Spurious correlation #4,999 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air quality in Bakersfield, California and the second variable is Google searches for 'ice bath'. The chart goes from 2004 to 2023, and the two variables track closely in value over that time.

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Air quality in Bakersfield, California and the second variable is Google searches for 'ice bath'. The chart goes from 2004 to 2023, and the two variables track closely in value over that time.

Download png, svg

AI explanation

As the air quality improved, the local residents suddenly had more energy and a zest for life. This led to a surge in interest in fitness and recovery methods, including taking ice baths. It's amazing what a little extra oxygen can do - Bakersfield became the coolest spot for chilling out, quite literally!

^{Show image generation prompt} Model: dalle-3
Prompt: Creating a serene and revitalizing scene with DALL-E-3, how about generating some refreshing imagery for the prompt? The new prompt could be: [ Scalar art ] A group of friends gathered by the local park in Bakersfield, California, taking turns to plunge into icy baths. The cool mist from the baths mingles with the fresh air, creating a refreshing and invigorating scene. The depiction should include only scenes, people, and objects, it should not include text or speech bubbles.

This image generation prompt was also generated by AI, using the following sequence:

Model: gpt-3.5-turbo-1106
System prompt: You select one of a few potential scene descriptors that seems to go along with the variables described. You respond only with the scene descriptions provided and say nothing else.
User prompt: Here are two variables: Air quality in Bakersfield, California and Google searches for 'ice bath'. Given these, which of the following image style descriptions seems most appropriate? Pick the one that seems to be related to one of the variables at hand. Please respond with only one of the following potential descriptions: Futuristic Scalar art Cute cartoon Charcoal Scalar art
ChatGPT: Scalar art

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both Air quality in Bakersfield, California and Google searches for 'ice bath', in the following situation: As the air quality improved, the local residents suddenly had more energy and a zest for life. This led to a surge in interest in fitness and recovery methods, including taking ice baths. It's amazing what a little extra oxygen can do - Bakersfield became the coolest spot for chilling out, quite literally!. Keep the description simple.
ChatGPT: The air in Bakersfield, California cleared up, leading to a distinct change in the atmosphere. People were out and about, feeling revitalized and full of energy. As they roamed around, the streets buzzed with conversation about fitness and recovery methods. A group of friends gathered by the local park, taking turns to plunge into icy baths, laughing and cheering each other on. The cool mist from the baths mingled with the fresh air, creating a refreshing and invigorating scene in the heart of Bakersfield.

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: [ Scalar art ] and depicting this scene: The air in Bakersfield, California cleared up, leading to a distinct change in the atmosphere. People were out and about, feeling revitalized and full of energy. As they roamed around, the streets buzzed with conversation about fitness and recovery methods. A group of friends gathered by the local park, taking turns to plunge into icy baths, laughing and cheering each other on. The cool mist from the baths mingled with the fresh air, creating a refreshing and invigorating scene in the heart of Bakersfield. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: Creating a serene and revitalizing scene with DALL-E-3, how about generating some refreshing imagery for the prompt? The new prompt could be: [ Scalar art ] A group of friends gathered by the local park in Bakersfield, California, taking turns to plunge into icy baths. The cool mist from the baths mingles with the fresh air, creating a refreshing and invigorating scene.

*Variations in the User Prompts from chart to chart are just the result of random number generation in Python. I wrote a few arrays of various styles and methods to ask questions to change up the results. Every time this site writes an explanation or generates an image, the script picks from each at random.

I sequence the requests into multiple prompts because I find GPT 3.5 to perform much better with short, well-managed contexts. Thus, I track the context directly in Python and only ask ChatGPT targeted questions.
^{Show prompt for explanation} Model: gpt-3.5-turbo-1106 (fine-tuned)
System prompt: You provide humorous responses in the form of plausible sounding explanations for correlations. You assume the correlation is causative for the purpose of the explanation even if it is ridiculous. You do not chat with the user, you only reply with the causal connection explanation and nothing else.
User prompt: Please make up a funny explanation for how an increase in Air quality in Bakersfield, California caused ice bath (Google searches for 'ice bath') to increase. Make it feel plausible.

AI academic paper

(Because p < 0.01)

Chilling Correlations: The Relationship Between Air Quality in Bakersfield, California, and Google Searches for 'Ice Bath'

The Journal of Quirky Climate Connections

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 Air quality in Bakersfield, California and Google searches for 'ice bath'. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences.

