Spurious correlation #1,730 · View random
A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is Master's degrees awarded in law enforcement and firefighting and the second variable is Gender pay gap in the U.S.. The chart goes from 2012 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 Master's degrees awarded in law enforcement and firefighting and the second variable is Gender pay gap in the U.S.. The chart goes from 2012 to 2021, and the two variables track closely in value over that time.

Download png, svg

AI explanation

Master's of Disaster: As the number of M.A. holders in homeland security, law enforcement, and firefighting surged, so did the gender pay gap. It seems that instead of extinguishing inequality, these degrees were just adding fuel to the fire. Perhaps they were simply too adept at maintaining the status quo, creating a fiery gap in wages between male and female professionals. It's a heated issue, but it looks like these master's programs might need to work on promoting equal pay for blaze! For now, it's clear that when it comes to the gender pay gap, these master's degrees might be part of the problem rather than the solution.

^{Show image generation prompt} Model: dalle-3
Prompt: [ A photo-realistic image ] of a graduation ceremony is taking place in a large outdoor amphitheater, with a diverse group of students holding Master's degrees in Homeland Security, Law Enforcement, and Firefighting. The students are wearing caps and gowns, with beaming smiles as they receive their diplomas. Notably, the male graduates are being handed larger-sized diplomas, while their female counterparts receive smaller-sized diplomas, symbolizing the gender pay gap in the U.S. The background is filled with cheering family members and faculty, all captured in vivid detail and rich colors. For the DALL·E-3 image prompt, the focus is on capturing the emotional and visual impact of the scene, highlighting the diversity of the students, the significance of their achievements, and the powerful statement on gender inequality reflected in the diploma sizes. The result should visually convey the momentous occasion while effectively addressing the social issue within the graduation setting. 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: Master's degrees awarded in Homeland security, law enforcement, and firefighting and Gender pay gap in the U.S.. 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: Vaporwave An image that looks like it is a scene from 'Star Wars' Low poly A photo-realistic image Cubism
ChatGPT: A photo-realistic image

Model: gpt-3.5-turbo-1106
System prompt: You describe simple visual scenes that depict the two variables stated. You combine both variables into one scene.
User prompt: Please describe a visual scene that prominently depicts both Master's degrees awarded in Homeland security, law enforcement, and firefighting and Gender pay gap in the U.S. together. Keep the description simple.
ChatGPT: A graduation ceremony is taking place, with a diverse group of students holding Master's degrees in Homeland Security, Law Enforcement, and Firefighting. Among them, the male graduates are being handed larger-sized diplomas, while their female counterparts receive smaller-sized diplomas, symbolizing the gender pay gap in the U.S.

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 photo-realistic image ] and depicting this scene: A graduation ceremony is taking place, with a diverse group of students holding Master's degrees in Homeland Security, Law Enforcement, and Firefighting. Among them, the male graduates are being handed larger-sized diplomas, while their female counterparts receive smaller-sized diplomas, symbolizing the gender pay gap in the U.S. Keep the visual depiction simple. Do not include any words or speech bubbles.
ChatGPT: [ A photo-realistic image ] of a graduation ceremony is taking place in a large outdoor amphitheater, with a diverse group of students holding Master's degrees in Homeland Security, Law Enforcement, and Firefighting. The students are wearing caps and gowns, with beaming smiles as they receive their diplomas. Notably, the male graduates are being handed larger-sized diplomas, while their female counterparts receive smaller-sized diplomas, symbolizing the gender pay gap in the U.S. The background is filled with cheering family members and faculty, all captured in vivid detail and rich colors. For the DALL·E-3 image prompt, the focus is on capturing the emotional and visual impact of the scene, highlighting the diversity of the students, the significance of their achievements, and the powerful statement on gender inequality reflected in the diploma sizes. The result should visually convey the momentous occasion while effectively addressing the social issue within the graduation setting.

*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 Master's degrees awarded in Homeland security, law enforcement, and firefighting caused Gender pay gap in the U.S. to increase. Include one good pun.

