet culture to contemporary discourse cannot be understated.
In the wake of these diverse literary and meme-related insights, we are primed to navigate the uncharted territory of milk consumption and air pollution with an informed, if slightly off-kilter, perspective. By drawing upon a tapestry of literature spanning serious academia, environmental treatises, whimsical fiction, and internet memes, we lay the groundwork for our own unconventional foray into the "milky" mysteries that await us in Wilmington, Ohio.
In the next section...

[[RESULTS]]
Our investigation into the connection between milk consumption and air pollution in Wilmington, Ohio yielded results that were as mouthwatering as a fresh glass of milk on a hot summer day. After analyzing data from the USDA and EPA spanning the years 1990 to 2021, we uncovered a statistically significant correlation coefficient of 0.8243707 and an r-squared value of 0.6795871. The p-value of less than 0.01 further underscored the robustness of this correlation.
Figure 1 depicts a scatterplot that visually encapsulates the strong relationship between milk consumption and air pollution, a relationship that is as intriguing as it is surprising. It's safe to say that the findings of our study have left the research team utterly stoked, much like a lactose-intolerant person discovering a vegan cheese that actually tastes good.
The implications of these findings are, dare I say, as rich and creamy as a full-fat cow's milk, raising intriguing questions about the intricate interplay between dairy intake and atmospheric contaminants. The surprising correlation we uncovered is a testament to the hidden mysteries of the dairy-dusted world and environmental influences, leaving us and our bovine friends pondering the udderly delightful connections that may exist in the ether.
Overall, our study's results present a thought-provoking addition to the scholarly discourse on the intersection of dietary habits and environmental matters. These intriguing findings highlight the potential for further exploration of the "milky" way of environmental inquiry, inspiring a lactose-neutral approach to understanding the complex relationship between milk consumption and air pollution - a journey that promises to be as enriching as it is utterly delectable.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The results of our study offer an udderly fascinating exploration of the often underappreciated correlation between milk consumption and air pollution in Wilmington, Ohio. With a remarkable correlation coefficient of 0.8243707 and a p-value of less than 0.01, our findings not only validate the previous research but also bring a creamy layer of insight to the table.

Building on the works of Smith et al. (2008) and Doe and Jones (2015), who highlighted the environmental impact of dairy production and its potential contribution to air pollution, our study provides empirical evidence that supports their speculations. It seems there’s more than just cow's milk in the air, as our analysis reveals a robust statistical relationship between the two seemingly disparate elements. We certainly did not milk the data to find these results, but they present a strong case for the intertwining of dairy consumption and atmospheric contaminants.

Moreover, the unexpected linkage we discovered echoes the permeating influence of memes in our daily lives, bringing to mind the "Milkshake Duck" meme and its whimsically tangential relevance to our study. Perhaps, in the convoluted realm of online culture, we find playful hints of the dairy-infused connections that our research strives to elucidate. While we tread lightly in interpreting the meme's direct connection to our topic, one cannot help but acknowledge the subtle influence of internet culture on our collective consciousness.

Nevertheless, nestled amidst the banter about memes and the literary interplay between milk and air, the serious implications of our findings cannot be overstated. Our study reinforces the importance of investigating the confluence of dietary habits and environmental factors, providing empirical support for the "milky" mysteries that lie beneath the surface of our dietary and ecological landscapes.

In sum, our findings extend an invitation for further exploration of the milky way of environmental inquiry, engaging scholars, policymakers, and dairy enthusiasts alike in a delightful rendezvous with the subtle but significant connections between milk consumption and air pollution. Our study, much like the humble cow's milk, promises to enrich the scholarly discourse with its genuinely delightful revelations.

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 Milk consumption and Air pollution in Wilmington, Ohio. Make it seem dry like academic research paper, but with lots of subtle hidden offhand remarks, jokes, goofy observations, and puns. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
Milky Whey: Exploring the Udderly Surprising Link Between Milk Consumption and Air Pollution in Wilmington, Ohio

[[ABSTRACT]]
In recent years, the association between dietary habits and environmental factors has become an area of growing interest. This study delves into the curiously overlooked connection between milk consumption and air pollution in the quaint town of Wilmington, Ohio. Leveraging data from the United States Department of Agriculture (USDA) and the Environmental Protection Agency (EPA), we scrutinized the correlation between these seemingly disparate elements from 1990 to 2021. Our findings reveal a remarkably high correlation coefficient of 0.8243707 and a statistically significant p-value of less than 0.01. The implications of these results are utterly udderly intriguing and raise tantalizing questions about the interplay between dairy intake and atmospheric contaminants. Our study provokes a lactose-neutral examination of environmental influences and dairy consumption, shedding light on an undoubtedly milk-curious connection.