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

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

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

Here is the title and abstract of the paper:
[[TITLE]]
"Chilling Correlations: The Relationship Between Air Quality in Bakersfield, California, and Google Searches for 'Ice Bath'"

[[ABSTRACT]]
This paper examines the peculiar and unexpected connection between the air quality in Bakersfield, California, and the frequency of Google searches for 'ice bath'. Utilizing data from the Environmental Protection Agency and Google Trends, we applied rigorous statistical analysis to investigate this intriguing association. Our findings reveal a remarkably strong correlation coefficient of 0.8981417 and a statistically significant p-value of less than 0.01 for the period spanning from 2004 to 2023.

The results indicate that as air quality deteriorates in Bakersfield, there is a significant uptick in the number of Google searches related to 'ice bath'. This intriguing relationship suggests that individuals in Bakersfield may be seeking respite from the poor air quality by utilizing the cooling effects of an ice bath, providing a whole new meaning to the term "cooling off".

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
Air quality is a matter of significant public health concern, particularly in regions with high levels of air pollution. Bakersfield, California, situated in the heart of the San Joaquin Valley, is no stranger to this issue. With its location in one of the most air-polluted regions in the United States, Bakersfield has long grappled with challenges related to air quality. One might say they've had to "weather the smog storm" more than their fair share.
This study investigates a rather unexpected and seemingly incongruous phenomenon—the relationship between Bakersfield's air quality and the prevalence of Google searches for the term 'ice bath'. Yes, you heard that right. We are analyzing the intersection of respiratory health and indulgence in an activity typically associated with post-exercise recovery or dare we say, a "frosty" indulgence.
The research was driven by the desire to understand the motivation behind this peculiar correlation and to decipher whether individuals in Bakersfield were indeed turning to the chilly embrace of an ice bath as a response to the region's air quality. One might say that we are about to embark on a "chilling" exploration of unprecedented connections.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

Numerous studies have delved into the impact of air quality on public health and behavior. Smith et al. (2015) identified a clear link between air pollution and respiratory illnesses, while Doe and Jones (2018) conducted a comprehensive analysis of the psychological effects of poor air quality. Their findings provide a solid foundation for understanding the potential consequences of compromised air quality.

In "The Air Pollution Primer" by Clean Air Publishing, the authors emphasize the detrimental effects of air pollution on respiratory health and overall well-being. This significant contribution to the field sets the stage for comprehending the broader implications of poor air quality. One might say it provides a breath of fresh air in understanding the topic.

Turning our focus to more unconventional connections, "The Icy Obsession: Exploring the Cultural Significance of Cold Water Immersion" by Frosty Waters explores the historical and cultural significance of cold water immersion practices. While not directly related to air quality, the concepts discussed in this book shed light on the potential psychological and physiological factors that may drive individuals to seek cooling remedies.

In a surprising turn of events, "The Iceberg Mystery" by Chilly McFreeze presents a fictional narrative involving a community that turns to ice baths as a creative solution to combat air pollution. While this work is purely a product of imagination, the parallels it draws between air quality and the human pursuit of unconventional remedies cannot be ignored.

Further expanding the realms of literature to include unconventional sources, the back labels of various shampoo bottles were perused in search of any dispersed insights on the matter. Regrettably, no substantial evidence related to the correlation between air quality in Bakersfield and Google searches for 'ice bath' was found. However, it did provide an unexpectedly refreshing change of pace in the research process.

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 Air quality in Bakersfield, California and Google searches for 'ice bath'. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

Limit your response to 500 tokens.

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

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

[[TITLE]]
"Chilling Correlations: The Relationship Between Air Quality in Bakersfield, California, and Google Searches for 'Ice Bath'"

[[ABSTRACT]]
This paper examines the peculiar and unexpected connection between the air quality in Bakersfield, California, and the frequency of Google searches for 'ice bath'. Utilizing data from the Environmental Protection Agency and Google Trends, we applied rigorous statistical analysis to investigate this intriguing association. Our findings reveal a remarkably strong correlation coefficient of 0.8981417 and a statistically significant p-value of less than 0.01 for the period spanning from 2004 to 2023.

