σ σ r = x i x N Statistics Formulas Sample Mean Population Mean Interquartile Range Population Variance Population Standard Deviation

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Sherman Phelps
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1 Stattc Formula Samle Mea Poulato Mea µ Iterquartle Rae IQR Q 3 Q Samle Varace ( ) Samle Stadard Devato ( ) Poulato Varace Poulato Stadard Devato ( µ ) Coecet o Varato Stadard Devato CV 00% Mea ( µ ) -Score or Samle Covarace y µ ( )( y y) Poulato Covarace y ( µ )( y µ ) y Pearo Product Momet Correlato Coecet (Pearo R): Samle Data Poulato Data r y y y y ρ y y - -

2 Stattc Formula - - Wehted Mea w w w Samle Mea or Groued Data Poulato Mea or Groued Data M M µ Samle Varace or Groued Data Poulato Varace or Groued Data M M µ Samle Stadard Devato or Groued Data Poulato Stadard Devato or Groued Data M M µ

3 Stattc Formula Cout Rule or Combato C r! r!( r)! Cout Rule or Permutato P r! ( r)! Comut Probablty U the Comlemet C A) A ) Addto Law A A) A Codtoal Probablty A A or B A) A A) Multlcato Law P ( A A or P ( A A) B A) Multlcato Law or Ideedet vet P ( A A) ected Value o a Dcrete Radom Varable µ Varace o a Dcrete Radom Varable Var µ Bomal Probablty Fucto!!( )! ( ) ected Value ad Varace or the Bomal Dtrbuto ) µ ( Var( ) ( ) Poo Probablty Fucto e! µ µ where () the robablty o occurrece a terval µ the eected value or mea umber o occurrece a terval e

4 Stattc Formula Saml & Saml Dtrbuto Stadard Devato o (Stadard rror) For a Fte Poulato For a Ite Poulato Saml Proorto Stadard Devato o (Stadard rror) For a Fte Poulato For a Ite Poulato q Iterval tmate o a Poulato Mea: Kow ± Where Iterval tmate o a Poulato Mea: Ukow ± t Where q Samle Sze or a Iterval tmate o a Poulato Mea Iterval tmate o a Poulato Proorto ± q Samle Sze or a Iterval tmate o a Poulato Proorto * q * - 4 -

5 Stattc Formula Saml Proorto Tet Stattc or Hyothe Tet About a Poulato Proorto Stadard Devato o (Stadard rror) For a Fte Poulato For a Ite Poulato Iterval tmate o a Poulato Mea: Kow ± Where ± Iterval tmate o a Poulato Mea: Ukow ± Where t ± t Iterval tmate o a Poulato Proorto ± Iterval tmate o the Derece Betwee Two Poulato Proorto ± Samle Sze or a Iterval tmate o Poulato Proorto ad ormal Dtrbuto * * q α

6 Stattc Formula Value Formula or ormal ad Aromately ormal Dtrbuto Calculato o Tet Stattc µ Kow S t 0 µ Ukow Tet Stattc or Hyothe Tet About Two Ideedet Proorto Stadard rror o Deree o Freedom or the t Dtrbuto U Two Ideedet Radom Samle.. d Tet Stattc or Hyothe Tet About Two Ideedet Mea; Poulato Stadard Devato Ukow 0 D t Tet Stattc or Hyothe Tet Ivolv Matched Samle d t d µ d

7 Stattc Formula Mea Derece Ivolv Matched (or Deedet) Samle d ( d ) Stadard Devato otato Ued or Matched Samle d ( d d ) Iterval tmate o Mea o Matched Samle S d d ± tα / Tet Stattc or Hyothe Tet About a Poulato Varace χ χ d.. 0 Tet Stattc or Hyothe Tet About Two Poulato Varace whe F d umerator ad d deomato r Iterval tmate o the Derece Betwee Two Poulato Mea: ad Kow ad Ukow ± α / ( kow) S ± tα / ( ukow) Pooled Samle Stadard Devato (Aumto that ad are equal ad oulato are aromately ormal) & Tet Stattc or Comaro o Ideedet Samle ( ) S ( ) S S d.. t S ( ) S D 0-7 -

