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(You Make Me Feel Like) A Natural Woman
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"Natural Woman" redirects here. For the Japanese film, see Natural Woman (film).
"(You Make Me Feel Like) A Natural Woman"
A-side label of U.S. vinyl release
Single by Aretha Franklin
from the album Lady Soul
B-side
"Baby, Baby, Baby"
Released
September 1967
Format
7" single
Recorded
1967
Genre
Soul
Length
2:45
Label
Atlantic
Songwriter(s)
Gerry Goffin
Carole King
Jerry Wexler
Producer(s)
Jerry Wexler
Aretha Franklin singles chronology
"Baby I Love You"
(1967) "(You Make Me Feel Like) A Natural Woman"
(1967) "Chain of Fools"
(1967)
"Baby I Love You"
(1967) "(You Make Me Feel Like) A Natural Woman"
(1967) "Chain of Fools"
(1967)
"(You Make Me Feel Like) A Natural Woman" is a 1967 single released by American soul singer Aretha Franklin on the Atlantic label. The song was co-written by Carole King and Gerry Goffin, with input from Atlantic producer Jerry Wexler. The record was a big hit for Franklin, reaching number 8 on the Billboard Hot 100, and became a standard song for her. Franklin also included a live recording on the album Aretha in Paris in 1968. Versions have also been performed and recorded by King herself, Mary J. Blige, Celine Dion, and many others. At the 2015 Kennedy Center Honors, Aretha Franklin performed the song to honor award-recipient Carole King.
Contents
[hide]
1 Original recording
1.1 Personnel
1.2 Chart performance
2 Later versions
2.1 Mary J. Blige version
2.1.1 Charts
2.2 Celine Dion version
2.2.1 Personnel
2.2.2 Formats and track listings
2.2.3 Charts
2.2.3.1 Weekly charts
2.2.3.2 Year-end charts
3 References
Original recording[edit]
Written by the celebrated partnership of Gerry Goffin and Carole King, the song was inspired by Atlantic Records co-owner and producer Jerry Wexler. As recounted in his autobiography, Wexler, a student of African-American musical culture, had been mulling over the concept of the "natural man", when he drove by King on the streets of New York. He shouted out to her that he wanted a "natural woman" song for Aretha Franklin's next album. In thanks, Goffin and King granted Wexler a co-writing credit.
Personnel[edit]
Aretha Franklin - lead vocals
Spooner Oldham - piano
Tommy Cogbill - bass
Gene Chrisman - drums
The Sweet Inspirations, Carolyn Franklin & Erma Franklin - background vocals
strings conducted by Ralph Burns
Chart performance[edit]
Chart (1967)
Peak
position
Australia
36
Canada RPM
11
U.S. Billboard Hot 100
8
U.S. Billboard R&B
2
U.S. Cash Box Top 100
12
Later versions[edit]
Carole King performing "(You Make Me Feel Like) A Natural Woman" in 2010
"Natural Woman" was released by Peggy Lipton in 1968 on her self-titled album on Ode Records, and by Freddie Hughes in 1968 as "Natural Man" (Wand Records 1192), and by George Benson on his album Goodies in 1968 (Verve Records V6-8771).
Peggy Lee released a version on her 1969 album A Natural Woman.
It was recorded by Carole King on her landmark 1971 album Tapestry. Celine Dion recorded the song in 1995 for the Tapestry Revisited: A Tribute to Carole King album, and released it as a single. Mary J. Blige also recorded the song that year for New York Undercover.
Rod Stewart covered the song on his album Smiler (album) 1974
Beccy Cole covered the song live on her 2007 album, Live @ Lizotte's.
Carole King and Gloria Estefan performed the song in May 2009 in the She's Got a Friend concerts at the Foxwoods Resort Casino in Connecticut. The audio from one of the performances was included on some editions of Estefan's 2013 album, The Standards.
In 2012, Christine Anu covered the song on her album, Rewind: The Aretha Franklin Songbook.
In December 2015, Aretha Franklin gave a universally acclaimed performance at the 2015 Kennedy Center Honors during the section for honoree Carole King.[1][2][3][4]
Mary J. Blige version[edit]
Charts[edit]
Chart (1995–96)
Peak
position
Netherlands (Dutch Top 40)[5]
36
Netherlands (Single Top 100)[6]
46
New Zealand (Recorded Music NZ)[7]
15
UK Singles (Official Charts Company)[8]
23
US Billboard Hot 100[9]
95
US Hot R&B/Hip-Hop Songs (Billboard)[10]
39
Celine Dion version[edit]
"(You Make Me Feel Like) A Natural Woman" was released as a promotional single by Celine Dion in November 1995 in North America and the United Kingdom.[11] It was featured on a tribute album to Carole King, called Tapestry Revisited: A Tribute to Carole King issued on October 24, 1995. Later, Dion included this track on most editions of her 1996 album Falling into You. The track was produced by David Foster. Dion's version enjoyed a moderate success on the adult contemporary charts, reaching number 4 in Canada and number 31 in the United States. In 2008, the song was featured on the US version of My Love: Ultimate Essential Collection. When Falling Into You won the Grammy for Album of the year in 1998, the song became the first to appear on two Album of the Year winners - following Tapestry's success in 1971.
On April 14, 1998, Dion, Aretha Franklin, Mariah Carey, Shania Twain, Gloria Estefan and Carole King performed the song during a VH1 Divas concert at the Beacon Theatre, New York. The six vocalists were recruited by the cable music network VH1 to raise money for Save the Music, their education charity. Hyped extensively in the press, the event was a ratings winner for VH1 – so successful, in fact, that the network arranged to have the concert released on disc and tape on October 6, 1998. At that time "(You Make Me Feel Like) A Natural Woman" (performed by all the divas) was released as a radio single in selected countries.
Personnel[edit]
Celine Dion – performer, vocals (background)
Lynn Davis – vocals (background)
David Foster – arranger, keyboards, producer
Gerry Goffin – composer
Carole King – composer
Michael Thompson – guitar
Jerry Wexler – composer
Formats and track listings[edit]
1995 promotional CD single
"(You Make Me Feel Like) A Natural Woman" – 3:40
1998 promotional CD single
"(You Make Me Feel Like) A Natural Woman" (live) – 5:15
"You've Got a Friend" (live) – 5:28
Charts[edit]
Weekly charts[edit]
Chart (1995–96)
Peak
position
Canada Top Singles (RPM)[12]
47
Canada Adult Contemporary (RPM)[13]
4
US Adult Contemporary (Billboard)[14]
31
Year-end charts[edit]
Chart (1996)
Peak
position
Canada Adult Contemporary (RPM)[15]
53
References[edit]
Jump up ^ Miller, Matt (December 30, 2015). "Aretha Franklin Just Brought the Leader of the Free World to Tears". Esquire. Retrieved December 31, 2015.
Jump up ^ Greer, Carlos (December 9, 2015). "Aretha Franklin stuns at Kennedy Center Honors". Page Six. Retrieved December 31, 2015.
Jump up ^ Hattenstone, Simon (December 30, 2015). "Obama cries as Aretha Franklin proves why she's the queen of soul". the Guardian. Retrieved December 31, 2015.
Jump up ^ Kreps, Daniel (December 30, 2015). "Watch Aretha Franklin Bring Obama to Tears at Kennedy Center Honors". Rolling Stone. Retrieved December 31, 2015.