AI academic paper

(Because p < 0.01)

Securing the Bag: An Investigation into the Link between Master's Degrees in Homeland Security, Law Enforcement, and Firefighting and the Gender Pay Gap in the United States

The Journal of Gendered Occupational Economics

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 Master's degrees awarded in Homeland security, law enforcement, and firefighting and Gender pay gap in the U.S.. 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 cite some social media posts you read that seem to be related.

Here is the title and abstract of the paper:
[[TITLE]]
"Securing the Bag: An Investigation into the Link between Master's Degrees in Homeland Security, Law Enforcement, and Firefighting and the Gender Pay Gap in the United States"

[[ABSTRACT]]
This paper investigates the relationship between the number of Master's degrees awarded in Homeland Security, Law Enforcement, and Firefighting and the gender pay gap in the United States. Using data from the National Center for Education Statistics and Statista for the years 2012 to 2021, our research team examined the correlation coefficient and p-value to unravel this intriguing connection.

Between 2012 and 2021, we observed a remarkably strong correlation coefficient of 0.9803335 and a p-value of less than 0.01, signifying a robust statistical relationship. Our findings suggest that the higher the number of Master's degrees conferred in these fields, the wider the gender pay gap tends to be. It appears that the quest for national security and public safety might be inadvertently contributing to gender-based disparities in compensation.

Now, let's not jump to conclusions, but it seems that while these professionals are focused on extinguishing fires and enforcing the law, they may be unintentionally fueling the flames of the gender pay gap. Keep your hose and your earnings in check, folks!

-------

And here is the introduction section that led to this literature review:
[[INTRODUCTION]]
The gender pay gap has been a longstanding issue in labor markets across various industries, reflecting disparities in earnings between men and women. While extensive research has examined factors contributing to this phenomenon, such as educational attainment, occupational segregation, and discrimination, the influence of Master's degrees awarded in Homeland Security, Law Enforcement, and Firefighting on the gender pay gap remains relatively unexplored. This knowledge gap warrants investigation to comprehensively understand the dynamics at play.
One might say these fields are "firing" on all cylinders, but are they "enforcing" or "extinguishing" pay parity between genders? It's time to "arrest" these underlying trends and "put out the fire" of inequality.

-------

Your response should start like this:

[[LITERATURE REVIEW]]

ChatGPT:
[[LITERATURE REVIEW]]

The findings of Smith et al. (2015) indicate a positive correlation between the number of Master's degrees awarded in Homeland Security, Law Enforcement, and Firefighting and the gender pay gap in the United States. Smith et al. suggest that as the number of Master's degrees in these fields increases, the gender pay gap widens. Such evidence raises questions about the unintended consequences of educational pursuits in these areas.

Now, let's "arrest" any premature assumptions about these findings, but it seems like the gender pay gap might be in need of some "firefighting" of its own. If we're not careful, we might have to call in the "homeland security" team to address this issue!

In "Doe" (2018), the authors similarly observe a significant relationship between educational attainment in homeland security, law enforcement, and firefighting and gender pay disparities. Doe highlights the need for further investigation into the underlying mechanisms driving this association, emphasizing the potential implications for workforce equality and fairness.

It appears that while these professionals aim to protect and serve, they might also unwittingly be serving up some gender pay gap disparities. As firefighting techniques evolve, perhaps so should the strategies for achieving equal pay.

Turning to the real-world impact, a study by Jones (2019) underscores the tangible effects of these trends on the labor market. Jones' work reveals a concerning pattern: as the number of Master's degrees awarded in public safety and security fields rises, the gender pay gap widens, reinforcing the notion that there may be systemic issues at play.

It seems we may need to think about "putting out the fire" of the gender pay gap with more than just water and foam. Maybe a sprinkle of gender equality sensitivity training and a dash of fair compensation strategies is in order!

In "Lorem and Ipsum" (2020), the authors provide further evidence of the link between Master's degrees in these fields and gender-based wage disparities. This study emphasizes the need for policymakers and educational institutions to consider the broader implications of educational choices on societal equality and economic welfare.

One could say these findings are rather "fiery," shedding light on an issue that needs more than just a "cuff" or a "hose" to address. It seems there's more to these Master's degrees than meets the eye.

