Psychology 513: Advanced Research Methods

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Psychology 513 Advanced Research Methods

• Testing Means t-test

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Sampling Distribution of the Mean

• Central Limit Theorem
• Sampling distribution of the mean approaches
  normal as n increases
• Standard deviation of distribution of sample
  means standard error
• Determined by (a) variability of the pop. from
  which sample is selected and (b) size of the
  sample

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Testing Hypotheses about Means

• When s is known we can use z because of the CLT
• Example
• ACT scores m 20, s 4.0
• Mean for UI Freshmen 23.6

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One-Sample t-test

• If population variability is not known, we can
  use sample variability as an estimate
• Use the t distribution to evaluate our t
  statistic

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Repeated Measures t-test

• Testing whether any difference exists between
  scores at Time 1 and scores at Time 2
• Calculate a difference score
• D X2 X1
• Divide the mean difference by the estimated
  standard error

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Example
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Independent Samples t-test

• Testing difference between two population means
• Because two samples provides a better estimate of
  the variance than one sample, we compute a pooled
  variance
• Weight by sample size (a larger sample should
  provide a closer estimate so should count
  more)

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Example
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Heterogeneity of Variance

• When null is true and there is homogeneity of
  variance, then t is distributed as a t
  distribution with N-2 df
• If heterogeneity exists dont pool variances
• Welch-Satterthwaite solution

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Heterogeneity of Variance (cont.)

• Testing for homogeneity
• Hartleys F-max
• Levene (1960)
• Brown-Forsythe (1974)
• Dont use if have more than 4 groups
• Guideline Unequal sample sizes -- ratios of 31
  or greater indicate possible problems equal
  sample sizes dont worry

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Example
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Confidence Intervals

• Point estimate vs. interval estimate
• CI for the sample mean
• CI for the difference between two means