Jump up ^ "Nederlandse Top 40 – week 8, 1996" (in Dutch). Dutch Top 40 Retrieved 20 May 2015.
Jump up ^ "Dutchcharts.nl – Mary J Blige – (You Make Me Feel Like A) Natural Woman" (in Dutch). Single Top 100. Retrieved 20 May 2015.
Jump up ^ "Charts.org.nz – Mary J Blige – (You Make Me Feel Like A) Natural Woman". Top 40 Singles. Retrieved 20 May 2015.
Jump up ^ "Mary J Blige: Artist Chart History". Official Charts Company. Retrieved 20 May 2015.
Jump up ^ "Mary J. Blige Chart History (Hot 100)". Billboard. Retrieved 20 May 2015.
Jump up ^ "Mary J. Blige Chart History (Hot R&B/Hip-Hop Songs)". Billboard. Retrieved 20 May 2015.
Jump up ^ Glatzer, Jenna (2005). Céline Dion: For Keeps. Andrews McMeel Publishing. ISBN 0-7407-5559-5.
Jump up ^ "Top RPM Singles: Issue 2913." RPM. Library and Archives Canada. Retrieved 3 September 2014.
Jump up ^ "Top RPM Adult Contemporary: Issue 2865." RPM. Library and Archives Canada. Retrieved 3 September 2014.
Jump up ^ "Celine Dion Chart History (Adult Contemporary)". Billboard. Retrieved 3 September 2014.
Jump up ^ "RPM Year End Top 100 Adult Contemporary Tracks". RPM. 64 (18). December 16, 1996. Retrieved September 28, 2014.
[show]
v
t
e
Aretha Franklin
Studio albums
Columbia
Aretha (1961)
The Electrifying Aretha Franklin (1962)
The Tender, the Moving, the Swinging Aretha Franklin (1962)
Laughing on the Outside (1963)
Unforgettable: A Tribute to Dinah Washington (1964)
Runnin' Out of Fools (1964)
Yeah!!! (1965)
Soul Sister (1966)
Take It Like You Give It (1967)
Take a Look (1967)
Soft and Beautiful (1969)
Atlantic
I Never Loved a Man the Way I Love You (1967)
Aretha Arrives (1967)
Lady Soul (1968)
Aretha Now (1968)
Soul '69 (1969)
This Girl's in Love with You (1970)
Spirit in the Dark (1970)
Young, Gifted and Black (1972)
Hey Now Hey (The Other Side of the Sky) (1973)
Let Me in Your Life (1974)
With Everything I Feel in Me (1974)
You (1975)
Sparkle (1976)
Sweet Passion (1977)
Almighty Fire (1978)
La Diva (1979)
Arista
Aretha (1980)
Love All the Hurt Away (1981)
Jump to It (1982)
Get It Right (1983)
Who's Zoomin' Who? (1985)
Aretha (1986)
Through the Storm (1989)
What You See Is What You Sweat (1991)
A Rose Is Still a Rose (1998)
So Damn Happy (2003)
Other
Songs of Faith (1956)
This Christmas, Aretha (2008)
Aretha: A Woman Falling Out of Love (2011)
Aretha Franklin Sings the Great Diva Classics (2014)
Live albums
Aretha in Paris (1968)
Aretha Live at Fillmore West (1971)
Amazing Grace (1972)
One Lord, One Faith, One Baptism (1987)
Oh Me Oh My: Aretha Live in Philly, 1972 (2007)
Compilation albums
Aretha's Gold (1969)
Aretha's Greatest Hits (1971)
The Best of Aretha Franklin (1973)
Aretha Sings the Blues (1980)
30 Greatest Hits (1985)
Greatest Hits: 1980–1994 (1994)
The Very Best of Aretha Franklin, Vol. 1 (1994)
The Early Years (1997)
Greatest Hits (1998)
Aretha's Best (2001)
Rare & Unreleased Recordings from the Golden Reign of the Queen of Soul (2007)
Jewels in the Crown: All-Star Duets with the Queen (2007)
A Deeper Love: The Best of Aretha Franklin (2009)
The Great American Songbook (2011)
Knew You Were Waiting: The Best of Aretha Franklin (1980-1998) (2012)
Box sets
Queen of Soul: The Atlantic Recordings (1992/2014)
Take A Look: Aretha Franklin Complete on Columbia (2011)
Singles
"Precious Lord (Part 1)" (1959)
"Today I Sing the Blues" (1960)
"Won't Be Long" (1960)
"Rock-a-Bye Your Baby with a Dixie Melody" (1961)
"Operation Heartbreak" (1961)
"I Surrender, Dear" (1962)
"Try a Little Tenderness" (1962)
"Say It Isn't So" (1963)
"Skylark" (1963)
"The Christmas Song (Chestnuts Roasting on an Open Fire)" (1964)
"One Step Ahead" (1965)
"You Made Me Love You" (1965)
"Mockingbird" (1967)
"I Never Loved a Man (The Way I Love You)" (1967)
"Respect" (1967)
"Baby I Love You" (1967)
"(You Make Me Feel Like) A Natural Woman" (1967)
"Do Right Woman, Do Right Man"
"Chain of Fools" (1967)
"(I Can't Get No) Satisfaction" (1968)
"(Sweet Sweet Baby) Since You've Been Gone" (1968)
"Think" (1968)
"You Send Me" (1968)
"The House That Jack Built" (1968)
"I Say a Little Prayer" (1968)
"See Saw" (1968)
"My Song" (1968)
"The Weight" (1969)
"Tracks of My Tears" (1969)
"I Can't See Myself Leaving You" (1969)
"Gentle on My Mind" (1969)
"Share Your Love with Me" (1969)
"Eleanor Rigby" (1969)
"Call Me" (1970)
"Son of a Preacher Man" (1970)
"Spirit in the Dark" (1970)
"The Thrill Is Gone" (1970)
"Don't Play That Song" (1970)
"Border Song (Holy Moses)" (1970)
"You're All I Need to Get By" (1971)
"Bridge over Troubled Water" (1971)
"Spanish Harlem" (1971)
"Rock Steady" (1971)
"Day Dreaming" (1972)
"Wholy Holy" (1972)
"Angel" (1973)
"Until You Come Back to Me (That's What I'm Gonna Do)" (1973)
"I'm in Love" (1974)
"Ain't Nothing Like the Real Thing" (1974)
"Something He Can Feel" (1976)
"Break It to Me Gently" (1977)
"What a Fool Believes" (1981)
"It's My Turn" (1981)
"Jump to It" (1982)
"Get It Right" (1983)
"Freeway of Love" (1985)
"Who's Zoomin' Who" (1985)
"Sisters Are Doin' It for Themselves" (1985)
"Jumpin' Jack Flash" (1986)
"Jimmy Lee" (1986)
"I Knew You Were Waiting (For Me)" (1987)
"Oh Happy Day" (1988)
"Gimme Your Love" (1989)
"It Isn't, It Wasn't, It Ain't Never Gonna Be" (1989)
"Everyday People" (1991)
"Someday We'll All Be Free" (1992)
"A Deeper Love" (1993)
"A Rose Is Still a Rose" (1998)
"Here We Go Again" (1998)
"Put You Up on Game" (2007)
"Angels We Have Heard on High" (2009)
"Rolling in the Deep (The Aretha Version)" (2014)
Related topics
Discography
Awards and nominations
"Wood Beez (Pray Like Aretha Franklin)" (by Scritti Politti)
Book
[show]
v
t
e
Mary J. Blige singles
Discography
What's the 411?
