Comparing Means: Independent-samples t-test Lesson 13 Population APopulation B Sample 1Sample 2 OR

Independent-samples t test n Select 2 independent samples l are they from same population? n Experiment l Select 2 samples l Each gets 1 level of independent variable n H 0 : there is no difference l samples from same population n H 1 : there is a difference l Samples from different populations ~

t test: Independent-Samples n Same basic structure as single sample n Independent samples n Sample statistic: [df = N 1 + N 2 - 2]

Estimated Standard Error n Standard error of difference between 2 sample means l s 2 p = pooled variance ~

Pooled Variance (s 2 p ) n Average of 2 sample variances l weighted average if N 1  N 2

Assumptions: Independent-samples t test 1. Samples are independent 2. Samples come from normal populations 3. Assume equal variance  2 1 =  2 2 u does not require s 2 1 = s 2 2 l Homogeneity of variance n t test is robust u violation of assumptions u Little effect on p(rejecting H 0 ) ~

Example : Independent-samples n Does exercising longer have greater health benefits? n Participants (N=14) l Randomly assigned to 2 groups l N=7 per group n Manipulation (IV) l Group 1 exercised 2 hrs/week l Group 2 exercised 5 hrs/week n Outcome (DV): Health rating ~

SPSS Independent -Sample T Test n Data entry l 2 columns l 1 for IV, 1 for DV n Menu l Analyze l Compare Means l Independent-Sample T Test n Dialog box l Test Variable(s) (DV) l Options (to change confidence intervals) ~