Two-Group Designs Independent samples t-test & paired samples t-test. Chapter 10

Transcription

1 Two-Group Deign Independen ample -e & paired ample -e Chaper 0

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3 Previou e (Ch 7 and 8) Z-e z M N -e (one-ample) M N M = andard error of he mean p Remember: = variance M = eimaed andard error p. - M n M n

4 Laeralizaion effec: Percepion of Emoion Two chimeric face which one i happier (or younger example)? Emoion i proceed in he righ hemiphere Dependen variable: Toal core: -36 o +36 where 0 = no laeralizaion Wha are he hypohee? Null hypohei: Toal core = 0 Alernaive hypohei: Toal core 0

5 -e example Laeralizaion udy (N = 73); -ailed hypohei H 0 : ocore = 0; H : ocore 0 Tocore M = -.7, SD = 6.6, S = 76 -e: = -.7 = qr(76/73).6 M N -9.8?? Look up cv or * in able df = 7, bu ue df = 0: cv p =.05; cv p =.0; cv = p =.00 Rejec he null hypohei (7) = -9.8, p <.00 95% CI = M +/- *( M ) = -.7 +/-.98 (.6) = -9.0 o -4.9

6 Laeralizaion reul Paricipan demonraed a aiically ignifican laeralizaion effec, (7) = -9.8, p <.05. Emoion wa more influenced by he righ hemiphere (M = -.7, CI (.95) = -9.0 o -4.9), a oppoed o wha would be expeced by chance (M = 0).

7 New parameric e (Ch 0) Independen-ample -e ( M ( m M m ) ) Paired-ample -e M D M D D

8 Do women and men differ in heir elf-repored drinking? n M SU male uden drink X SU female uden drink Are hee mean differen by an amoun ha i aiically ignifican?

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10 Independen -e Independen-meaure or beween-ubjec deign Null hypohei H 0 : µ - µ = 0 (or µ = µ ) Alernaive hypohei H : µ - µ 0 (or µ µ or µ < µ or µ > µ ) -e: double elemen of ingle -e formula = 0 M m ( M M ( m ) ( ) m ) Compare mean difference (op) wih difference expeced by chance (boom)

11 Sandard error of he difference beween he mean -ample andard error Each ample ha own populaion mean and error When = n, add andard error of he mean ogeher M n Equaion aume equal ample ize When n n, need o calculae pooled variance Le SPSS do i! ( M M ) n n

12 Alcohol Daa DRWEEK NDRWEEK PDRWEEK NPDRWEEK GENDER Group Saiic Sd. Error N Mean Sd. Dev iaion Mean Independen Sample Te DRWEEK NDRWEEK PDRWEEK NPDRWEEK Equal variance aumed Equal variance no aumed Equal variance aumed Equal variance no aumed Equal variance aumed Equal variance no aumed Equal variance aumed Equal variance no aumed Lev ene' Te for Equaliy of Variance F Sig. df Sig. (-ailed) -e f or Equaliy of Mean Mean Dif f erence 95% Conf idence Inerv al of he Sd. Error Dif f erence Dif f erence Lower Upper

13 # drink Alcohol wrie-up Men were found o drink ignificanly more (M = 4.99, SD = 3.8) compared o women (M = 9.65, SD = 7.9), (8) = 3.3, p <.00, wo-ailed men women

14 Calculaion Calculae op: Calculae boom: Calculae : Calculae df = (n )+(n -) Look up criical * Doe value exceed criical value? ( ) n n M M ) ( ) ( m m M M ( ) M M ) ( ) ( m m M M

15 able For independen -e df = (n )+(n -) Doe he calculaed a or above he *? Given df and α level eleced If ye, hen ignifican difference beween mean

16 Do women and men differ in heir elf-repored drinking? n SU male uden drink X SU female uden drink Are hee mean differen by an amoun ha i aiically ignifican?