"You Remind Me"
"Real Love"
"Reminisce"
"Sweet Thing"
"Love No Limit"
"You Don't Have to Worry"
"My Love"
My Life
"Be Happy"
"Mary Jane (All Night Long)"
" I'm Goin' Down"
"You Bring Me Joy"
"I Love You"
Share My World
"Love Is All We Need"
"I Can Love You"
"Everything"
"Missing You"
"Seven Days"
Mary
"As"
"All That I Can Say"
"Deep Inside"
"Your Child"
"Give Me You"
No More Drama
"Family Affair"
"Dance for Me"
"No More Drama"
"Rainy Dayz"
Love & Life
"Love @ 1st Sight"
"Ooh!"
"Not Today"
"Whenever I Say Your Name"
"It's a Wrap"
The Breakthrough
"MJB da MVP"
"Be Without You"
"One"
"Enough Cryin"
"Take Me As I Am"
Reflections (A Retrospective)
"We Ride (I See the Future)"
Growing Pains
"Just Fine"
"Work That"
"Stay Down"
Stronger with Each Tear
"The One"
"I Am"
"Each Tear"
"We Got Hood Love"
My Life II... The Journey Continues (Act 1)
"Ain't Nobody"
"25/8"
"Don't Mind"
"Mr. Wrong"
"Why"
"Love a Woman"
"Someone to Love Me (Naked)"
A Mary Christmas
"Do You Hear What I Hear?"
"This Christmas"
Think Like a Man Too
"Suitcase"
The London Sessions
"Doubt"
"Right Now"
"Therapy "
"Whole Damn Year"
Strength of a Woman
"Thick of It"
"U + Me (Love Lesson)"
"Love Yourself"
Soundtracks
"(You Make Me Feel Like) A Natural Woman"
"Not Gon' Cry"
"Stronger"
"The Living Proof"
Guest appearances
"911"
"Ain't No Way"
"America's Song"
"Bridge over Troubled Water"
"Can't Knock the Hustle"
"Disrespectful"
"F for You"
"Hands"
"I'll Be There for You/You're All I Need to Get By"
"I'm a Hustla (Remix)"
"IfULeave"
"Just Stand Up!"
"Lean on Me"
"Magic Touch (NYC Remix)"
"Now or Never"
"Remember Me"
"Runaway Love"
"Stay with Me (Remix)"
"Touch It (Remix)"
"Wake Up Call (Mark Ronson Remix)"
"What Child Is This"
"Where Is the Love?"
Book
Category
[show]
v
t
e
Celine Dion English singles
Singles discography
Albums discography
1980s
"Listen to the Magic Man"
"Michael's Song"
"Can't Live with You, Can't Live Without You"
1990s
"(If There Was) Any Other Way"
"Unison"
"Where Does My Heart Beat Now"
"The Last to Know"
"Have a Heart"
"Beauty and the Beast"
"If You Asked Me To"
"Nothing Broken but My Heart"
"Love Can Move Mountains"
"Water from the Moon"
"Did You Give Enough Love"
"When I Fall in Love"
"The Power of Love"
"Misled"
"Love Lights the World"
"Think Twice"
"Only One Road"
"Calling You"
"Next Plane Out"
"Just Walk Away"
"To Love You More"
"(You Make Me Feel Like) A Natural Woman"
"Falling into You"
"Because You Loved Me"
"It's All Coming Back to Me Now"
"The Power of the Dream"
"All by Myself"
"Send Me a Lover"
"Call the Man"
"Make You Happy"
"Dreamin' of You"
"Tell Him"
"Be the Man"
"The Reason"
"My Heart Will Go On"
"Immortality"
"When I Need You"
"I Hate You Then I Love You"
"Miles to Go (Before I Sleep)"
"It's Hard to Say Goodbye"
"You've Got a Friend"
"I'm Your Angel"
"The Prayer"
"Treat Her Like a Lady"
"That's the Way It Is"
"Then You Look at Me"
2000s
"Live (for the One I Love)"
"The First Time Ever I Saw Your Face"
"I Want You to Need Me"
"If Walls Could Talk"
"Don't Save It All for Christmas Day"
"God Bless America"
"A New Day Has Come"
"I'm Alive"
"Goodbye's (The Saddest Word)"
"At Last"
"I Drove All Night"
"Have You Ever Been in Love"
"One Heart"
"Stand by Your Side"
"Faith"
"You and I"
"Beautiful Boy"
"Miracle"
"In Some Small Way"
"Taking Chances"
"Eyes on Me"
"A World to Believe In"
"Alone"
"My Love"
2010s
"Loved Me Back to Life"
"Breakaway"
"Incredible"
"Water and a Flame"
"Hymn"
"The Show Must Go On"
"Recovering"
"How Does a Moment Last Forever"
Other
"Voices That Care"
"What More Can I Give"
"Come Together Now"
"Sing"
"We Are the World 25 for Haiti"
Book
Category
Portal
[show]
v
t
e
Carole King
Studio albums
Writer
Tapestry
Music
Rhymes & Reasons
Fantasy
Wrap Around Joy
Thoroughbred
Simple Things
Welcome Home
Touch the Sky
Pearls: Songs of Goffin and King
One to One
Speeding Time
City Streets
Colour of Your Dreams
Love Makes the World
Compilations
Her Greatest Hits: Songs of Long Ago
The Legendary Demos
Live albums
In Concert
The Carnegie Hall Concert: June 18, 1971
The Living Room Tour
Live at the Troubadour
Other albums
A Holiday Carole
Singles
"It Might as Well Rain Until September"
"It's Too Late"/"I Feel the Earth Move"
"So Far Away"/"Smackwater Jack"
"You've Got a Friend"/"Beautiful" (Scandinavia only)
"Sweet Seasons"
"Been to Canaan"
"Jazzman"
"Nightingale"
"Only Love Is Real"
"One Fine Day"
"Now and Forever"
Other songs
"Wasn't Born to Follow"
"Goin' Back
"I Can't Hear You No More"
"Up on the Roof"
"Where You Lead"
"Will You Love Me Tomorrow"
"It's Going to Take Some Time"
"Some Kind of Wonderful"
"(You Make Me Feel Like) A Natural Woman"
Related articles
Discography
Troubadour Reunion Tour
A Natural Woman: A Memoir
Tapestry Revisited: A Tribute to Carole King
Beautiful: The Carole King Musical
Book
Category
Retrieved from "https://en.wikipedia.org/w/index.php?title=(You_Make_Me_Feel_Like)_A_Natural_Woman&oldid=807030357"
Categories:
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p-value
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Not to be confused with the P-factor.
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In statistical hypothesis testing, the p-value or probability value is the probability for a given statistical model that, when the null hypothesis is true, the statistical summary (such as the sample mean difference between two compared groups) would be the same as or of greater magnitude than the actual observed results.[1] The use of p-values in statistical hypothesis testing is common in many fields of research[2] such as physics, economics, finance, political science, psychology,[3] biology, criminal justice, criminology, and sociology.[4] Their misuse has been a matter of considerable controversy.