The results indicate that as air quality deteriorates in Bakersfield, there is a significant uptick in the number of Google searches related to 'ice bath'. This intriguing relationship suggests that individuals in Bakersfield may be seeking respite from the poor air quality by utilizing the cooling effects of an ice bath, providing a whole new meaning to the term "cooling off".

[[LITERATURE REVIEW]]
Numerous studies have delved into the impact of air quality on public health and behavior. Smith et al. (2015) identified a clear link between air pollution and respiratory illnesses, while Doe and Jones (2018) conducted a comprehensive analysis of the psychological effects of poor air quality. Their findings provide a solid foundation for understanding the potential consequences of compromised air quality.
In "The Air Pollution Primer" by Clean Air Publishing, the authors emphasize the detrimental effects of air pollution on respiratory health and overall well-being. This significant contribution to the field sets the stage for comprehending the broader implications of poor air quality. One might say it provides a breath of fresh air in understanding the topic.
Turning our focus to more unconventional connections, "The Icy Obsession: Exploring the Cultural Significance of Cold Water Immersion" by Frosty Waters explores the historical and cultural significance of cold water immersion practices. While not directly related to air quality, the concepts discussed in this book shed light on the potential psychological and physiological factors that may drive individuals to seek cooling remedies.
In a surprising turn of events, "The Iceberg Mystery" by Chilly McFreeze presents a fictional narrative involving a community that turns to ice baths as a creative solution to combat air pollution. While this work is purely a product of imagination, the parallels it draws between air quality and the human pursuit of unconventional remedies cannot be ignored.
Further expanding the realms of literature to include unconventional sources, the back labels of various shampoo bottles were perused in search of any dispersed insights on the matter. Regrettably, no substantial evidence related to the correlation between air quality in Bakersfield and Google searches for 'ice bath' was found. However, it did provide an unexpectedly refreshing change of pace in the research process.

[[RESULTS]]
The statistical analysis revealed a remarkably strong correlation between air quality in Bakersfield, California, and Google searches for 'ice bath', with a correlation coefficient of 0.8981417, indicating a robust relationship between the two variables. This substantial correlation suggests that as air quality worsened in Bakersfield, there was a notable increase in the frequency of Google searches for 'ice bath', hinting at a potentially chilling response to the environmental conditions.
The r-squared value of 0.8066585 further underscores the strength of the association, indicating that approximately 80.67% of the variance in the frequency of 'ice bath' searches can be explained by the changes in Bakersfield's air quality. One might say that the causal relationship here is as crystal clear as ice!
Moreover, the p-value of less than 0.01 provides strong evidence to reject the null hypothesis, signifying that the correlation observed is not due to random chance. In other words, this relationship is as solid as, well, ice.
Fig. 1 illustrates the compelling correlation between air quality in Bakersfield and Google searches for 'ice bath', showcasing a clear pattern that reinforces the strength of the statistical findings. One might say that the correlation depicted in the figure is as "cool" as a cucumber – or should we say an ice bath?

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The results of our study provide compelling evidence in support of the unexpected relationship between air quality in Bakersfield, California, and Google searches for 'ice bath'. Our findings align with prior research on the impact of air quality on human behavior, particularly in response to environmental stressors. The robust correlation coefficient and statistically significant p-value lend credence to the notion that deteriorating air quality in Bakersfield coincides with an increased interest in ice baths as a potential cooling remedy.

The startling connection between air quality and the appeal of ice baths underscores the multifaceted ways in which individuals may seek relief from environmental challenges. As postulated by Frosty Waters in "The Icy Obsession," the psychological and physiological effects of cold water immersion practices appear to manifest in response to environmental factors, providing a chilling yet effective coping mechanism. One might say that residents of Bakersfield are undoubtedly finding inventive ways to keep their cool amidst the less-than-ideal air quality.

Furthermore, the fictional narrative presented in "The Iceberg Mystery" by Chilly McFreeze, though creatively imagined, has inadvertently captured an element of truth in portraying the human inclination to seek out unconventional remedies in the face of environmental adversity. The uncanny parallels between the narrative and our empirical findings suggest that sometimes, truth may indeed be stranger than fiction. It seems that the idea of turning to ice baths as a response to air pollution is not merely a pipe dream but a tangible phenomenon supported by our rigorous statistical analysis.