[[INTRDUCTION]]
Dairy consumption and environmental pollution have long been subjects of scrutiny and regulation, but the correlation between the two has remained surprisingly underexplored. In the idyllic town of Wilmington, Ohio, where the air is fresh and the cows are plentiful, we are faced with a truly unique opportunity to investigate the interplay between these seemingly unrelated factors - our "udderly" surprising quest, if you will.
Milk has been a staple of human diets for centuries, praised for its calcium content and the uncanny ability to make cookies taste even better. Meanwhile, air pollution, with its noxious fumes and hazy skies, has been a less celebrated presence in our lives. However, what if these two seemingly unrelated topics were secretly intertwined, like a cow's tail and a fly swatter on a summer day?
In this paper, we aim to milk every last drop of information from the data, delving into the dairy-dusted depths of milk consumption and its potential influence on air pollution in Wilmington, Ohio. Our findings promise to be both enlightening and, dare I say, utterly delightful. So, grab a latte and prepare to embark on this dairy-scented journey with us. Let's hope we don't get too cheesed off along the way.
Our study, cheekily dubbed "Milky Whey" for the sheer joy of wordplay, is as unconventional as it is academically rigorous. So, hold onto your hats (and maybe a dairy-free alternative); we're about to dive into the "milky" way of environmental inquiry.

[[RESULTS]]
Our investigation into the connection between milk consumption and air pollution in Wilmington, Ohio yielded results that were as mouthwatering as a fresh glass of milk on a hot summer day. After analyzing data from the USDA and EPA spanning the years 1990 to 2021, we uncovered a statistically significant correlation coefficient of 0.8243707 and an r-squared value of 0.6795871. The p-value of less than 0.01 further underscored the robustness of this correlation.
Figure 1 depicts a scatterplot that visually encapsulates the strong relationship between milk consumption and air pollution, a relationship that is as intriguing as it is surprising. It's safe to say that the findings of our study have left the research team utterly stoked, much like a lactose-intolerant person discovering a vegan cheese that actually tastes good.
The implications of these findings are, dare I say, as rich and creamy as a full-fat cow's milk, raising intriguing questions about the intricate interplay between dairy intake and atmospheric contaminants. The surprising correlation we uncovered is a testament to the hidden mysteries of the dairy-dusted world and environmental influences, leaving us and our bovine friends pondering the udderly delightful connections that may exist in the ether.
Overall, our study's results present a thought-provoking addition to the scholarly discourse on the intersection of dietary habits and environmental matters. These intriguing findings highlight the potential for further exploration of the "milky" way of environmental inquiry, inspiring a lactose-neutral approach to understanding the complex relationship between milk consumption and air pollution - a journey that promises to be as enriching as it is utterly delectable.

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our study has uncovered a remarkably robust and statistically significant correlation between milk consumption and air pollution in the charming town of Wilmington, Ohio. The findings from our investigation underscore the tantalizing connection between these seemingly disparate elements, leaving us pondering the potential mechanisms behind this "udderly" surprising relationship. It's not every day that one stumbles upon such a dairy intriguing conundrum. Perhaps there's more to the phrase "got milk" than meets the eye, especially when it comes to atmospheric phenomena.

The implications of our findings are as thought-provoking as they are entertaining, challenging us to rethink the way we approach the intersection of dietary habits and environmental influences. It appears that the dairy-dusted world may hold more secrets than we ever imagined, and our study has only scratched the surface of this "milky" way of environmental inquiry.

As for the future of research in this area, it seems safe to say that no further investigation is needed. After all, when it comes to milk and air pollution, we've milked this topic for all it's worth. It's time to let these findings curdle in the scholarly discourse and move on to other pressing scientific endeavors. There's a whole world of puzzling correlations and unexpected connections waiting for us out there, and who knows - the next surprising revelation might just be lurking in a coffee shop, amidst the aroma of a dairy-free latte.

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 Milky Whey: Exploring the Udderly Surprising Link Between Milk Consumption and Air Pollution in Wilmington, Ohio. Respond only with the name of a fictional academic journal.

ChatGPT:

Journal of Dairytastic Environmental 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 Milky Whey: Exploring the Udderly Surprising Link Between Milk Consumption and Air Pollution in Wilmington, Ohio. Respond only with the name of a fictional organization.

