PSY 311 1st Editiom Lecture 6Outline of Last Lecture I. Effect Size - r²II. Point Estimates III. Interval Estimates a. How do we find µIV. A Much More Insignificant Goal Outline of Current Lecture I. Inependent Samples a. Two groups II. The formula officially III. Estimated Standard Error IV. The formula usually Current Lecture : The t Test Two Independent Samples I. Independent Samples- Assigned randomly to one of two groups- Randomness ensures no systematic difference between group one and group two- No systematic relationship between the members of the group- Between-subjects design- Are independent random samples a. Two groups • Group 1 vs. Group 2– Treatment A vs. Treatment B– Experimental vs. Control– Population means:– Group 1: μ1– Group 2: μ2• HypothesesH0: μ1 – μ2 = 0H1: μ1 – μ2 ≠ 0II. The Formula --- Officially- t = [(M1 – M2) – (μ1 – μ2)] / s(M1 – M2) - M1 – M2 = sample mean difference - μ1 – μ2 = population mean difference - s(M1 – M2) = estimated standard error III. Estimated Standard Error • We make the assumption that the population variance (σ2) in both groupsare the same which is called homogeneity • As we DO NOT know σ2, we need to estimate it using the sample variance from BOTH groups (pooled variance)Sp2 = (SS1 + SS2) / (df1 + df2)• Two-sample estimated standard errors(M1 – M2) = √[(Sp2 / n1) + (Sp2 / n2)]• Standard difference by chance between M1 and M2IV. The formula --- Usually - t = [(M1 – M2) – (μ1 – μ2)] / s(M1 – M2)Assuming H0:- t = (M1 – M2) / s(M1 – M2)- df = df1 +