While our investigation may have strayed into unconventional territories, such as perusing the back labels of shampoo bottles, it is precisely these unorthodox explorations that add a refreshing dimension to the research process. Despite the lack of substantive insights from shampoo bottles, this whimsical detour reinforces the notion that scholarly inquiry can benefit from the occasional unexpected diversion. One might say that it provides a splash of humor in an otherwise serious pursuit of knowledge.

In essence, this study not only sheds light on the intricate relationship between air quality and human behavior but also highlights the relevance of considering unconventional factors in empirical investigations. It invites scholars to embrace the unexpected, acknowledging that even seemingly unrelated phenomena can yield meaningful insights. One might say that in the world of research, staying open to the unconventional can lead to some truly "cool" discoveries.

Fig. 1, depicting the correlation between air quality in Bakersfield and Google searches for 'ice bath', serves as a visual testament to the compelling nature of the relationship uncovered in this study. The figure stands as a visual reminder that sometimes, correlations can be as clear as the ice in an ice bath – and just as chilling!

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 Air quality in Bakersfield, California and Google searches for 'ice bath'. You can't resist a good dad joke. Add a relevant dad joke related to the content every couple of sentences. Stay serious and dry most of the time, but then occasionally let your wit shine through.

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

Here are the title, abstract, introduction, and results sections.
[[TITLE]]
"Chilling Correlations: The Relationship Between Air Quality in Bakersfield, California, and Google Searches for 'Ice Bath'"

[[ABSTRACT]]
This paper examines the peculiar and unexpected connection between the air quality in Bakersfield, California, and the frequency of Google searches for 'ice bath'. Utilizing data from the Environmental Protection Agency and Google Trends, we applied rigorous statistical analysis to investigate this intriguing association. Our findings reveal a remarkably strong correlation coefficient of 0.8981417 and a statistically significant p-value of less than 0.01 for the period spanning from 2004 to 2023.

The results indicate that as air quality deteriorates in Bakersfield, there is a significant uptick in the number of Google searches related to 'ice bath'. This intriguing relationship suggests that individuals in Bakersfield may be seeking respite from the poor air quality by utilizing the cooling effects of an ice bath, providing a whole new meaning to the term "cooling off".

[[INTRDUCTION]]
Air quality is a matter of significant public health concern, particularly in regions with high levels of air pollution. Bakersfield, California, situated in the heart of the San Joaquin Valley, is no stranger to this issue. With its location in one of the most air-polluted regions in the United States, Bakersfield has long grappled with challenges related to air quality. One might say they've had to "weather the smog storm" more than their fair share.
This study investigates a rather unexpected and seemingly incongruous phenomenon—the relationship between Bakersfield's air quality and the prevalence of Google searches for the term 'ice bath'. Yes, you heard that right. We are analyzing the intersection of respiratory health and indulgence in an activity typically associated with post-exercise recovery or dare we say, a "frosty" indulgence.
The research was driven by the desire to understand the motivation behind this peculiar correlation and to decipher whether individuals in Bakersfield were indeed turning to the chilly embrace of an ice bath as a response to the region's air quality. One might say that we are about to embark on a "chilling" exploration of unprecedented connections.

[[RESULTS]]
The statistical analysis revealed a remarkably strong correlation between air quality in Bakersfield, California, and Google searches for 'ice bath', with a correlation coefficient of 0.8981417, indicating a robust relationship between the two variables. This substantial correlation suggests that as air quality worsened in Bakersfield, there was a notable increase in the frequency of Google searches for 'ice bath', hinting at a potentially chilling response to the environmental conditions.
The r-squared value of 0.8066585 further underscores the strength of the association, indicating that approximately 80.67% of the variance in the frequency of 'ice bath' searches can be explained by the changes in Bakersfield's air quality. One might say that the causal relationship here is as crystal clear as ice!
Moreover, the p-value of less than 0.01 provides strong evidence to reject the null hypothesis, signifying that the correlation observed is not due to random chance. In other words, this relationship is as solid as, well, ice.
Fig. 1 illustrates the compelling correlation between air quality in Bakersfield and Google searches for 'ice bath', showcasing a clear pattern that reinforces the strength of the statistical findings. One might say that the correlation depicted in the figure is as "cool" as a cucumber – or should we say an ice bath?

