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Comparing Means: Independent-samples t- test

Population A. Population B. Comparing Means: Independent-samples t- test . Lesson 14. OR. Sample 1. Sample 2. Independent Measures Hypothesis Test. Select 2 independent samples are they from same population? Experiment select 2 samples 1 receives treatment

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Comparing Means: Independent-samples t- test

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

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

  3. Experimental Outcomes • Do not expect to be exactly equal • sampling error • How big a difference to reject H0 ? ~

  4. Hypotheses: Independent Measures • Nondirectional • H0: m1 = m2 H1: m1m2 • Directional (depends on prediction ) • H0: m1<m2 H1: m1 > m2 • no value specified for either • Group 1 scores = Group 2 scores~~

  5. Sample statistic: t test: Independent-Samples • Same basic structure as single sample • Independent samples [df = N1 + N2 - 2]

  6. Estimated Standard Error • Standard error of difference between 2 sample means • s2p = pooled variance ~

  7. Pooled Variance (s2p) • Average of 2 sample variances • weighted average if n1n2

  8. Assumptions: Independent-samples t test 1. Samples are independent 2. Samples come from normal populations 3. Assume equal variance s21 = s22 • does not require s21 = s22 • Homogeneity of variance • t test is robust • violation of assumptions • Little effect on p(rejecting H0) ~

  9. Example: n1¹n2 • Does the amount of sleep the night before an exam have an effect exam performance? • Dependent variable? • independent variable • Grp 1: 4 hrs sleep (n = 6) • Grp 1: 8 hrs sleep (n = 7) ~

  10. Example: n1¹n2 1. State Hypotheses H0:m1 = m2 H1:m1¹ m2 2. Set criterion for rejecting H0: nondirectional a = .05 df = (n1 + n2 - 2) tCV = ~

  11. 3. select sample, compute statistics do experiment mean exam scores for each group Group 1: ; s1= 3; n1 = 6 Group 2: ; s2= 2; n2 = 7 Compute Example: n1¹n2

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

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

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