Comparing Means: Independent-samples t-test

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Comparing Means Independent-samples t-test
Population A
Population B
OR
Sample 1
Sample 2

• Lesson 14

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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?

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Experimental Outcomes

• Do not expect to be exactly equal
• sampling error
• How big a difference to reject H0 ?

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Hypotheses Independent Measures

• Nondirectional
• H0 m1 m2 H1 m1 ? m2
• Directional (depends on prediction )
• H0 m1 lt m2 H1 m1 gt m2
• no value specified for either
• Group 1 scores Group 2 scores

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t test Independent-Samples

• Same basic structure as single sample

• Independent samples

df N1 N2 - 2
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Estimated Standard Error

• Standard error of difference between 2 sample
  means

• s2p pooled variance

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Pooled Variance (s2p)

• Average of 2 sample variances
• weighted average if n1 ? n2

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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)

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Example n1 ¹ n2

• 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)

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Example n1 ¹ n2

• 1. State Hypotheses
• H0m1 m2
• H1m1 ¹ m2
• 2. Set criterion for rejecting H0
• nondirectional
• a .05
• df (n1 n2 - 2)
• t CV

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Example n1 ¹ n2

• 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

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Example Independent-samples

• Does exercising longer have greater health
  benefits?
• Participants (N14)
• Randomly assigned to 2 groups
• N7 per group
• Manipulation (IV)
• Group 1 exercised 2 hrs/week
• Group 2 exercised 5 hrs/week
• Outcome (DV) Health rating

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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)