-------

Your response should start like this:

[[CONCLUSION]]

ChatGPT:

[[CONCLUSION]]

In conclusion, our investigation into the peculiar relationship between air quality in Bakersfield, California, and the frequency of Google searches for 'ice bath' has yielded intriguing findings. The robust correlation coefficient and the statistically significant p-value affirm the compelling nature of the association, suggesting that as air quality declines, there is a palpable surge in the interest in submerging oneself in an ice bath. One might say that the residents of Bakersfield are not just "chilling out," but literally "chilling in."

Furthermore, the r-squared value illustrates the substantial proportion of variance in 'ice bath' searches that can be attributed to changes in air quality, underscoring the substantial impact of environmental conditions on individuals' inclination to seek out icy remedies. It seems that when the going gets tough, the tough get freezing!

The findings of this study not only highlight the unexpected ways in which individuals may respond to environmental challenges but also raise intriguing questions about the potential therapeutic and psychological motivations behind seeking cold immersion in the face of air pollution. Perhaps the residents of Bakersfield are redefining the concept of "cool-headed" problem-solving.

Therefore, it is imperative for public health authorities and policymakers to consider the multifaceted implications of air quality on individuals' coping mechanisms. This research sheds light on the need to explore unconventional responses to environmental stressors, as the adoption of 'cool' interventions such as ice baths may serve as an unconventional yet effective strategy for mitigating the impact of poor air quality on well-being.

In light of these compelling findings, it is evident that no additional research in this area is needed. The results of this study have sufficiently iced the debate, leaving no room for further chilly contemplation on the matter.

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 Chilling Correlations: The Relationship Between Air Quality in Bakersfield, California, and Google Searches for 'Ice Bath'. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Quirky Climate Connections

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 Chilling Correlations: The Relationship Between Air Quality in Bakersfield, California, and Google Searches for 'Ice Bath'. Respond only with the name of a fictional organization.

ChatGPT:

Institute for Synchronized Climate and Wellness 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 Chilling Correlations: The Relationship Between Air Quality in Bakersfield, California, and Google Searches for 'Ice Bath' with an abstract of This paper examines the peculiar and unexpected connection between the air quality in Bakersfield, California, and the frequency of Google searches for 'ice bath'. Utilizing data from the Environmental Protection Agency and Google Trends, we applied rigorous statistical analysis to investigate this intriguing association. Our findings reveal a remarkably strong correlation coefficient of 0.8981417 and a statistically significant p-value of less than 0.01 for the period spanning from 2004 to 2023.
The results indicate that as air quality deteriorates in Bakersfield, there is a significant uptick in the number of Google searches related to 'ice bath'. This intriguing relationship suggests that individuals in Bakersfield may be seeking respite from the poor air quality by utilizing the cooling effects of an ice bath, providing a whole new meaning to the term "cooling off".

ChatGPT:

Bakersfield, California, air quality, Google searches, ice bath, correlation, association, environmental impact, health effects, cooling effects, pollution, respiratory health, Google Trends, statistical analysis, data analysis, EPA, search frequency, search trends

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

Random correlation

Discover a new correlation

View all correlations

View all research papers

Report an error

Data details

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

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

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

Correlation r = 0.8981417 (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 = 0.8066585 (Coefficient of determination)
This means 80.7% of the change in the one variable (i.e., Google searches for 'ice bath') is predictable based on the change in the other (i.e., Air quality in Bakersfield, California) over the 20 years from 2004 through 2023.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 7.71E-8.^Show 0.0000000770520012591772600000
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 0.9 in 7.71E-6% of random cases. Said differently, if you correlated 12,978,248 random variables^Note You don't actually need 12 million variables to find a correlation like this one. I don't have that many variables in my database. You can also correlate variables that are not independent. I do this a lot.

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

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

Just to be clear: I'm being completely transparent about the calculations. There is no math trickery. This is just how statistics shakes out when you calculate hundreds of millions of random correlations.
with the same 19 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 19 because we have two variables measured over a period of 20 years. It's just the number of years minus ( the number of variables minus one ), which in this case simplifies to the number of years minus one.
you would randomly expect to find a correlation as strong as this one.

[ 0.76, 0.96 ] 95% correlation confidence interval (using the Fisher z-transformation)
^{Read more about the confidence interval} The confidence interval is an estimate the range of the value of the correlation coefficient, using the correlation itself as an input. The values are meant to be the low and high end of the correlation coefficient with 95% confidence.

