Brittay s ote 4/6/207 Lecture 9: Idepedet s & Repeated Measures t-test Review: Sigle Sample z-test Populatio (o-treatmet) Sample (treatmet) Need to kow mea ad stadard deviatio Problem with this? Sigle Sample t-test Populatio (o-treatmet) Sample (treatmet) Do t kow populatio iformatio Might be give mea or stadard deviatio, but ot both 2 ew cocepts used to estimate populatio iformatio Variace (s 2 ): estimates populatio stadard deviatio Degrees of freedom (df): correctio factor Sum of the Squares (SS) z-test is a better test tha t-test, but t-test is good eough whe we do t kow populatio iformatio Sigle Sample tests are BAD desigs Why? You do t wat to compare somethig small (sample) to somethig large (populatio), you wat to compare them to somethig comparable (i.e. other samples) 2 Idepedet s/samples Desig comparig 2 groups/samples that are comparable to each other E.g. To test the effectiveess of pai medicatio o headaches, oe group takes Tyleol, other takes Ibuprofe. Populatio IV m DV Equivalet 2 We assume that the groups are fairly EQUIVALENT (equal, the same) Equal distributio of males/females, ethicities, ages, headache experieces, etc Stregths: you get to compare two differet treatmets with two equivalet groups Weakesses: the groups might ot be equivalet ad you eed more people
Brittay s ote 4/6/207 Repeated Measures Desig E.g. You wat to determie peoples favorite soda drik, Coke () vs. Dr. Pepper () so you have them drik Coke first, the Dr. Pepper, the ask which is their favorite. Populatio m You ca add additioal treatmets, like RC Cola, etc... Stregths: o issues of equivalecy (b/c there s oly group) Weakesses: Order Effect: the order they receive the treatmets could make a differece Carry Over Effect: secod treatmet (IV) might be effected by the first treatmet Practice Effect: experiece with the first treatmet might affect expectatios for the secod How do we accout for these weakesses? COUNTER BALANCE Have participats experiece the treatmets i all possible orders E.g. If the three treatmets were Coke (C), Dr. Pepper(D), & RC Cola (R), all possible combiatios would be: CDR, CRD, DRC, DCR, RCD, RDC So it s geerally best to stick to oly a few treatmets Populatio m m Weakesses: requires more time & resources
Brittay s ote 4/6/207 CLASS DEMO: Idepedet s Populatio: subjects (o descriptors give) : give cadle, matches, ad tacks iside a box 2: give a cadle, matches, tacks, ad a box (tacks ot iside the box) Diagram Your Research (Hypothesis Testig) Pop. DV m = 9.2 = 26.2 SS = 2746.8 2 Hypotheses H: presetatio of box mattered 2 Outcomes 2 Decisios 2 = 43.3 = 6.33 SS2 = 066.8 H0: presetatio of box did ot matter (CHANCE/samplig error) Prob. Calc. t-test HIGH α =.0 LOW Accept H0 Reject H0, Accept H
Brittay s ote 4/6/207 Our research questio: did the presetatio of the objects make a differece? No-directioal (two-tailed); α =.0 Idepedet Variable: how the objects are preseted 2 treatmets: : items preseted iside the box : items preseted outside of the box Depedet Variable: amout of time it takes to mout cadle o wall Iitial Calculatios Because we re give raw data, we eed to first calculate the meas, stadard deviatios, ad SSs, for our 2 groups/samples (x) x 2 2 (x2) x2 2 = = 28 6384 42 764 60 2600 24 76 3 2769 68 4624 0 020 3 22 94 8836 47 2209 x = 96 x 2 = 73790 x2 = 26 x2 2 = 0398 ( x) 2 = 326 ( x2) 2 = 4666 Calculate mea: Calculate mea: m = x = 96 = 9.2 Calculate stadard deviatio: = x = 26 = 43.3 Calculate stadard deviatio: = x2 ( x)2 = SS df = x2 ( x)2 = SS df df = = 4 df2 = = 4 SS = x 2 ( x)2 = 2746.8 4 = 73790 326 = 73790 7043.2 = 2746.8 = 686.7 = 26.2 SS2 = x 2 ( x)2 = 066.8 4 = 0398 4666 = 0398 933.2 = 066.8 = 266.7 = 6.33 ext you ll wat to write these umbers ito your diagram so that you ca keep track of them whe you calculate probability later
Brittay s ote 4/6/207 Determie CRITICAL REGIONS Two tailed, α =.0 df = df + df2 = 4 + 4 = 8 t-critical = +/- 3.3 PROBABILTIY CALCULATIONS. Variace (s 2 p) s 2 p = SS +SS 2 = 2746.8+066.8 = 383.6 = 476.7 df +df 2 4+4 8 2. Stadard Error (sm-) sm- = s p 2 + s 2 p = 476.7 + 476.7 = 9.34 + 9.34 = 90.68 = 3.8 3. t-test (t) t = m m 2 = 9.2 43.3 = 7.9 =. s m 3.8 3.9 The calculated t falls i the low probability regio, so we reject the ull & accept the alterative Report Results Professioally The box of items group performed slower (M= 9.2, SD= 26.2) tha the box ad items group (M= 43.2, SD=6.33). This differece was sigificat, t(8)=., p<.0, two-tailed.