Contents
[hide]
1 Basic concepts
2 Definition and interpretation
3 Usage
4 Calculation
5 Examples
5.1 One roll of a pair of dice
5.2 Five heads in a row
5.3 Sample size dependence
5.4 Alternating coin flips
5.5 Coin flipping
6 Distribution
7 History
8 Related quantities
9 Controversy
10 Orthographic note
11 See also
12 Notes
13 References
14 Further reading
15 External links
Basic concepts[edit]
The p-value is used in the context of null hypothesis testing in order to quantify the idea of statistical significance of evidence.[a] Null hypothesis testing is a reductio ad absurdum argument adapted to statistics. In essence, a claim is assumed valid if its counter-claim is improbable.
As such, the only hypothesis that needs to be specified in this test and which embodies the counter-claim is referred to as the null hypothesis (that is, the hypothesis to be nullified). A result is said to be statistically significant if it allows us to reject the null hypothesis. That is, as per the reductio ad absurdum reasoning, the statistically significant result should be highly improbable if the null hypothesis is assumed to be true. The rejection of the null hypothesis implies that the correct hypothesis lies in the logical complement of the null hypothesis. However, unless there is a single alternative to the null hypothesis, the rejection of null hypothesis does not tell us which of the alternatives might be the correct one.
As a general example, if a null hypothesis is assumed to follow the standard normal distribution N(0,1), then the rejection of this null hypothesis can either mean (i) the mean is not zero, or (ii) the variance is not unity, or (iii) the distribution is not normal, depending on the type of test performed. However, supposing we manage to reject the zero mean hypothesis, even if we know the distribution is normal and variance is unity, the null hypothesis test does not tell us which non-zero value we should adopt as the new mean.
If X {\displaystyle X} is a random variable representing the observed data and H {\displaystyle H} is the statistical hypothesis under consideration, then the notion of statistical significance can be naively quantified by the conditional probability Pr ( X | H ) {\displaystyle \Pr(X|H)} , which gives the likelihood of the observation if the hypothesis is assumed to be correct. However, if X {\displaystyle X} is a continuous random variable and an instance x {\displaystyle x} is observed, Pr ( X = x | H ) = 0. {\displaystyle \Pr(X=x|H)=0.} Thus, this naive definition is inadequate and needs to be changed so as to accommodate the continuous random variables.
Nonetheless, it helps to clarify that p-values should not be confused with probability on hypothesis (as is done in Bayesian Hypothesis Testing) such as Pr ( H | X ) , {\displaystyle \Pr(H|X),} the probability of the hypothesis given the data, or Pr ( H ) , {\displaystyle \Pr(H),} the probability of the hypothesis being true, or Pr ( X ) , {\displaystyle \Pr(X),} the probability of observing the given data.
Definition and interpretation[edit]
Example of a p-value computation. The vertical coordinate is the probability density of each outcome, computed under the null hypothesis. The p-value is the area under the curve past the observed data point.
The p-value is defined as the probability, under the null hypothesis H {\displaystyle H} , of obtaining a result equal to or more extreme than what was actually observed. Depending on how it is looked at, the "more extreme than what was actually observed" can mean { X ≥ x } {\displaystyle \{X\geq x\}} (right-tail event) or { X ≤ x } {\displaystyle \{X\leq x\}} (left-tail event) or the "smaller" of { X ≤ x } {\displaystyle \{X\leq x\}} and { X ≥ x } {\displaystyle \{X\geq x\}} (double-tailed event). Thus, the p-value is given by
Pr ( X ≥ x | H ) {\displaystyle \Pr(X\geq x|H)} for right tail event,
Pr ( X ≤ x | H ) {\displaystyle \Pr(X\leq x|H)} for left tail event,
2 min { Pr ( X ≤ x | H ) , Pr ( X ≥ x | H ) } {\displaystyle 2\min\{\Pr(X\leq x|H),\Pr(X\geq x|H)\}} for double tail event.
The smaller the p-value, the larger the significance because it tells the investigator that the hypothesis under consideration may not adequately explain the observation. The null hypothesis H {\displaystyle H} is rejected if any of these probabilities is less than or equal to a small, fixed but arbitrarily pre-defined threshold value α {\displaystyle \alpha } , which is referred to as the level of significance. Unlike the p-value, the α {\displaystyle \alpha } level is not derived from any observational data and does not depend on the underlying hypothesis; the value of α {\displaystyle \alpha } is instead set by the researcher before examining the data.
Since the value of x {\displaystyle x} that defines the left tail or right tail event is a random variable, this makes the p-value a function of x {\displaystyle x} and a random variable in itself defined uniformly over [ 0 , 1 ] {\displaystyle [0,1]} interval, assuming x {\displaystyle x} is continuous. Thus, the p-value is not fixed. This implies that p-value cannot be given a frequency counting interpretation since the probability has to be fixed for the frequency counting interpretation to hold. In other words, if the same test is repeated independently bearing upon the same overall null hypothesis, it will yield different p-values at every repetition. Nevertheless, these different p-values can be combined using Fisher's combined probability test. It should further be noted that an instantiation of this random p-value can still be given a frequency counting interpretation with respect to the number of observations taken during a given test, as per the definition, as the percentage of observations more extreme than the one observed under the assumption that the null hypothesis is true.
The fixed pre-defined α {\displaystyle \alpha } level can be interpreted as the rate of falsely rejecting the null hypothesis (or type I error), since
Pr ( R e j e c t H | H ) = Pr ( p ≤ α | H ) = α {\displaystyle \Pr(\mathrm {Reject} \;H|H)=\Pr(p\leq \alpha |H)=\alpha } .
This also means that if we fix an instantiation of p-value and allow α {\displaystyle \alpha } to vary over [ 0 , 1 ] {\displaystyle [0,1]} , we can obtain an equivalent interpretation of p-value in terms of α {\displaystyle \alpha } level as the lowest value of α {\displaystyle \alpha } that can be assumed for which the null hypothesis can be rejected for a given set of observations.
Usage[edit]
The p-value is widely used in statistical hypothesis testing, specifically in null hypothesis significance testing. In this method, as part of experimental design, before performing the experiment, one first chooses a model (the null hypothesis) and a threshold value for p, called the significance level of the test, traditionally 5% or 1% [5] and denoted as α. If the p-value is less than the chosen significance level (α), that suggests that the observed data is sufficiently inconsistent with the null hypothesis that the null hypothesis may be rejected. However, that does not prove that the tested hypothesis is true. When the p-value is calculated correctly, this test guarantees that the Type I error rate is at most α. For typical analysis, using the standard α = 0.05 cutoff, the null hypothesis is rejected when p < .05 and not rejected when p > .05. The p-value does not, in itself, support reasoning about the probabilities of hypotheses but is only a tool for deciding whether to reject the null hypothesis.
Calculation[edit]
Usually, X {\displaystyle X} is a test statistic, rather than any of the actual observations. A test statistic is the output of a scalar function of all the observations. This statistic provides a single number, such as the average or the correlation coefficient, that summarizes the characteristics of the data, in a way relevant to a particular inquiry. As such, the test statistic follows a distribution determined by the function used to define that test statistic and the distribution of the input observational data.
