Comparing Means: Independent-samples t-test Lesson 14 Population APopulation B Sample 1Sample 2 OR

Independent Measures Hypothesis Test n Select 2 independent samples l are they from same population? n Experiment l select 2 samples l 1 receives treatment l are the samples the same? ~

Experimental Outcomes n Do not expect to be exactly equal l sampling error n How big a difference to reject H 0 ? ~

Hypotheses: Independent Measures n Nondirectional H 0 :  1 =  2 H 1 :  1   2 n Directional (depends on prediction ) H 0 :  1  2 n no value specified for either l Group 1 scores = Group 2 scores ~ ~

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: n 1  n 2 n Does the amount of sleep the night before an exam have an effect exam performance? n Dependent variable? n independent variable l Grp 1: 4 hrs sleep (n = 6) l Grp 1: 8 hrs sleep (n = 7) ~

Example: n 1  n 2 1. State Hypotheses H 0 :  1 =  2 H 1 :  1  2 2. Set criterion for rejecting H 0 : nondirectional  =.05 df = (n 1 + n 2 - 2) t CV = ~

Example: n 1  n 2 n 3. select sample, compute statistics do experiment mean exam scores for each group l Group 1: ; s 1 = 3; n 1 = 6 l Group 2: ; s 2 = 2; n 2 = 7 n Compute

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 ~

PASW 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) ~