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Spurious correlation #14,476 · View random

A linear line chart with years as the X-axis and two variables on the Y-axis. The first variable is The number of movies Morgan Freeman appeared in and the second variable is The number of exercise physiologists in Connecticut.  The chart goes from 2012 to 2022, and the two variables track closely in value over that time. Small Image
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Data details

The number of movies Morgan Freeman appeared in
Source: The Movie DB
Additional Info: Driving Miss Daisy (1989); Se7en (1995); The Contract (2006); Edison (2005); Along Came a Spider (2001); 10 Items or Less (2006); Nurse Betty (2000); Hard Rain (1998); Dreamcatcher (2003); Invictus (2009); The Maiden Heist (2009); Amistad (1997); The Hunting of the President (2004); Kiss the Girls (1997); Cosmic Voyage (1996); The Power of One (1992); Feast of Love (2007); Death of a Prophet (1981); Lean On Me (1989); Thick as Thieves (2009); Prom Night in Mississippi (2009); Dolphin Tale (2011); Guilty by Association (2003); Born to Be Wild (2011); Breaking the Taboo (2011); The Magic of Belle Isle (2012); The True Story of Glory Continues (1991); The Long Way Home (1997); The Eastwood Factor (2010); Genius. A Night for Ray Charles (2004); JFK: A President Betrayed (2013); Island of Lemurs: Madagascar (2014); Dolphin Tale 2 (2014); We the People (2014); 5 Flights Up (2014); The Editor and The Dragon: Horace Carter Fights the Klan (2013); Le frontiere dell'Astronomia - EP-7 Vite aliene nel cosmo (2012); The President's Photographer: Fifty Years Inside the Oval Office (2010); Clint Eastwood: Out of the Shadows (2000); Going in Style (2017); Scandalize My Name: Stories from the Blacklist (1998); Just Getting Started (2017); The C Word (2016); Inside the White House (1996); The Massachusetts 54th Colored Infantry (1991); Where the Water Meets the Sky (2008); Partners of the Heart (2002); Survivors of the Shoah: Visual History Foundation (2004); All on Accounta Pullin' a Trigger (2002); The 16th Man (2010); Into Nature's Wild (2020); Coriolanus (1979); JFK & LBJ: A Time for Greatness (2015); The Ritual Killer (2023); Echoes 'Cross the Tracks (2012); Follow the Drinking Gourd (1990); 761st Tank Battalion: The Original Black Panthers (2023); Panama Canal in 3D a Land Divided a World United (2019); Morgan Freeman: Breaking Barriers (2021); Lucky Number Slevin (2006); The Shawshank Redemption (1994); Bruce Almighty (2003); Unleashed (2005); Evan Almighty (2007); Under Suspicion (2000); The Sum of All Fears (2002); Levity (2003); High Crimes (2002); The Bucket List (2007); Robin Hood: Prince of Thieves (1991); Chain Reaction (1996); The Big Bounce (2004); The People Speak (2009); Moll Flanders (1996); Resting Place (1986); Oblivion (2013); B.B. King: The Life of Riley (2012); Last Vegas (2013); The Marva Collins Story (1981); Tales from the Warner Bros. Lot (2013); Fight for Life (1987); Lucy (2014); Laddie: The Man Behind the Movies (2017); Last Knights (2015); Momentum (2015); Angel Has Fallen (2019); March of the Penguins 2: The Next Step (2017); America's Musical Journey (2018); The Poison Rose (2019); The Comeback Trail (2020); A Good Person (2023); Vanquish (2021); 57 Seconds (2023); Unforgiven (1992); Million Dollar Baby (2004); Johnny Handsome (1989); An Unfinished Life (2005); Gone Baby Gone (2007); Magnificent Desolation: Walking on the Moon (2005); Outbreak (1995); Wanted (2008); Clean and Sober (1988); RED (2010); Clinton and Nadine (1988); The Execution of Raymond Graham (1985); Eastwood Directs: The Untold Story (2013); Blues Divas (2005); Shawshank: The Redeeming Feature (2001); Die Clint Eastwood Story (2018); Rita Moreno: Just a Girl Who Decided to Go for It (2021); The Minute You Wake Up Dead (2022); Paradise Highway (2022); Heroes & Villains (2022); Glory (1989); Marie (1985); The Lego Movie (2014); Attica (1980); Wish Wizard (2014); Now You See Me 2 (2016); London Has Fallen (2016); Ted 2 (2015); Ben-Hur (2016); For Love of Liberty: The Story of America's Black Patriots (2010); Declaration of Independence (2003); Blacklist: Hollywood on Trial (1996); Sidney (2022); March of the Penguins (2005); Deep Impact (1998); Stephen King: Shining in the Dark (1999); Hitman's Wife's Bodyguard (2021); The Electric Company's Greatest Hits & Bits (2006); Hollow Image (1979); Robin Hood: The Myth, the Man, the Movie (1991); Brubaker (1980); The Bonfire of the Vanities (1990); Street Smart (1987); Olympus Has Fallen (2013); AFI: 100 Years... 100 Movies... 10th Anniversary Edition (2007); Betty White's 90th Birthday: A Tribute to America's Golden Girl (2012); The Nutcracker and the Four Realms (2018); Oscar Micheaux: The Superhero of Black Filmmaking (2021); The Dark Knight (2008); Batman Begins (2005); That Was Then... This Is Now (1985); Harry and Son (1984); Now You See Me (2013); Transcendence (2014); Meeting the Beatles in India (2020); Betty White: A Celebration (2022); The Dark Knight Rises (2012); Roll of Thunder, Hear My Cry (1978); Clint Eastwood's West (2011); All About Us (2007); Dave Chappelle: The Kennedy Center Mark Twain Prize (2020); Boffo! Tinseltown's Bombs and Blockbusters (2006); Clint Eastwood: A Cinematic Legacy (2021); Eyewitness (1981); Brian Banks (2019); Ending the Knight (2012); The Words That Built America (2017); Fast Times at Ridgemont High: A Virtual Table Read (2020); Teachers (1984); Eastwood & Co.: Making 'Unforgiven' (2002); The Earth Day Special (1990); Coming 2 America (2021); Clint Eastwood: The Last Legend (2022); A Century of Cinema (1994); Conan the Barbarian (2011); A Raisin in the Sun (2008); The Fire Rises: The Creation and Impact of The Dark Knight Trilogy (2013); A Concert for Hurricane Relief (2005); The Best of The Tony Awards: The Plays (2006); The Disney Family Singalong - Volume II (2020); Night of 100 Stars III (1990); War of the Worlds (2005); Never Sleep Again: The Elm Street Legacy (2010)