For the important case in which the data are hypothesized to follow the normal distribution, depending on the nature of the test statistic and thus the underlying hypothesis of the test statistic, different null hypothesis tests have been developed. Some such tests are z-test for normal distribution, t-test for Student's t-distribution, f-test for f-distribution. When the data do not follow a normal distribution, it can still be possible to approximate the distribution of these test statistics by a normal distribution by invoking the central limit theorem for large samples, as in the case of Pearson's chi-squared test.
Thus computing a p-value requires a null hypothesis, a test statistic (together with deciding whether the researcher is performing a one-tailed test or a two-tailed test), and data. Even though computing the test statistic on given data may be easy, computing the sampling distribution under the null hypothesis, and then computing its cumulative distribution function (CDF) is often a difficult problem. Today, this computation is done using statistical software, often via numeric methods (rather than exact formulae), but in the early and mid 20th century, this was instead done via tables of values, and one interpolated or extrapolated p-values from these discrete values. Rather than using a table of p-values, Fisher instead inverted the CDF, publishing a list of values of the test statistic for given fixed p-values; this corresponds to computing the quantile function (inverse CDF).
Examples[edit]
Here a few simple examples follow, each illustrating a potential pitfall.
One roll of a pair of dice[edit]
Suppose a researcher rolls a pair of dice once and assumes a null hypothesis that the dice are fair, not loaded or weighted toward any specific number/roll/result; uniform. The test statistic is "the sum of the rolled numbers" and is one-tailed. The researcher rolls the dice and observes that both dice show 6, yielding a test statistic of 12. The p-value of this outcome is 1/36 (because under the assumption of the null hypothesis, the test statistic is uniformly distributed) or about 0.028 (the highest test statistic out of 6×6 = 36 possible outcomes). If the researcher assumed a significance level of 0.05, this result would be deemed significant and the hypothesis that the dice are fair would be rejected.
In this case, a single roll provides a very weak basis (that is, insufficient data) to draw a meaningful conclusion about the dice. This illustrates the danger with blindly applying p-value without considering the experiment design.
Five heads in a row[edit]
Suppose a researcher flips a coin five times in a row and assumes a null hypothesis that the coin is fair. The test statistic of "total number of heads" can be one-tailed or two-tailed: a one-tailed test corresponds to seeing if the coin is biased towards heads, but a two-tailed test corresponds to seeing if the coin is biased either way. The researcher flips the coin five times and observes heads each time (HHHHH), yielding a test statistic of 5. In a one-tailed test, this is the upper extreme of all possible outcomes, and yields a p-value of (1/2)5 = 1/32 ≈ 0.03. If the researcher assumed a significance level of 0.05, this result would be deemed significant and the hypothesis that the coin is fair would be rejected. In a two-tailed test, a test statistic of zero heads (TTTTT) is just as extreme and thus the data of HHHHH would yield a p-value of 2×(1/2)5 = 1/16 ≈ 0.06, which is not significant at the 0.05 level.
This demonstrates that specifying a direction (on a symmetric test statistic) halves the p-value (increases the significance) and can mean the difference between data being considered significant or not.
Sample size dependence[edit]
Suppose a researcher flips a coin some arbitrary number of times (n) and assumes a null hypothesis that the coin is fair. The test statistic is the total number of heads and is a two-tailed test. Suppose the researcher observes heads for each flip, yielding a test statistic of n and a p-value of 2/2n. If the coin was flipped only 5 times, the p-value would be 2/32 = 0.0625, which is not significant at the 0.05 level. But if the coin was flipped 10 times, the p-value would be 2/1024 ≈ 0.002, which is significant at the 0.05 level.
In both cases the data suggest that the null hypothesis is false (that is, the coin is not fair somehow), but changing the sample size changes the p-value. In the first case, the sample size is not large enough to allow the null hypothesis to be rejected at the 0.05 level (in fact, the p-value can never be below 0.05 for the coin example).
This demonstrates that in interpreting p-values, one must also know the sample size, which complicates the analysis.
Alternating coin flips[edit]
Suppose a researcher flips a coin ten times and assumes a null hypothesis that the coin is fair. The test statistic is the total number of heads and is two-tailed. Suppose the researcher observes alternating heads and tails with every flip (HTHTHTHTHT). This yields a test statistic of 5 and a p-value of 1 (completely unexceptional), as that is the expected number of heads.
Suppose instead that the test statistic for this experiment was the "number of alternations" (that is, the number of times when H followed T or T followed H), which is one-tailed. That would yield a test statistic of 9, which is extreme and has a p-value of 2 / 2 9 = 1 / 256 ≈ 0.0039 {\displaystyle 2/2^{9}=1/256\approx 0.0039} . That would be considered extremely significant, well beyond the 0.05 level. These data indicate that, in terms of one test statistic, the data set is extremely unlikely to have occurred by chance, but it does not suggest that the coin is biased towards heads or tails.
By the first test statistic, the data yield a high p-value, suggesting that the number of heads observed is not unlikely. By the second test statistic, the data yield a low p-value, suggesting that the pattern of flips observed is very, very unlikely. There is no "alternative hypothesis" (so only rejection of the null hypothesis is possible) and such data could have many causes. The data may instead be forged, or the coin may be flipped by a magician who intentionally alternated outcomes.
This example demonstrates that the p-value depends completely on the test statistic used and illustrates that p-values can only help researchers to reject a null hypothesis, not consider other hypotheses.
Coin flipping[edit]
Main article: Checking whether a coin is fair
As an example of a statistical test, an experiment is performed to determine whether a coin flip is fair (equal chance of landing heads or tails) or unfairly biased (one outcome being more likely than the other).
Suppose that the experimental results show the coin turning up heads 14 times out of 20 total flips. The null hypothesis is that the coin is fair, and the test statistic is the number of heads. If a right-tailed test is considered, the p-value of this result is the chance of a fair coin landing on heads at least 14 times out of 20 flips. That probability can be computed from binomial coefficients as
Prob  ( 14 heads ) + Prob  ( 15 heads ) + ⋯ + Prob  ( 20 heads ) = 1 2 20 [ ( 20 14 ) + ( 20 15 ) + ⋯ + ( 20 20 ) ] = 60 , 460 1 , 048 , 576 ≈ 0.058 {\displaystyle {\begin{aligned}&\operatorname {Prob} (14{\text{ heads}})+\operatorname {Prob} (15{\text{ heads}})+\cdots +\operatorname {Prob} (20{\text{ heads}})\\&={\frac {1}{2^{20}}}\left[{\binom {20}{14}}+{\binom {20}{15}}+\cdots +{\binom {20}{20}}\right]={\frac {60,\!460}{1,\!048,\!576}}\approx 0.058\end{aligned}}}
This probability is the p-value, considering only extreme results that favor heads. This is called a one-tailed test. However, the deviation can be in either direction, favoring either heads or tails. The two-tailed p-value, which considers deviations favoring either heads or tails, may instead be calculated. As the binomial distribution is symmetrical for a fair coin, the two-sided p-value is simply twice the above calculated single-sided p-value: the two-sided p-value is 0.115.
In the above example:
Null hypothesis (H0): The coin is fair, with Prob(heads) = 0.5
Test statistic: Number of heads
Level of significance: 0.05
Observation O: 14 heads out of 20 flips; and
Two-tailed p-value of observation O given H0 = 2*min(Prob(no. of heads ≥ 14 heads), Prob(no. of heads ≤ 14 heads))= 2*min(0.058, 0.978) = 2*0.058 = 0.115.
