PSYCH 210 Lecture 16Outline of Last LectureI. One-sample t testa. Variation: no μb. AssumptionsII. Independent-sample t testa. Rationale for new testb. New formula c. Dog Training ExamplesOutline of Current Lecture I. Finish independent-sample t-testa. Application of hypothesis testing stepsb. Assumptions for independent-samples t-testII. Related-samples t-testCurrent LectureI. Exama. Know how to derive standard error from: s2, s and SSII. Independent-sample t-testa. Examples from dog training1. IV: Timing of reward for Staya. Levels: reward during stay vs. reward after stay is overii. Research question: Does the timing of the reward for teaching stay (during vs. after stay) affect the number of breaks the dog makes on a 3-minute test stay?1. DV: number of breaks on a 3-minute test stayb. Hypothesis Testing Stepsi. Hypotheses (two-tailed example)1. H0: μ1-μ2=0These 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.2. H1:μ1-μ2 ≠0ii. Critical value(s) of t1. Duringa. n1= 122. Aftera. n2= 83. df = n1 + n2 – 2a. (Or: df1 + df2)4. n=20, df = 185. α= 0.056. two-tailed7. t= +/-2.101iii. Observed value of t1. t= [(M1-M2)-(μ1-μ2)]/Sm1-2a. Calculate from data set:i. M1=13ii. S21=14.36iii. M2=22.13iv. S22=11.55b. From Hypothesis, μ1-μ2 always equals 0!c. Calculate standard Error (denominator)i. If sample sizes are equal1. SM1-2 = √S21/n1 + S22/n2ii. If sample sizes unequal1. Find pooled Variancea. S2p = (df1s21 + df2s22)/(df1 + df2)i. Like a weighted mean!b. S2p= [11(14.36) + 7(11.55)]/[11+7]i. =13.272. Find standard errora. Sm1-2 = √S2p/n1 + S2p/n2b. √13.27/12 + 13.27/8 = 1.662. tobs = [(13.22.13) – 0]/1.66 = -5.50iv. Make decision about H01. -5.50 < -2.101a. Reject H0v. Conclusion1. Includea. Tx/IV/levelsb. Specific DVc. Sig diff?d. Full comparison2. Ex) Rewarding dogs during stay results in significantly fewer breakson a 3-min test stay compared to rewarding dogs after stay is over.c. Assumptions for Independent-Sample t-testi. Interval or ratio dataii. Independent observationsiii. Normal distributioniv. Homogeneity of variance1. s21 ≈ s22III. Related-samples t-testa. Rationale for new testi. Procedure for independent-samples t1. Take on large sample of Participants2. Split into 2 equal groups using random assignment (different Participants in each group)3. Group 1 receives Tx A; Group 2 receives Tx B 4. Compare sample means from each groupii. Alternative procedure1. Use the same set of Participants in both Tx groups2. This is a repeated-measures, dependent-samples, or related-samples design3. Why would we want to make this change?a. Ex) Use an independent-samples design to study effect of Head Start programi. 2 Tx groups of preschool children: Head Start vs. no Head Startii. DV: Reading comprehension at end of first gradeiii. If we found a significant difference between means of the two groups, what could be some reasons for this difference?1. MHS = 722. MNo HS= 80a. SESb. Reading at homec. Teacher Expectaionsd. Use of languagee. Nutrition3. Variability due to the Tx (IV) = ‘good’ variability4. Variability die to individual differences = ‘bad’ variabilitya. Larger standard errorsiv. If variability in scores due to individual differences is unwanted, how can we minimize these differences?1. Use a related-samples