Below are the following formulas for the z-scores section.
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1 Statitic 010: Statitic for the Social ad Behavioral Sciece Formula Hadout Below are the followig formula for the z-core ectio. eaure of cetral tedecy ad variability ea Rage Rage = highet lowet Variace (ote that SD ad SD i rarely if ever ued. We will lear the commo variace ad tadard deviatio formula for a amle later i the emeter ( SD ( Stadard Deviatio ( SD ( Other formula Full Rage Full Rage = highet lowet + 1 Percet Frequecy ercet % (100 Freq.% (100 Skewe med med k (3 k (3 Skewe Table Lower Uer Lower Uer Page 1
2 Below are the followig formula for z-core, the z-tet ad t-tet. Z-core ( z ad z( Z-Tet z ( Stadard error of the mea Stadard deviatio for a oulatio Effect Size ( d Cofidece Iterval z z ( ( ( amle amle Sigle Samle T-Tet ( t Etimated tadard error of the mea Stadard deviatio for etimatig i a oulatio ( ( 1 Page
3 Effect Size ( d Cofidece Iterval t t ( ( amle amle Paired Samle T-Tet ( t t Etimated tadard error of the mea erece Stadard deviatio of core erece for etimatig i a oulatio ( 1 Effect Size ( d Cofidece Iterval t t ( ( amle amle ( d Ideedet Samle T-Tet ( ( t ( t _ A Show i Cla Etimated tadard error of the erece betwee mea Page 3
4 Etimated variace ooled ( ( ( A Show i Textbook Etimated tadard error of the erece betwee mea erece erece Etimated variace of the erece betwee mea Etimated variace for ditributio of erece betwee mea for ooled x Etimated variace for ditributio of erece betwee mea for ooled y Etimated variace ooled df x ooled df Tot Etimated variace for x 1 Etimated variace for y 1 Effect Size d erece ( x y df df Tot ad y (i cla (i textbook or ooled ooled Cofidece Iterval (i cla ( ( t t ( ( ( ( amle amle Page 4
5 (i textbook ( ( Below are the followig formula for F-tet, r-tet, ad regreio. Betwee grou AOVA t t ( ( erece erece ( ( amle amle S F S betwee withi Degree of freedom df bt = (K - 1 df wi = ( - K df tot = ( 1 Sum of Square A Show i Cla _ b/t = x ( G + y ( G + z ( Z G w/i = Σ( + Σ( + Σ(Z Z tot = Σ( G + Σ( G + Σ(Z G A Show i Textbook b/t = Σ( G w/i = Σ( tot = Σ( G ea Square S b/t = b/t / df b/t S w/i = w/i / df w/i Effect ize b/ t R tot Page 5
6 Pot-hoc tet C K( K 1 ( q S ' withi ' 1 ( K 1 1 Z Withi grou AOVA S F S betwee withi Degree of freedom df bt = (K - 1 df ubj = ( 1 df w/i = (K - 1( - 1 df tot = ( 1 Sum of Square A Show i Cla _ b/t = x ( G + y ( G + z ( Z G ubj = k[σ( art. G ] w/i = tot - b/t - ubj = Σ( art. + G + Σ( art. + G + Σ(Z Z art. + G tot = Σ( G + Σ( G + Σ(Z G A Show i Textbook b/t = Σ( G ubject = Σ( articiat G w/i = tot b/t ubject tot = Σ( G Page 6
7 ea Square S b/t = b/t / df b/t S ubj = ubj / df ubj S w/i = w/i / df w/i Effect ize R b/ t tot ubj Pot-hoc tet C K( K 1 ( q S withi Pearo Correlatio ad Regreio Aalyi r [( [ ( ( ] ][ ( ] OR [( r ( ( ( ] Degree of freedom Skewe formula Stadard deviatio ( med df = k ( ( 1 Regreio Aalyi Regreio equatio A Show i Cla _ Ŷ = a + b( a = b ( b A Show i Textbook Page 7
8 Ŷ = a + b( a = (whe = 0 Ste 1: z SD Ste : z r( z Ste 3: Ŷ = z b = (whe = 1 Ste 1: z ( SD SD Ste : z r ( z Ste 3: Ŷ = z ( SD Ste 4: Subtract the firt calculated Ŷ whe = 0 from the ecod calculated Ŷ whe = 1 Effect ize R reg tot Stadard Error of the Etimate SE S withi Page 8
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