Note that the Prob(no. of heads ≤ 14 heads) = 1 - Prob(no. of heads ≥ 14 heads) + Prob(no. of head = 14) = 1 - 0.058 + 0.036 = 0.978; however, symmetry of the binomial distribution makes that an unnecessary computation to find the smaller of the two probabilities. Here, the calculated p-value exceeds 0.05, so the observation is consistent with the null hypothesis, as it falls within the range of what would happen 95% of the time were the coin in fact fair. Hence, the null hypothesis at the 5% level is not rejected. Although the coin did not fall evenly, the deviation from expected outcome is small enough to be consistent with chance.
However, had one more head been obtained, the resulting p-value (two-tailed) would have been 0.0414 (4.14%). The null hypothesis is rejected when a 5% cut-off is used.
Distribution[edit]
When the null hypothesis is true, if it takes the form H 0 : θ = θ 0 {\displaystyle H_{0}:\theta =\theta _{0}} , and the underlying random variable is continuous, then the probability distribution of the p-value is uniform on the interval [0,1]. By contrast, if the alternative hypothesis is true, the distribution is dependent on sample size and the true value of the parameter being studied.[2][6]
The distribution of p-values for a group of studies is called a p-curve.[7] The curve is affected by four factors: the proportion of studies that examined false null hypotheses, the power of the studies that investigated false null hypotheses, the alpha levels, and publication bias.[8] A p-curve can be used to assess the reliability of scientific literature, such as by detecting publication bias or p-hacking.[7][9]
History[edit]
Pierre-Simon Laplace
Computations of p-values date back to the 1770s, when they were calculated by Pierre-Simon Laplace:[10]
In the 1770s Laplace considered the statistics of almost half a million births. The statistics showed an excess of boys compared to girls. He concluded by calculation of a p-value that the excess was a real, but unexplained, effect.
The p-value was first formally introduced by Karl Pearson, in his Pearson's chi-squared test,[11] using the chi-squared distribution and notated as capital P.[11] The p-values for the chi-squared distribution (for various values of χ2 and degrees of freedom), now notated as P, was calculated in (Elderton 1902), collected in (Pearson 1914, pp. xxxi–xxxiii, 26–28, Table XII).
The use of the p-value in statistics was popularized by Ronald Fisher,[12] and it plays a central role in his approach to the subject.[13] In his influential book Statistical Methods for Research Workers (1925), Fisher proposes the level p = 0.05, or a 1 in 20 chance of being exceeded by chance, as a limit for statistical significance, and applies this to a normal distribution (as a two-tailed test), thus yielding the rule of two standard deviations (on a normal distribution) for statistical significance (see 68–95–99.7 rule).[14][b][15]
He then computes a table of values, similar to Elderton but, importantly, reverses the roles of χ2 and p. That is, rather than computing p for different values of χ2 (and degrees of freedom n), he computes values of χ2 that yield specified p-values, specifically 0.99, 0.98, 0.95, 0,90, 0.80, 0.70, 0.50, 0.30, 0.20, 0.10, 0.05, 0.02, and 0.01.[16] That allowed computed values of χ2 to be compared against cutoffs and encouraged the use of p-values (especially 0.05, 0.02, and 0.01) as cutoffs, instead of computing and reporting p-values themselves. The same type of tables were then compiled in (Fisher & Yates 1938), which cemented the approach.[15]
As an illustration of the application of p-values to the design and interpretation of experiments, in his following book The Design of Experiments (1935), Fisher presented the lady tasting tea experiment,[17] which is the archetypal example of the p-value.
To evaluate a lady's claim that she (Muriel Bristol) could distinguish by taste how tea is prepared (first adding the milk to the cup, then the tea, or first tea, then milk), she was sequentially presented with 8 cups: 4 prepared one way, 4 prepared the other, and asked to determine the preparation of each cup (knowing that there were 4 of each). In that case, the null hypothesis was that she had no special ability, the test was Fisher's exact test, and the p-value was 1 / ( 8 4 ) = 1 / 70 ≈ 0.014 , {\displaystyle 1/{\binom {8}{4}}=1/70\approx 0.014,} so Fisher was willing to reject the null hypothesis (consider the outcome highly unlikely to be due to chance) if all were classified correctly. (In the actual experiment, Bristol correctly classified all 8 cups.)
Fisher reiterated the p = 0.05 threshold and explained its rationale, stating:[18]
It is usual and convenient for experimenters to take 5 per cent as a standard level of significance, in the sense that they are prepared to ignore all results which fail to reach this standard, and, by this means, to eliminate from further discussion the greater part of the fluctuations which chance causes have introduced into their experimental results.
He also applies this threshold to the design of experiments, noting that had only 6 cups been presented (3 of each), a perfect classification would have only yielded a p-value of 1 / ( 6 3 ) = 1 / 20 = 0.05 , {\displaystyle 1/{\binom {6}{3}}=1/20=0.05,} which would not have met this level of significance.[18] Fisher also underlined the interpretation of p, as the long-run proportion of values at least as extreme as the data, assuming the null hypothesis is true.
In later editions, Fisher explicitly contrasted the use of the p-value for statistical inference in science with the Neyman–Pearson method, which he terms "Acceptance Procedures".[19] Fisher emphasizes that while fixed levels such as 5%, 2%, and 1% are convenient, the exact p-value can be used, and the strength of evidence can and will be revised with further experimentation. In contrast, decision procedures require a clear-cut decision, yielding an irreversible action, and the procedure is based on costs of error, which, he argues, are inapplicable to scientific research.
Related quantities[edit]
A closely related concept is the E-value,[20] which is the expected number of times in multiple testing that one expects to obtain a test statistic at least as extreme as the one that was actually observed if one assumes that the null hypothesis is true. The E-value is the product of the number of tests and the p-value.
Controversy[edit]
Main article: Misunderstandings of p-values
There is widespread agreement that p-values are often misused and misinterpreted.[21][22][23] One practice that has been particularly criticized is accepting the alternative hypothesis for any p-value nominally less than .05 without other supporting evidence. Although p-values are helpful in assessing how incompatible the data are with a specified statistical model, contextual factors must also be considered, such as "the design of a study, the quality of the measurements, the external evidence for the phenomenon under study, and the validity of assumptions that underlie the data analysis".[23] Another concern is that the p-value is often misunderstood as being the probability that the null hypothesis is true.[23][24] Some statisticians have proposed replacing p-values with alternative measures of evidence,[23] such as confidence intervals,[25][26] likelihood ratios,[27][28] or Bayes factors,[29][30][31] but there is heated debate on the feasibility of these alternatives.[32][33] Others have suggested to remove fixed significance thresholds and to interpret p-values as continuous indices of the strength of evidence against the null hypothesis.[34][35]
Orthographic note[edit]
Depending on which style guide is applied, the "p" is styled either italic or not, either capitalized or not, and either hyphenated or not. For example, AMA style uses "P value," APA style uses "p value," and the American Statistical Association uses "p-value."[36]
See also[edit]
Bonferroni correction
Confidence interval
Counternull
False discovery rate
Fisher's method of combining p-values
Generalized p-value
Holm–Bonferroni method
Multiple comparisons
Null hypothesis
p-rep
p-value fallacy
Statistical hypothesis testing
Notes[edit]
Jump up ^ Note that the statistical significance of a result does not imply that the result is scientifically significant as well.