It's worth noting that literature beyond academia also provides insights into the intersection of education and gender pay gaps. Social media posts have surfaced discussing the potential influence of specific fields of study on income disparities, with many users expressing surprise at the connection between public safety Master's degrees and the gender pay gap. One such user states, "Who knew that aiming to protect the nation and uphold the law could also contribute to a wider gender pay gap? It's time to "secure" equality!"

The connection between educational pursuits in homeland security, law enforcement, and firefighting and gender pay inequalities seems to be "blazing" a trail in the research, offering unexpected insights into the dynamics of wage differentials. These findings certainly add a "spark" to the discussion!

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 Master's degrees awarded in Homeland security, law enforcement, and firefighting and Gender pay gap in the U.S.. 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]]
"Securing the Bag: An Investigation into the Link between Master's Degrees in Homeland Security, Law Enforcement, and Firefighting and the Gender Pay Gap in the United States"

[[ABSTRACT]]
This paper investigates the relationship between the number of Master's degrees awarded in Homeland Security, Law Enforcement, and Firefighting and the gender pay gap in the United States. Using data from the National Center for Education Statistics and Statista for the years 2012 to 2021, our research team examined the correlation coefficient and p-value to unravel this intriguing connection.

Between 2012 and 2021, we observed a remarkably strong correlation coefficient of 0.9803335 and a p-value of less than 0.01, signifying a robust statistical relationship. Our findings suggest that the higher the number of Master's degrees conferred in these fields, the wider the gender pay gap tends to be. It appears that the quest for national security and public safety might be inadvertently contributing to gender-based disparities in compensation.

Now, let's not jump to conclusions, but it seems that while these professionals are focused on extinguishing fires and enforcing the law, they may be unintentionally fueling the flames of the gender pay gap. Keep your hose and your earnings in check, folks!

[[LITERATURE REVIEW]]
The findings of Smith et al. (2015) indicate a positive correlation between the number of Master's degrees awarded in Homeland Security, Law Enforcement, and Firefighting and the gender pay gap in the United States. Smith et al. suggest that as the number of Master's degrees in these fields increases, the gender pay gap widens. Such evidence raises questions about the unintended consequences of educational pursuits in these areas.
Now, let's "arrest" any premature assumptions about these findings, but it seems like the gender pay gap might be in need of some "firefighting" of its own. If we're not careful, we might have to call in the "homeland security" team to address this issue!
In "Doe" (2018), the authors similarly observe a significant relationship between educational attainment in homeland security, law enforcement, and firefighting and gender pay disparities. Doe highlights the need for further investigation into the underlying mechanisms driving this association, emphasizing the potential implications for workforce equality and fairness.
It appears that while these professionals aim to protect and serve, they might also unwittingly be serving up some gender pay gap disparities. As firefighting techniques evolve, perhaps so should the strategies for achieving equal pay.
Turning to the real-world impact, a study by Jones (2019) underscores the tangible effects of these trends on the labor market. Jones' work reveals a concerning pattern: as the number of Master's degrees awarded in public safety and security fields rises, the gender pay gap widens, reinforcing the notion that there may be systemic issues at play.
It seems we may need to think about "putting out the fire" of the gender pay gap with more than just water and foam. Maybe a sprinkle of gender equality sensitivity training and a dash of fair compensation strategies is in order!
In "Lorem and Ipsum" (2020), the authors provide further evidence of the link between Master's degrees in these fields and gender-based wage disparities. This study emphasizes the need for policymakers and educational institutions to consider the broader implications of educational choices on societal equality and economic welfare.
One could say these findings are rather "fiery," shedding light on an issue that needs more than just a "cuff" or a "hose" to address. It seems there's more to these Master's degrees than meets the eye.
It's worth noting that literature beyond academia also provides insights into the intersection of education and gender pay gaps. Social media posts have surfaced discussing the potential influence of specific fields of study on income disparities, with many users expressing surprise at the connection between public safety Master's degrees and the gender pay gap. One such user states, "Who knew that aiming to protect the nation and uphold the law could also contribute to a wider gender pay gap? It's time to "secure" equality!"
The connection between educational pursuits in homeland security, law enforcement, and firefighting and gender pay inequalities seems to be "blazing" a trail in the research, offering unexpected insights into the dynamics of wage differentials. These findings certainly add a "spark" to the discussion!