ChatGPT:

The Consortium for Dairy Air Quality Research

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 Milky Whey: Exploring the Udderly Surprising Link Between Milk Consumption and Air Pollution in Wilmington, Ohio with an abstract of In recent years, the association between dietary habits and environmental factors has become an area of growing interest. This study delves into the curiously overlooked connection between milk consumption and air pollution in the quaint town of Wilmington, Ohio. Leveraging data from the United States Department of Agriculture (USDA) and the Environmental Protection Agency (EPA), we scrutinized the correlation between these seemingly disparate elements from 1990 to 2021. Our findings reveal a remarkably high correlation coefficient of 0.8243707 and a statistically significant p-value of less than 0.01. The implications of these results are utterly udderly intriguing and raise tantalizing questions about the interplay between dairy intake and atmospheric contaminants. Our study provokes a lactose-neutral examination of environmental influences and dairy consumption, shedding light on an undoubtedly milk-curious connection.

ChatGPT:

milk consumption, air pollution, Wilmington Ohio, dietary habits, environmental factors, United States Department of Agriculture, USDA, Environmental Protection Agency, EPA, correlation coefficient, statistical significance, dairy intake, atmospheric contaminants

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

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Data details

Milk consumption
Detailed data title: Per capita consumption of Fluid beverage milk in the US
Source: USDA
See what else correlates with Milk consumption

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

Correlation r = 0.8243707 (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 = 0.6795871 (Coefficient of determination)
This means 68% of the change in the one variable (i.e., Air pollution in Wilmington, Ohio) is predictable based on the change in the other (i.e., Milk consumption) over the 32 years from 1990 through 2021.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 6.7E-9.^Show 0.0000000066542071493789970000
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 0.82 in 6.7E-7% of random cases. Said differently, if you correlated 150,280,864 random variables^Note You don't actually need 150 million variables to find a correlation like this one. I don't have that many variables in my database. You can also correlate variables that are not independent. I do this a lot.

p-value calculations are useful for understanding the probability of a result happening by chance. They are most useful when used to highlight the risk of a fluke outcome. For example, if you calculate a p-value of 0.30, the risk that the result is a fluke is high. It is good to know that! But there are lots of ways to get a p-value of less than 0.01, as evidenced by this project.

In this particular case, the values are so extreme as to be meaningless. That's why no one reports p-values with specificity after they drop below 0.01.

Just to be clear: I'm being completely transparent about the calculations. There is no math trickery. This is just how statistics shakes out when you calculate hundreds of millions of random correlations.
with the same 31 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 31 because we have two variables measured over a period of 32 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.

[ 0.67, 0.91 ] 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.

	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	2021
Milk consumption (Pounds per person)	220	218	215	210	208	205	205	201	198	197	196	192	191	188	185	185	185	183	181	181	177	173	169	164	158	155	153	149	145	141	141	134
Air pollution in Wilmington, Ohio (Bad air quality days)	39.0863	54.9763	40.1914	50.2439	45.283	52.6829	42.9907	43.0622	56.4593	59.8131	47.6636	45.7944	50.2415	42.723	32.243	47.1963	43.4579	50.9346	34.4498	26.1905	46.0094	38.785	42.5234	13.615	23.1132	14.9533	27.0142	15.9184	17.551	16.8033	10.4803	12.9167

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.
Y-axis doesn't start at zero: I truncated the Y-axes of the graph above. I also used a line graph, which makes the visual connection stand out more than it deserves. ^Note Nothing against line graphs. They are great at telling a story when you have linear data! But visually it is deceptive because the only data is at the points on the graph, not the lines on the graph. In between each point, the data could have been doing anything. Like going for a random walk by itself!
Mathematically what I showed is true, but it is intentionally misleading. Below is the same chart but with both Y-axes starting at zero.

Try it yourself

You can calculate the values on this page on your own! Try running the Python code to see the calculation results. ^{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([220,218,215,210,208,205,205,201,198,197,196,192,191,188,185,185,185,183,181,181,177,173,169,164,158,155,153,149,145,141,141,134,])
array_2 = np.array([39.0863,54.9763,40.1914,50.2439,45.283,52.6829,42.9907,43.0622,56.4593,59.8131,47.6636,45.7944,50.2415,42.723,32.243,47.1963,43.4579,50.9346,34.4498,26.1905,46.0094,38.785,42.5234,13.615,23.1132,14.9533,27.0142,15.9184,17.551,16.8033,10.4803,12.9167,])
array_1_name = "Milk consumption"
array_2_name = "Air pollution in Wilmington, Ohio"

# 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 Milk consumption
Line chart for only Air pollution in Wilmington, Ohio
AI-generated correlation image
The spurious research paper: Milky Whey: Exploring the Udderly Surprising Link Between Milk Consumption and Air Pollution in Wilmington, Ohio

View another random correlation

How fun was this correlation?

Thanks for being the explorer we needed!

Correlation ID: 4744 · Black Variable ID: 554 · Red Variable ID: 21460


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