Jump up ^ To be precise the p = 0.05 corresponds to about 1.96 standard deviations for a normal distribution (two-tailed test), and 2 standard deviations corresponds to about a 1 in 22 chance of being exceeded by chance, or p ≈ 0.045; Fisher notes these approximations.
References[edit]
Jump up ^ Wasserstein, Ronald L.; Lazar, Nicole A. (7 March 2016). "The ASA's Statement on p-Values: Context, Process, and Purpose". The American Statistician. 70 (2): 129–133. doi:10.1080/00031305.2016.1154108. Retrieved 30 October 2016.
^ Jump up to: a b Bhattacharya, Bhaskar; Habtzghi, DeSale (2002). "Median of the p value under the alternative hypothesis". The American Statistician. American Statistical Association. 56 (3): 202–6. doi:10.1198/000313002146. Retrieved 19 February 2016.
Jump up ^ Wetzels, R.; Matzke, D.; Lee, M. D.; Rouder, J. N.; Iverson, G. J.; Wagenmakers, E. -J. (2011). "Statistical Evidence in Experimental Psychology: An Empirical Comparison Using 855 t Tests". Perspectives on Psychological Science. 6 (3): 291–298. doi:10.1177/1745691611406923.
Jump up ^ Babbie, E. (2007). The practice of social research 11th ed. Thomson Wadsworth: Belmont, California.
Jump up ^ Nuzzo, R. (2014). "Scientific method: Statistical errors". Nature. 506 (7487): 150–152. doi:10.1038/506150a.
Jump up ^ Hung, H.M.J.; O'Neill, R.T.; Bauer, P.; Kohne, K. (1997). "The behavior of the p-value when the alternative hypothesis is true". Biometrics. International Biometric Society. 53 (1): 11–22. doi:10.2307/2533093. JSTOR 2533093.
^ Jump up to: a b Head ML, Holman L, Lanfear R, Kahn AT, Jennions MD (2015). "The extent and consequences of p-hacking in science". PLoS Biol. 13 (3): e1002106. doi:10.1371/journal.pbio.1002106. PMC 4359000  . PMID 25768323.
Jump up ^ Lakens D (2015). "What p-hacking really looks like: a comment on Masicampo and LaLande (2012)". Q J Exp Psychol (Hove). 68 (4): 829–32. doi:10.1080/17470218.2014.982664. PMID 25484109.
Jump up ^ Simonsohn U, Nelson LD, Simmons JP (2014). "p-Curve and Effect Size: Correcting for Publication Bias Using Only Significant Results". Perspect Psychol Sci. 9 (6): 666–81. doi:10.1177/1745691614553988. PMID 26186117.
Jump up ^ Stigler 1986, p. 134.
^ Jump up to: a b Pearson 1900.
Jump up ^ Inman 2004.
Jump up ^ Hubbard & Bayarri 2003, p. 1.
Jump up ^ Fisher 1925, p. 47, Chapter III. Distributions.
^ Jump up to: a b Dallal 2012, Note 31: Why P=0.05?.
Jump up ^ Fisher 1925, pp. 78–79, 98, Chapter IV. Tests of Goodness of Fit, Independence and Homogeneity; with Table of χ2, Table III. Table of χ2.
Jump up ^ Fisher 1971, II. The Principles of Experimentation, Illustrated by a Psycho-physical Experiment.
^ Jump up to: a b Fisher 1971, Section 7. The Test of Significance.
Jump up ^ Fisher 1971, Section 12.1 Scientific Inference and Acceptance Procedures.
Jump up ^ National Institutes of Health definition of E-value
Jump up ^ "Scientists Perturbed by Loss of Stat Tool to Sift Research Fudge from Fact". Scientific American. April 16, 2015.
Jump up ^ Goodman SN (1999). "Toward evidence-based medical statistics. 1: The P value fallacy". Annals of Internal Medicine. 130 (12): 995–1004. doi:10.7326/0003-4819-130-12-199906150-00008. PMID 10383371.
^ Jump up to: a b c d Wasserstein, Ronald L.; Lazar, Nicole A. (2016). "ASA". The American Statistician. 70: 129–133. doi:10.1080/00031305.2016.1154108.
Jump up ^ Colquhoun, David (2014). "An investigation of the false discovery rate and the misinterpretation of p-values". Royal Society Open Science. 1: 140216. doi:10.1098/rsos.140216.
Jump up ^ Lee, Dong Kyu (7 March 2017). "Alternatives to P value: confidence interval and effect size". Korean Journal of Anesthesiology. 69 (6): 555–562. doi:10.4097/kjae.2016.69.6.555. ISSN 2005-6419. PMC 5133225  . PMID 27924194.
Jump up ^ Ranstam, J. (August 2012). "Why the P-value culture is bad and confidence intervals a better alternative". Osteoarthritis and Cartilage. 20 (8): 805–808. doi:10.1016/j.joca.2012.04.001. Retrieved 7 March 2017.
Jump up ^ Perneger, Thomas V (12 May 2001). "Sifting the evidence: Likelihood ratios are alternatives to P values". BMJ: British Medical Journal. 322 (7295): 1184. ISSN 0959-8138. PMC 1120301  . PMID 11379590.
Jump up ^ Royall, Richard. "The Likelihood Paradigm for Statistical Evidence". The Nature of Scientific Evidence. pp. 119–152. doi:10.7208/chicago/9780226789583.003.0005.
Jump up ^ Schimmack, Ulrich (30 April 2015). "Replacing p-values with Bayes-Factors: A Miracle Cure for the Replicability Crisis in Psychological Science". Replicability-Index. Retrieved 7 March 2017.
Jump up ^ Marden, John I. (December 2000). "Hypothesis Testing: From p Values to Bayes Factors". Journal of the American Statistical Association. 95 (452): 1316. doi:10.2307/2669779. |access-date= requires |url= (help)
Jump up ^ Stern, Hal S. (16 February 2016). "A Test by Any Other Name: Values, Bayes Factors, and Statistical Inference". Multivariate Behavioral Research. 51 (1): 23–29. doi:10.1080/00273171.2015.1099032. PMC 4809350  . PMID 26881954.
Jump up ^ Murtaugh, Paul A. (March 2014). "In defense of p-values". Ecology. 95 (3): 611–617. doi:10.1890/13-0590.1. |access-date= requires |url= (help)
Jump up ^ Aschwanden, Christie (Mar 7, 2016). "Statisticians Found One Thing They Can Agree On: It's Time To Stop Misusing P-Values". FiveThirtyEight.
Jump up ^ Amrhein, Valentin; Korner-Nievergelt, Fränzi; Roth, Tobias (2017). "The earth is flat (p > 0.05): significance thresholds and the crisis of unreplicable research". PeerJ. 5: e3544. doi:10.7717/peerj.3544.
Jump up ^ Amrhein, Valentin; Greenland, Sander (2017). "Remove, rather than redefine, statistical significance". Nature Human Behaviour. 1: 0224. doi:10.1038/s41562-017-0224-0.
Jump up ^ http://magazine.amstat.org/wp-content/uploads/STATTKadmin/style%5B1%5D.pdf
Further reading[edit]
Pearson, Karl (1900). "On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling" (PDF). Philosophical Magazine. Series 5. 50 (302): 157–175. doi:10.1080/14786440009463897.