This one is a bit more complciated than the other calculations, but I include it because many people have been pushing for confidence intervals instead of p-value calculations (for example: NEJM. However, if you are dredging data, you can reliably find yourself in the 5%. That's my goal!

All values for the years included above: ^Note If I were being very sneaky, I could trim years from the beginning or end of the datasets to increase the correlation on some pairs of variables. I don't do that because there are already plenty of correlations in my database without monkeying with the years.

Still, sometimes one of the variables has more years of data available than the other. This page only shows the overlapping years. To see all the years, click on "See what else correlates with..." link above.

	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
Air quality in Bakersfield, California (Good air quality)	6.55738	12.8767	15.3425	8.21918	9.28962	10.6849	21.9178	17.8082	17.4863	9.58904	8.76712	12.0548	19.1257	20.8219	17.8082	32.6027	21.3115	17.8082	17.8082	72.0833
Google searches for 'ice bath' (Rel. search volume)	8.91667	8.75	8.08333	9	9.66667	9.83333	12.25	13.6667	17.1667	17.5	19	19.9167	20.3333	20.9167	21.8333	23.5	23.75	27.0833	38.3333	86.2

Why this works

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

Try it yourself

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

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

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

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

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

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

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

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

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

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

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

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

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

    return correlation, r_squared, p_value

# These are the arrays for the variables shown on this page, but you can modify them to be any two sets of numbers
array_1 = np.array([6.55738,12.8767,15.3425,8.21918,9.28962,10.6849,21.9178,17.8082,17.4863,9.58904,8.76712,12.0548,19.1257,20.8219,17.8082,32.6027,21.3115,17.8082,17.8082,72.0833,])
array_2 = np.array([8.91667,8.75,8.08333,9,9.66667,9.83333,12.25,13.6667,17.1667,17.5,19,19.9167,20.3333,20.9167,21.8333,23.5,23.75,27.0833,38.3333,86.2,])
array_1_name = "Air quality in Bakersfield, California"
array_2_name = "Google searches for 'ice bath'"

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

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

Reuseable content

You may re-use the images on this page for any purpose, even commercial purposes, without asking for permission. The only requirement is that you attribute Tyler Vigen. ^Note Attribution can take many different forms. If you leave the "tylervigen.com" link in the image, that satisfies it just fine. If you remove it and move it to a footnote, that's fine too. You can also just write "Charts courtesy of Tyler Vigen" at the bottom of an article.

You do not need to attribute "the spurious correlations website," and you don't even need to link here if you don't want to. I don't gain anything from pageviews. There are no ads on this site, there is nothing for sale, and I am not for hire.

For the record, I am just one person. Tyler Vigen, he/him/his. I do have degrees, but they should not go after my name unless you want to annoy my wife. If that is your goal, then go ahead and cite me as "Tyler Vigen, A.A. A.A.S. B.A. J.D." Otherwise it is just "Tyler Vigen."

When spoken, my last name is pronounced "vegan," like I don't eat meat.

Full license details.
For more on re-use permissions, or to get a signed release form, see tylervigen.com/permission.

Download images for these variables:

High resolution line chart ^Note The image linked here is a Scalable Vector Graphic (SVG). It is the highest resolution that is possible to achieve. It scales up beyond the size of the observable universe without pixelating. You do not need to email me asking if I have a higher resolution image. I do not. The physical limitations of our universe prevent me from providing you with an image that is any higher resolution than this one.

If you insert it into a PowerPoint presentation (a tool well-known for managing things that are the scale of the universe), you can right-click > "Ungroup" or "Create Shape" and then edit the lines and text directly. You can also change the colors this way.

Alternatively you can use a tool like Inkscape.
High resolution line chart, optimized for mobile
Alternative high resolution line chart
Scatterplot
Portable line chart (png)
Portable line chart (png), optimized for mobile
Line chart for only Air quality in Bakersfield, California
Line chart for only Google searches for 'ice bath'
AI-generated correlation image
The spurious research paper: Chilling Correlations: The Relationship Between Air Quality in Bakersfield, California, and Google Searches for 'Ice Bath'

View another random correlation

How fun was this correlation?

Your dedication to rating warms my heart!

Correlation ID: 4999 · Black Variable ID: 20317 · Red Variable ID: 1408


Problem variable:
Issue:
Additional details: Optional
Confirm you are a human: