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UW-Madison PSYCH 210 - Related-Samples t-test

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PSYCH 210 Lecture 17 Outline of Last Lecture I. Finish independent-sample t-testa. Application of hypothesis testing stepsb. Assumptions for independent-samples t-testII. Related-samples t-testOutline of Current Lecture I. Related-Samples Designa. Criteriab. Examplec. AssumptionsII. Variant on Related-Samples Designa. Matched-pairs tCurrent LectureI. Related-Samples Designa. Criteriai. Individual-sample t-test1. No pop info2. Two Tx groups (two M’s)3. Diff Participants in each groupii. Relative-sample t-test1. No pop info2. Two Tx groups (two M’s)3. Same Participants in both groupsb. Rel t = (MD - μD)/SMDi. SMD = SD/√nc. Ex) Cognitive study on link between weapons and aggression (words)i. Weapon words or neutral wordsii. Aggression word1. DV = Reaction Time (RT) to say 2nd (aggression) wordThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.a. Testing: ‘spreading activation’2. Research Question: test whether reaction time (RT) will be faster in weapon word condition vs. non-weapon word conditiona. Tx 1: weapon words (expected lower #s)b. Tx 2: non-weapon (neutral) words (higher #s)i. 1 – 2 (labeling arbitrary, but must be labeled because it will affect (not arbitrary for) H1!)1. Lower – Higher = Negativeiii. Hypothesis testing steps1. Hypotheses (one-tailed test)a. H0: μD ≥ 0b. H1: μD < 02. Critical value(s) of ta. α = 0.05 (one-tailed)b. n = 8 Psi. Each Ps generates 2 raw scoresc. df = 7i. df = n – 1 (# of Ps – 1; or # of pairs of scores – 1)d. tcrit = -1.8953. Observed value of ta. Raw datai. Find Difference between 2 scores1. Sign is important! (+/-)2. MD and SD of the Difference column!ii. MD = -1.625iii. S2D = 4.84; SD= 2.201. SMD = SD/√n2. 2.20/√8 = 0.78b. Rel t = (MD - μD)/SMDi. (-1.625 – 0)/.78 = -2.08 = tobs4. Make decision about H0a. -2.08 < -1.895b. Reject Null5. Conclusiona. Referencei. Weapon – Neutralii. Faster (lower) – Slower (higher) = Negative diff.b. Showing Participants Weapon words produced significantlyfaster (mean) reaction times at naming subsequent aggression words than showing the same Participants neutral words.II. Variant on Related-Samples design : Matched-Pairs ta. Instead of using the same Ps in both Tx groups, se different Ps that are matched on some dimension prior to testingb. Criteriai. No pop infoii. Two Tx groupsiii. Diff Ps in each group1. BUT Ps matched on some factor beforehandiv. Run as a rel. t!1. Act as if data coming from same personc. Matchingi. ‘Natural’ pairs1. Twins, spouses, etc.ii. Experimentally matched pairs1. Ex) Agility dogs in traininga. Dogs have no experience, humans have variable experiencei. Matching variable = human prior experience level (source of individual difference experimenter wantsto control for)1. P1: 982. P2: 96a. P1 & P2 = pair3. P3: 904. P4: 80a. P3 & P4 = pair (doesn’t matter how far apart, just rank order)5. Etc.b. Tx 1: Old method (10 Ps)i. P1, P4, etc.c. Tx 2: New method (10 Ps)i. P2, P3, etc.2. Stepsa. Pretest all Ps on matching variableb. Rank order Ps according to ‘score’ on matching variable testc. Form matched pairs with Ps close in rank orderd. Randomly assign pair mates to IVIII. Assumptions for related-samples ta. Interval or ratio datab. Independent observations (from one participant to the next participant)c. Population of difference scores must be normally


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