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__Data details__

**The distance between Uranus and the moon**

**Detailed data title:**The average distance between Uranus and the moon as measured on the first day of each month

**Source:**Caclculated using Astropy

**Additional Info:**I wrote a Python script using Astropy to calculate the distance between the named planets on the first day of each month for every year.

*See what else correlates with*

**The distance between Uranus and the moon****The number of movies Samuel L. Jackson appeared in**

**Source:**The Movie DB

**Additional Info:**Snakes on a Plane (2006); Shaft (2000); The 51st State (2001); No Good Deed (2002); The Great White Hype (1996); One Eight Seven (1997); Amos & Andrew (1993); Coach Carter (2005); The Caveman's Valentine (2001); The Man (2005); S.W.A.T. (2003); Farce of the Penguins (2007); The Negotiator (1998); Resurrecting the Champ (2007); Cleaner (2007); Freedomland (2006); Lakeview Terrace (2008); Home of the Brave (2006); Soul Men (2008); Afro Samurai: Resurrection (2009); Unthinkable (2010); In My Country (2004); African Cats (2011); The Samaritan (2012); Young Jeezy: A Hustlerz Ambition (2011); Zambezia (2012); Reasonable Doubt (2014); Any Given Wednesday (2000); From Star Wars to Star Wars: The Story of Industrial Light & Magic (1999); Assault at West Point: The Court-Martial of Johnson Whittaker (1994); Big Game (2014); The Hateful Eight (2015); In the Land of the Free... (2010); Kite (2014); Everything Is Samuel L. Jackson's Fault (2013); Quentin Tarantino: 20 Years of Filmmaking (2012); The Art of Action: Martial Arts in the Movies (2002); Shaft (2019); Shaquille O'Neal: Larger than Life (1996); Honor Deferred (2006); Comic Books & Superheroes (2001); I Am Not Your Negro (2017); Death to 2020 (2020); Respect Yourself: The Stax Records Story (2007); Enslaved with Samuel L Jackson (2020); Uneven Fairways (2009); Middle School Confessions (2002); Go the F**k to Sleep (2011); Marvel Studios Assembled: The Making of Secret Invasion (2023); A Night to Die For (1995); Jackie Brown (1997); Pulp Fiction (1994); Changing Lanes (2002); Die Hard: With a Vengeance (1995); Rules of Engagement (2000); 1408 (2007); The Long Kiss Goodnight (1996); xXx: State of the Union (2005); Black Snake Moan (2006); Against the Wall (1994); Unforgivable Blackness: The Rise and Fall of Jack Johnson (2004); National Lampoon's Loaded Weapon 1 (1993); Unbreakable (2000); Twisted (2004); The Sunset Limited (2011); Meeting Evil (2012); Paws of Fury: The Legend of Hank (2022); Cell (2016); Kong: Skull Island (2017); Unicorn Store (2017); The Hitman's Bodyguard (2017); Spider-Man: Far From Home (2019); Hitman's Wife's Bodyguard (2021); Captain Marvel (2019); Creating a King: Summoning a God (2017); Spiral: From the Book of Saw (2021); The Banker (2020); The Protégé (2021); George Lucas: Creating an Empire (2005); Mr. Incredible and Pals (2005); Hollywood Legenden (2004); Grand Theft Auto: San Andreas - The Introduction (2004); A Time to Kill (1996); Sphere (1998); Basic (2003); Kiss of Death (1995); Quantum Quest: A Cassini Space Odyssey (2012); Jumper (2008); The Spirit (2008); Fresh (1994); Eve's Bayou (1997); John Travolta: The Inside Story (2004); Kingsman: The Secret Service (2014); Miss Peregrine's Home for Peculiar Children (2016); Face of Unity (2014); The Legend of Tarzan (2016); Dead and Alive: The Race for Gus Farace (1991); Smokey Robinson: The Library of Congress Gershwin Prize for Popular Song (2017); Glass (2019); The Making of 'Unbreakable' (2001); The Kill Room (2023); Shaft: Still the Man (2000); The 100 Greatest Films (2001); Pulp Fiction: The Facts (2002); Hard Eight (1997); Eddie Murphy Raw (1987); White Sands (1992); Arena (2011); Turbo (2013); Oldboy (2013); Barely Lethal (2015); xXx (2002); The Trial of the Moke (1978); Eating You Alive (2016); An Audience with Adele (2021); Making of Pulp Fiction (2000); Star Wars: Episode III - Revenge of the Sith (2005); Star Wars: Episode II - Attack of the Clones (2002); Deep Blue Sea (1999); Menace II Society (1993); Mother and Child (2009); Juice (1992); Strictly Business (1991); xXx: Return of Xander Cage (2017); Django Unchained (2012); Def by Temptation (1990); Chi-Raq (2015); Incredibles 2 (2018); Dead Man Out (1989); Magic Sticks (1987); The Last Full Measure (2020); Jackie Brown: How It Went Down (2002); The Avengers: A Visual Journey (2012); Spike Lee & Company: Do It a Cappella (1990); The Marvels (2023); Coach Carter The Man Behind the Movie (2005); Jumpin' at the Boneyard (1991); The Incredibles (2004); The Return of Superfly (1990); The Search for One-eye Jimmy (1996); Eddie Murphy: One Night Only (2012); The Displaced Person (1977); Jungle Fever (1991); Building the Dream: Assembling the Avengers (2012); Johnny Suede (1991); Betsy's Wedding (1990); 50 Films to See Before You Die (2006); Iron Man 2 (2010); The Other Guys (2010); Losing Isaiah (1995); The Red Violin (1998); Hail Caesar (1994); Making 'Do the Right Thing' (1989); Life's Essentials with Ruby Dee (2014); R2-D2: Beneath the Dome (2001); Ultimate Iron Man: The Making of Iron Man 2 (2010); The Avengers (2012); Patriot Games (1992); Industrial Light & Magic: Creating the Impossible (2010); Marvel Studios: Assembling a Universe (2014); On the Shoulders of Giants (2011); Heavy Rain (2010); Kill Bill: Vol. 2 (2004); Our Friend, Martin (1999); Star Wars: Evolution of the Lightsaber Duel (2015); The Unauthorized 'Star Wars' Story (1999); My Date with Drew (2005); True Romance (1993); Astro Boy (2009); RoboCop (2014); Captain America: The Winter Soldier (2014); Trees Lounge (1996); Jurassic Park (1993); Unchained Memories: Readings from the Slave Narratives (2003); The N Word (2006); Do the Right Thing (1989); BaadAsssss Cinema (2002); Fathers and Sons (1992); I Ain't Scared of You: A Tribute to Bernie Mac (2012); Avengers: Age of Ultron (2015); Forever Hollywood (1999); Is That Black Enough for You?!? (2022); Coming to America (1988); With Great Power: The Stan Lee Story (2010); The Harlem Globetrotters: The Team That Changed the World (2005); School Daze (1988); Return to Jurassic Park (2011); Star Wars: The Clone Wars (2008); Life Itself (2018); Off the Menu: The Last Days of Chasen's (1998); The New Age (1994); Mo' Better Blues (1990); Uncle Tom's Cabin (1987); Captain America: The First Avenger (2011); The Words That Built America (2017); Quincy (2018); Fluke (1995); Kingsman: The Secret Service Revealed (2015); The Face Is Familiar (2009); The Journey of the African-American Athlete (1996); John Travolta, le miraculé d'Hollywood (2017); Parts of the Family (2003); Parkinson at 50 (2021); QT8: The First Eight (2019); Sea of Love (1989); Spider-Man: All Roads Lead to No Way Home (2022); The Exterminator (1980); Gospel Hill (2008); BET Presents Love & Happiness: An Obama Celebration (2016); Ragtime (1981); Star Wars: Episode I - The Phantom Menace (1999); Common Ground (1990); A West Wing Special to Benefit When We All Vote (2020); #UNFIT: The Psychology of Donald Trump (2020); Marvel Studios' 2021 Disney+ Day Special (2021); A Shock to the System (1990); Final Cut: Ladies and Gentlemen (2012); We Are One With President-Elect Barack Obama (2009); Out of Sight (1998); Kill Bill: The Whole Bloody Affair (2011); The Exorcist III (1990); Crítico (2008); GoodFellas (1990); Thor (2011); Avengers: Endgame (2019); 2021 Rock & Roll Hall of Fame Induction Ceremony (2021); Inglourious Basterds (2009); Avengers: Infinity War (2018); Iron Man (2008); One World: Together at Home (2020); Star Wars: The Rise of Skywalker (2019)