8 Stattc Formula Ch-Square Goode o Ft Tet Stattc χ ( ) o e ; d.. ( c e ) Ch-Square Tet or Ideedece Tet Stattc χ o e ; d.. ( c )( r e ) Tet or the qualty o k Poulato Mea AOVA Samle Mea or Treatmet Samle Varace or Treatmet Overall Samle Mea (Grad Mea) Mea Square Due to Treatmet Sum o Square Due to Treatmet Mea Square Due to rror k SSTR T MSTR k ( ) SSTR k k SS MS k T

9 Stattc Formula Sum o Square Due to rror SS Tet Stattc or the qualty o k Poulato Mea k Total Sum o Square Partto o Sum o Square SST F MSTR MS k SST SSTR SS Multle Comaro Procedure Tet Stattc or Fher LSD Procedure Fher LSD t MS ( ) Comletely Radomzed De Mea Square Due to Treatmet Mea Square Due to rror LSD t α / MS MSTR MS k k k ( ) T k - 9 -

10 Stattc Formula F Tet Stattc Radomzed Block De Total Sum o Square Sum o Square Due to Treatmet Sum o Square Due to Block SST F SSTR b MSTR MS b k k Sum o Square Due to rror SSBL k b SS SST SSTR SSBL Factoral ermet Total Sum o Square Sum o Square or Factor A Sum o Square or Factor B SST SSA br a b r k k a SSB ar b - 0 -

11 Stattc Formula Sum o Square or Iteracto Sum o Square or rror SSAB SS r a b ( ) SST SSA SSB SSAB Smle Lear Rereo Formula Smle Lear Rereo Model y 0 Smle Lear Rereo quato 0 β tmated Smle Lear Rereo quato y b0 b Leat Square Crtero β β ε ( y) β m Sloe ad y-itercet or the tmated Rereo quato Total Sum o Square Sum o Square Due to rror b ( y y ) ( )( y y) ( ) b0 y b ( y y) SST SS ( y y ) Sum o Square Due to Rereo ( y y) SSR - -

12 Stattc Formula Total Sum o Square or Rereo SST SSR SS Coecet o Determato Samle Correlato Coecet r SSR SST r y ( o b ) ( o b ) r Coecet o Determato Mea Square rror (tmate o ) Stadard rror o the tmate Stadard Devato o b tmated Stadard Devato o b t Tet Stattc Mea Square Rereo b b MSR MS MS t SS SS ( ) ( ) b b SSR # deedet varable - -

13 Stattc Formula F Tet Stattc tmated Stadard Devato o Codece Iterval or ( y ) ŷ y F MSR MS ( ) ( ) y ± tα / y tmated Stadard Devato o a Idvdual Value Predcto Iterval or y Redual or Obervato d Stadard Devato o the th Redual Stadardzed Redual or Obervato Leverae o Obervato ( ) ( ) y ± tα / d y y y y h y y y y h ( ) ( ) - 3 -

14 Stattc Formula oarametrc Method Formula Ma-Whtey-Wlcoo Tet (Lare Samle) Krukall-Wall Tet Stattc W Mea : µ T Stadard Devato: T k R 3 T T ( T ) ( ) Searma Rak Correlato Coecet r 6 d ( ) - 4 -

Formulas and Tables from Beginning Statistics

Formulas and Tables from Beginning Statistics Fmula ad Table from Begg Stattc Chater Cla Mdot Relatve Frequecy Chater 3 Samle Mea Poulato Mea Weghted Mea Rage Lower Lmt Uer Lmt Cla Frequecy Samle Se µ ( w) w f Mamum Data Value - Mmum Data Value Poulato