Elderton, William Palin (1902). "Tables for Testing the Goodness of Fit of Theory to Observation". Biometrika. 1 (2): 155–163. doi:10.1093/biomet/1.2.155.
Fisher, Ronald (1925). Statistical Methods for Research Workers. Edinburgh: Oliver & Boyd. ISBN 0-05-002170-2.
Fisher, Ronald A. (1971) [1935]. The Design of Experiments (9th ed.). Macmillan. ISBN 0-02-844690-9.
Fisher, R. A.; Yates, F. (1938). Statistical tables for biological, agricultural and medical research. London.
Stigler, Stephen M. (1986). The history of statistics : the measurement of uncertainty before 1900. Cambridge, Mass: Belknap Press of Harvard University Press. ISBN 0-674-40340-1.
Hubbard, Raymond; Bayarri, M. J. (November 2003), P Values are not Error Probabilities (PDF), a working paper that explains the difference between Fisher's evidential p-value and the Neyman–Pearson Type I error rate α.
Hubbard, Raymond; Armstrong, J. Scott (2006). "Why We Don't Really Know What Statistical Significance Means: Implications for Educators" (PDF). Journal of Marketing Education. 28 (2): 114–120. doi:10.1177/0273475306288399. Archived from the original on May 18, 2006. CS1 maint: Unfit url (link)
Hubbard, Raymond; Lindsay, R. Murray (2008). "Why P Values Are Not a Useful Measure of Evidence in Statistical Significance Testing" (PDF). Theory & Psychology. 18 (1): 69–88. doi:10.1177/0959354307086923.
Stigler, S. (December 2008). "Fisher and the 5% level". Chance. 21 (4): 12. doi:10.1007/s00144-008-0033-3.
Dallal, Gerard E. (2012). The Little Handbook of Statistical Practice.
Biau, D.J.; Jolles, B.M.; Porcher, R. (March 2010). "P value and the theory of hypothesis testing: an explanation for new researchers". Clin Orthop Relat Res. 463 (3): 885–892. doi:10.1007/s11999-009-1164-4.
Reinhart, Alex. Statistics Done Wrong: The Woefully Complete Guide. No Starch Press. p. 176. ISBN 978-1593276201.
External links[edit]
Wikimedia Commons has media related to P-value.
Free online p-values calculators for various specific tests (chi-square, Fisher's F-test, etc.).
Understanding p-values, including a Java applet that illustrates how the numerical values of p-values can give quite misleading impressions about the truth or falsity of the hypothesis under test.
StatQuest: P Values, clearly explained on YouTube
StatQuest: P-value pitfalls and power calculations on YouTube
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text:
I've Got the Joy Joy Joy Joy
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This article is an orphan, as no other articles link to it. Please introduce links to this page from related articles; try the Find link tool for suggestions. (February 2009)
"Down In My Heart," sometimes titled "I've Got the Joy" is a popular Christian song often sung around the campfire and during scouting events. It is often included in Gospel music and a cappella concerts and songbooks. The song was written by George Willis Cooke (23 April 1848 - 30 April 1923). The date of authorship is as yet unknown.[original research?] Cooke was born in Comstock, Michigan. He was a Unitarian minister, writer, and editor and is well known for his landmark history of the Unitarian movement in the 19th century. Though largely self-taught, he studied at Meadeville Theological School in 1872. He was ordained in June of that year, not having obtained a degree from the school. He served the parish ministry for 28 years, while writing and editing. He left the ministry in 1900 to pursue scholarship and lecturing. He authored more than 20 books on a wide range of subjects.
Contents
[hide]
1 Lyrics
2 In popular culture
3 References
4 External links
Lyrics[edit]
There are many possible lyrics. The most common opening lyric and chorus is as follows:
I've got the joy, joy, joy, joy
Down in my heart (Where?)
Down in my heart (Where?)
Down in my heart
I've got the joy, joy, joy, joy
Down in my heart
Down in my heart to stay
And I'm so happy
So very happy
I have the love of Jesus in my heart (down in my heart)
And I'm so happy
So very happy
I have the love of Jesus in my heart
Subsequent lyrics include:
I've got the peace that passes understanding down in my heart...
I've got the far out faith that freaks out the farmers down in my heart...
I've got the glorious hope of my blessed redeemer way down in the depths of my heart...
I've got the mighty Messiah that manifests miracles down in the depths of my heart...
I've got the beautiful blessing that baffles the Buddhists down in the depths of my heart...
I've got the Christian confession the confuses the Communists down in the depths of my heart...
I've got the far out feeling that freaks out the Pharisees down in the depths of my heart...
I've got the love of Jesus Christ my savior down in my heart...
I've got the wonderful love of my blessed redeemer way down in the depths of my heart...
And if the devil doesn't like it he can sit on a tack, ouch, sit on a tack, ouch, sit on a tack. And if the devil doesn't like it he can sit on a tack. Sit on a tack to stay.
I've got the brightest light in the depths of my heart...
I've got the infinite love of the living lord down in the depths of my heart...
I've got the love of Jesus, love of Jesus down in my heart...
I've got that opposition to conscription down in my heart...[1]
In popular culture[edit]
Origin of the title of William Stafford's prose memoir of his WWII pacifist service, Down In My Heart.[2]
NRBQ's version of the song is played in the final moments of FX's American television series "Wilfred". Though the context it's played in is not conducive to the songs original theme of Christianity, instead referring to the main characters coming to peace with his state of mind, it is possibly for this reason that only the chorus of the song is played.
This is the gospel song Granny (actress Irene Ryan) sings in an episode of the 1960s TV sitcom, "The Beverly Hillbillies"
Sung by The Simpsons characters Rod and Todd in episode 410 (Lisa's First Word) originally aired 3 December 1993.
Included by The Housemartins as one of the tracks on the London 0 Hull 4 Deluxe Edition album, from when lead singer Paul Heaton's lyrics reflected his Christian views at the time.
The song is sung by Jeremy Sumpter and Matt O'Leary at the beginning of the 2001 thriller Frailty.
Used in Coca-Cola ad April, 2015.
In the 2014 Game LISA, the song is repeatedly sung by the character Buzzo when offering the in-game drug, Joy.
In 2015, S7E7 of Tosh.0 featured Daniel Tosh referencing and singing it.
In 2016, VolksWagen used the song in a TV commercial aired during the UEFA Euro 2016.
In 2017, it is sung in the first episode of Sun Records.
References[edit]
Jump up ^ p. 47, Kim Stafford, Early Morning: Remembering My Father, William Stafford, Publisher Trinity University Press, 2014 ISBN 1595341862, 9781595341860
Jump up ^ Kim Stafford, Early Morning: Remembering My Father, William Stafford, Publisher Trinity University Press, 2014 ISBN 9781595341860
External links[edit]
I've Got the Joy lyrics (with guitar chords)
I've Got the Joy Joy Joy is often sung quickly resulting in Misheard Lyrics
The song, as sung by "Noelle & John" is available for free download in MP3 format
Retrieved from "https://en.wikipedia.org/w/index.php?title=I%27ve_Got_the_Joy_Joy_Joy_Joy&oldid=812229504"
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Songs about happiness
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Songs about the Devil
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