[[RESULTS]]
The analysis of Master's degrees awarded in the fields of Homeland Security, Law Enforcement, and Firefighting and their relationship with the gender pay gap revealed a strikingly high correlation coefficient of 0.9803335, which denotes a near-perfect positive linear relationship. This finding indicates that as the number of Master's degrees in these disciplines increased, so did the gender pay gap. It seems that an uptick in academic credentials in these subjects has exacerbated gender-based income disparities.
Additionally, the r-squared value of 0.9610538 further underscores the robustness of the relationship between Master's degrees in these fields and the gender pay gap. This high r-squared value implies that approximately 96.1% of the variation in the gender pay gap can be explained by the variation in Master's degrees awarded in Homeland Security, Law Enforcement, and Firefighting. In other words, the pursuit of advanced education in these domains is strongly associated with wider differences in compensation between genders.
Fig. 1 illustrates the compelling positive correlation between the variables. As the number of Master's degrees awarded in Homeland Security, Law Enforcement, and Firefighting increased, the gender pay gap expanded as well. The trendline in the scatterplot demonstrates a steep upward trajectory, emphasizing the notable association between these two factors.
It appears that the very fields dedicated to maintaining safety and security are inadvertently perpetuating an imbalance in earnings between men and women. One could say that while these professionals are extinguishing literal fires, they might unknowingly be stoking the flames of inequality in the realm of compensation. It seems the pursuit of higher education in these disciplines may inadvertently be fueling the gender pay gap, leaving society in need of some "extinguishers" for these unintended consequences.

-------

Your response should start like this:

[[DISCUSSION]]

ChatGPT:

[[DISCUSSION]]

The results of the current study align with previous research that has identified a positive relationship between the number of Master's degrees awarded in Homeland Security, Law Enforcement, and Firefighting and the gender pay gap. The findings support the notion that as the pursuit of advanced degrees in these fields increases, so does the disparity in earnings between genders. It is evident that the tireless efforts to maintain public safety and security may inadvertently be contributing to the widening gender pay gap, adding fuel to the financial disparity fire. Perhaps it's time for a new kind of rescue mission – one geared towards bridging the gender wage chasm in these domains.

The remarkably high correlation coefficient and r-squared value provide robust statistical evidence of the association between Master's degrees in these fields and gender-based wage differentials. The near-perfect positive linear relationship underscores the compelling influence of educational attainment in Homeland Security, Law Enforcement, and Firefighting on the gender pay gap. It seems that as the number of individuals pursuing Master's degrees in these disciplines grows, so too does the discrepancy in pay between men and women. One might say that these educational pursuits are inadvertently serving up a "homeland insecurity" when it comes to equal compensation.

These results prompt contemplation on the potential mechanisms underlying this association. It is plausible that the gender disparities in compensation within these fields may be influenced by a variety of factors, including organizational and institutional practices, implicit bias, and societal expectations. Such complexities warrant further investigation to disentangle the intricacies of this relationship and develop targeted interventions. It seems that beyond just addressing literal emergencies, the realms of Homeland Security, Law Enforcement, and Firefighting may need to focus on containing the fiscal "firestorms" brewing within their wage structures.

The implications of these findings extend beyond the realm of academia and bear relevance for policy and practice. As educational pursuits play a pivotal role in shaping workforce dynamics, it becomes imperative for policymakers and educational institutions to consider the broader societal impact of educational choices in perpetuating gender-based wage disparities. Perhaps it's time to honor not only those who defend and serve but also those who strive to create equitable compensation frameworks within these crucial domains. It's high time to "arrest" the growing gender pay gap and "extinguish" the unanticipated consequences of educational endeavors in public safety and security.

In conclusion, the present study contributes to the expanding body of research that underscores the relationship between Master's degrees in Homeland Security, Law Enforcement, and Firefighting and the gender pay gap. By shedding light on this substantial association, the study advocates for a reevaluation of priorities within these fields to ensure that the pursuit of education aligns with the promotion of gender equity in compensation. After all, it's about time for a different kind of emergency response – one that prioritizes not only public safety, but also financial security for all.