*See what else correlates with*

**The number of movies Samuel L. Jackson appeared in****Correlation r = 0.7996829**(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.

**r**(Coefficient of determination)

^{2}= 0.6394928This means

**63.9%**of the change in the one variable

*(i.e., The number of movies Samuel L. Jackson appeared in)*is predictable based on the change in the other

*(i.e., The distance between Uranus and the moon)*over the 47 years from 1977 through 2023.

**p < 0.01,**which is statistically significant(Null hypothesis significance test)

The

*p*-value is 1.6E-11. 0.0000000000156855145293347250

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 0.8 in 1.6E-9% of random cases. Said differently, if you correlated 63,753,088,758 random variables You don't actually need 63 billion 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 46 degrees of freedom, Degrees of freedom is a measure of how many free components we are testing. In this case it is

**46**because we have two variables measured over a period of

**47 years**. It's just the number of years minus ( the number of variables minus one ), which in this case simplifies to

**the number of years minus one**.

you would randomly expect to find a correlation as strong as this one.

**[ 0.67, 0.88 ] 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.

1977 | 1978 | 1979 | 1980 | 1981 | 1982 | 1983 | 1984 | 1985 | 1986 | 1987 | 1988 | 1989 | 1990 | 1991 | 1992 | 1993 | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | |

The distance between Uranus and the moon (Planetary distance (AU)) | 18.5659 | 18.6181 | 18.6763 | 18.7389 | 18.7982 | 18.8636 | 18.9279 | 18.9951 | 19.0599 | 19.1244 | 19.1902 | 19.2579 | 19.3212 | 19.3877 | 19.4535 | 19.5176 | 19.5817 | 19.6425 | 19.6999 | 19.7555 | 19.8053 | 19.8512 | 19.894 | 19.9294 | 19.9645 | 19.9955 | 20.0212 | 20.0443 | 20.0666 | 20.0823 | 20.0961 | 20.1015 | 20.1059 | 20.1047 | 20.0959 | 20.0797 | 20.0648 | 20.0405 | 20.0136 | 19.9804 | 19.9478 | 19.9116 | 19.8719 | 19.8254 | 19.7836 | 19.7342 | 19.6811 |

The number of movies Samuel L. Jackson appeared in (Movie appearances) | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 3 | 2 | 4 | 9 | 5 | 4 | 5 | 6 | 5 | 7 | 4 | 5 | 6 | 6 | 6 | 9 | 4 | 8 | 9 | 7 | 5 | 8 | 7 | 8 | 10 | 12 | 3 | 9 | 6 | 5 | 9 | 4 | 7 | 7 | 7 | 3 | 3 |

__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 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 Personally I don't find any p-value calculation to be 'simple,' but you know what I mean.

*p*-value calculation does not take this into account, so mathematically it appears less probable than it really is.**Y-axis doesn't start at zero:**I truncated the Y-axes of the graph above. I also used a line graph, which makes the visual connection stand out more than it deserves. Nothing against line graphs. They are great at telling a story when you have linear data! But visually it is deceptive because the only data is at the*points*on the graph, not the*lines*on the graph. In between each point, the data could have been doing anything. Like going for a random walk by itself!

Mathematically what I showed is true, but it is intentionally misleading. Below is the same chart but with both Y-axes starting at zero.**Outlandish outliers:**There are "outliers" in this data. In concept, "outlier" just means "way different than the rest of your dataset." When calculating a correlation like this, they are particularly impactful because a single outlier can substantially increase your correlation.

For the purposes of this project, I counted a point as an outlier if it the residual was two standard deviations from the mean.

(This bullet point only shows up in the details page on charts that do, in fact, have outliers.)

They stand out on the scatterplot above: notice the dots that are far away from any other dots. I intentionally mishandeled outliers, which makes the correlation look extra strong.

__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([18.5659,18.6181,18.6763,18.7389,18.7982,18.8636,18.9279,18.9951,19.0599,19.1244,19.1902,19.2579,19.3212,19.3877,19.4535,19.5176,19.5817,19.6425,19.6999,19.7555,19.8053,19.8512,19.894,19.9294,19.9645,19.9955,20.0212,20.0443,20.0666,20.0823,20.0961,20.1015,20.1059,20.1047,20.0959,20.0797,20.0648,20.0405,20.0136,19.9804,19.9478,19.9116,19.8719,19.8254,19.7836,19.7342,19.6811,])
array_2 = np.array([1,1,0,1,1,0,0,0,0,0,3,2,4,9,5,4,5,6,5,7,4,5,6,6,6,9,4,8,9,7,5,8,7,8,10,12,3,9,6,5,9,4,7,7,7,3,3,])
array_1_name = "The distance between Uranus and the moon"
array_2_name = "The number of movies Samuel L. Jackson appeared in"
# 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
The image linked here is a Scalable Vector Graphic (SVG). It is the highest resolution that is possible to achieve. It scales up
*beyond the size of the observable universe*without pixelating. You do not need to email me asking if I have a higher resolution image. I do not. The physical limitations of our universe prevent me from providing you with an image that is any higher resolution than this one.

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

Alternatively you can use a tool like Inkscape. - High resolution line chart, optimized for mobile
- Alternative high resolution line chart
- Scatterplot
- Portable line chart (png)
- Portable line chart (png), optimized for mobile
- Line chart for only
*The distance between Uranus and the moon* - Line chart for only
*The number of movies Samuel L. Jackson appeared in*

**How fun was this correlation?**

Your correlation inspection deserves a standing ovation!

Correlation ID: 6325 · Black Variable ID: 1963 · Red Variable ID: 26502