Chapter 10 The t Test for Two Independent Samples

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Chapter 10The t Test for Two Independent Samples

• PSY295 Spring 2003
• Summerfelt

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Overview

• Introduce the t test for two independent samples
• Discuss hypothesis testing procedure
• Vocabulary lesson
• New formulas
• Examples

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Learning Objectives

• Know when to use the t test for two independent
  samples for hypothesis testing with underlying
  assumptions
• Compute t for independent samples to test
  hypotheses about the mean difference between two
  populations (or between two treatment conditions)
• Evaluate the magnitude of the difference by
  calculating effect size with Cohens d or r2

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Introducing the t test for two independent
samples

• Allows researchers to evaluate the difference
  between two population means using data from two
  separate samples
• Independent samples
• Between two distinct populations (men vs. women)
• Between two treatment conditions (distraction v.
  non-distraction)
• No knowledge of the parameters of the populations
  (µ and s2)

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Vocabulary lesson

• Independent measures/Between-subjects design
• Design that uses separate sample for each
  condition
• Repeated measures/Within-subjects design
• Design that uses the same sample in each
  condition
• Pooled variance (weighted mean of two sample
  variances)
• Homogeneity of variance assumption

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Discuss hypothesis testing procedure

• State hypotheses and select a value for a
• Null hypothesis always state a specific value for
  µ
• Locate a critical region (sketch it out)
• Add the df from each sample and use the t
  distribution table
• Compute the test statistic
• Same structure as single sample but now we have
  two of everything
• Make a decision
• Reject or fail to reject null hypothesis

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The t Test formula

• Difference in the means over the standard error

One Sample
Two Samples
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Formula for the degrees of freedom in a t test
for two independent samples
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Estimating Population Variance

• Need variance estimate to calculate the standard
  error
• Since these variances are unknown, we must
  estimate them
• Pooling the sample variances proves to be the
  best way
• Add the sums of squares for each sample and
  divide by the sum of the df of each sample

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Calculating the Standard Error for the t
statistic

• Using the pooled variance estimate in the
  original formula for standard error

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Magnitude of difference by computing effect size

• Two methods for computing effect size
• Cohens d
• r2

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Example

• Researcher wants to assess the difference in
  memory ability between alcoholics and
  non-drinkers
• Sample of n10 alcoholics, sample of n10
  non-drinkers
• Each person given a memory test that provides a
  score
• Alcoholics mean43, SS400
• Non-Drinkers mean57, SS410

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Example, continued

• What if the introduction read
• A researcher wants to assess the damage to memory
  that is caused by chronic alcoholism
• Would that change the analysis?