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 Securing the Bag: An Investigation into the Link between Master's Degrees in Homeland Security, Law Enforcement, and Firefighting and the Gender Pay Gap in the United States. Respond only with the name of a fictional academic journal.

ChatGPT:

The Journal of Gendered Occupational Economics

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 Securing the Bag: An Investigation into the Link between Master's Degrees in Homeland Security, Law Enforcement, and Firefighting and the Gender Pay Gap in the United States. Respond only with the name of a fictional organization.

ChatGPT:

The Institute for Public Safety and Equity (IPSE)

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 Securing the Bag: An Investigation into the Link between Master's Degrees in Homeland Security, Law Enforcement, and Firefighting and the Gender Pay Gap in the United States with an abstract of This paper investigates the relationship between the number of Master's degrees awarded in Homeland Security, Law Enforcement, and Firefighting and the gender pay gap in the United States. Using data from the National Center for Education Statistics and Statista for the years 2012 to 2021, our research team examined the correlation coefficient and p-value to unravel this intriguing connection.
Between 2012 and 2021, we observed a remarkably strong correlation coefficient of 0.9803335 and a p-value of less than 0.01, signifying a robust statistical relationship. Our findings suggest that the higher the number of Master's degrees conferred in these fields, the wider the gender pay gap tends to be. It appears that the quest for national security and public safety might be inadvertently contributing to gender-based disparities in compensation.
Now, let's not jump to conclusions, but it seems that while these professionals are focused on extinguishing fires and enforcing the law, they may be unintentionally fueling the flames of the gender pay gap. Keep your hose and your earnings in check, folks!

ChatGPT:

Master's degrees, Homeland Security, Law Enforcement, Firefighting, gender pay gap, United States, correlation coefficient, p-value, National Center for Education Statistics, Statista, gender-based disparities, compensation, national security, public safety, professional gender pay gap

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

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Data details

Master's degrees awarded in law enforcement and firefighting
Detailed data title: Master's degrees conferred by postsecondary institutions in Homeland security, law enforcement, and firefighting
Source: National Center for Education Statistics
See what else correlates with Master's degrees awarded in law enforcement and firefighting

Gender pay gap in the U.S.
Source: Statista
See what else correlates with Gender pay gap in the U.S.

Correlation r = 0.9803335 (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 = 0.9610538 (Coefficient of determination)
This means 96.1% of the change in the one variable (i.e., Gender pay gap in the U.S.) is predictable based on the change in the other (i.e., Master's degrees awarded in law enforcement and firefighting) over the 10 years from 2012 through 2021.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 6.4E-7.^Show 0.0000006391454449067938000000
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 0.98 in 6.4E-5% of random cases. Said differently, if you correlated 1,564,589 random variables^Note You don't actually need 1 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 9 degrees of freedom, ^Note Degrees of freedom is a measure of how many free components we are testing. In this case it is 9 because we have two variables measured over a period of 10 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.

[ 0.92, 1 ] 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.

	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021
Master's degrees awarded in law enforcement and firefighting (Degrees awarded)	8420	8868	9310	9643	9775	10209	10293	10303	10606	11326
Gender pay gap in the U.S. (Percentage)	76.5	78.3	78.6	79.6	80.5	81.7	81.6	82.3	83.1	83.7

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([8420,8868,9310,9643,9775,10209,10293,10303,10606,11326,])
array_2 = np.array([76.5,78.3,78.6,79.6,80.5,81.7,81.6,82.3,83.1,83.7,])
array_1_name = "Master's degrees awarded in law enforcement and firefighting"
array_2_name = "Gender pay gap in the U.S."

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

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

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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 Master's degrees awarded in law enforcement and firefighting
Line chart for only Gender pay gap in the U.S.
AI-generated correlation image
The spurious research paper: Securing the Bag: An Investigation into the Link between Master's Degrees in Homeland Security, Law Enforcement, and Firefighting and the Gender Pay Gap in the United States

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Correlation ID: 1730 · Black Variable ID: 1326 · Red Variable ID: 356


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