See what else correlates with The number of movies Morgan Freeman appeared in

The number of exercise physiologists in Connecticut
Detailed data title: BLS estimate of exercise physiologists in Connecticut
Source: Bureau of Larbor Statistics
See what else correlates with The number of exercise physiologists in Connecticut

Correlation r = 0.9130116 (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 = 0.8335902 (Coefficient of determination)
This means 83.4% of the change in the one variable (i.e., The number of exercise physiologists in Connecticut) is predictable based on the change in the other (i.e., The number of movies Morgan Freeman appeared in) over the 11 years from 2012 through 2022.

p < 0.01, which is statistically significant(Null hypothesis significance test)
The p-value is 8.71E-5. 0.0000870965382062518800000000
The p-value is a measure of how probable it is that we would randomly find a result this extreme. 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 0.91 in 0.00871% of random cases. Said differently, if you correlated 11,482 random variables Which I absolutely did.
with the same 10 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is 10 because we have two variables measured over a period of 11 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.

[ 0.69, 0.98 ] 95% correlation confidence interval (using the Fisher z-transformation)
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: 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.
20122013201420152016201720182019202020212022
The number of movies Morgan Freeman appeared in (Movie appearances)79844534676
The number of exercise physiologists in Connecticut (Exercise Physiologists)8090805050505050606060




Why this works

  1. Data dredging: I have 25,237 variables in my database. I compare all these variables against each other to find ones that randomly match up. That's 636,906,169 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.
  2. Lack of causal connection: There is probably 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.
  3. 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 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. 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([7,9,8,4,4,5,3,4,6,7,6,])
array_2 = np.array([80,90,80,50,50,50,50,50,60,60,60,])
array_1_name = "The number of movies Morgan Freeman appeared in"
array_2_name = "The number of exercise physiologists in Connecticut"

# 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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Correlation ID: 14476 · Black Variable ID: 26600 · Red Variable ID: 18944
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