17 Sep-by-Sep Calculaion. Informaion given for problem: M m = 4.9, m = 4.7, n m = 89 M f = 9.6, f = 4.7, n f = 94. Calculae (m-m) SE of M for he difference SE Calculae he -aiic ( M M ( m ) ( ) m 4. Make a deciion ) = 3. Find * or cv Go o he able!

18 able df = df +df df = 88+93=8 look up df = 0 * =.98 (for.05) * =.67 (for.00) = 3. Deciion? Significan! (9) = 3., p <.00

19 Influencing facor How do we increae chance for ignifican reul when here really i an effec (POWER!) Difference beween mean Bigger difference larger -e Size of ample variance Larger variance maller -e Sample ize Larger ample higher probabiliy of ig -e (lile influence on effec ize)

20 Effec ize: Proporion of variance in DV accouned for by manipulaion of IV Cohen d Small >. Medium >.5 Large >.8 Variance accouned for (r ) Small >.0 Medium >.09 Large >.5 Reporing he aiic d Group X did more (M = #, SD = #) han group Y (M = #, SD = #). The difference wa (or wa no) found o be ignifican, (df) = #.#, p = 0.##, d = #.##. M M r df

21 Effec ize: Alcohol daa d M M d (8) = 3.3, p <.00, d = 0.47 While aiic i ignifican, effec ize i mall.

22 Confidence Inerval 95% confiden ha he inerval conain he difference beween he mean core If inerval doe NOT conain 0 hen ugge likely a rue difference beween group Independen group: CI.95 = M M +/- * ( m -m ) Where * i he criical value given df (a α=.05, -ailed) Alcohol example: CI = ( ) +/-.98 (.65) = 5.3 +/ =.03 o 8.57 Concluion: 95% confiden ha he difference beween men and women in he number of drink conumed per week from.03 o 8.57.

23 Aumpion of independen -e Daa are on inerval-raio cale Obervaion mu be independen Populaion diribuion mu be normal Two populaion mu have equal variance Average variance only if eimaing ame populaion variance Called homogeneiy of variance Imporan when ample ize are differen How do you know wih ample? Difference beween ample variance SPSS: Equal variance (no) aumed

24 Alcohol Daa DRWEEK NDRWEEK PDRWEEK NPDRWEEK GENDER Group Saiic Sd. Error N Mean Sd. Dev iaion Mean Independen Sample Te DRWEEK NDRWEEK PDRWEEK NPDRWEEK Equal variance aumed Equal variance no aumed Equal variance aumed Equal variance no aumed Equal variance aumed Equal variance no aumed Equal variance aumed Equal variance no aumed Lev ene' Te for Equaliy of Variance F Sig. df Sig. (-ailed) -e f or Equaliy of Mean Mean Dif f erence 95% Conf idence Inerv al of he Sd. Error Dif f erence Dif f erence Lower Upper

25 Chaper 9: Example of independen -e Daa in Table 0. p.5 Ue Excel o calculae -e Daa Excel Formula -e formula ( M M ) ( X M ) N n n mean diff mean variance paced maed x - M x - M x-m x-m e of difference L M N O P Q x - M x - M x-m x-m 3 5 =L5- =M5-6.9 =N5*N5 =O5*O5 8 0 =L6- =M6-6.9 =N6*N6 =O6*O6 5 =L7- =M7-6.9 =N7*N7 =O7*O7 5 =L8- =M8-6.9 =N8*N8 =O8*O8 0 4 =L9- =M9-6.9 =N9*N9 =O9*O9 4 6 =L30- =M =N30*N30 =O30*O30 8 =L3- =M3-6.9 =N3*N3 =O3*O3 4 9 =L3- =M3-6.9 =N3*N3 =O3*O3 4 =L33- =M =N33*N33 =O33*O33 7 =L34- =M =N34*N34 =O34*O34 -e ( M M ( m m ) ) =AVERAGE(L5:L34) =AVERAGE(M5:M34) =SUM(P5:P34) =SUM(Q5:Q34) =P36/9 =Q36/9 =L36-M36 =P37/0 =Q37/0 =SUM(P38+Q38) =SQRT(P39) =L38/P40