Testing Hypotheses About 2 Related MeansThe PairedSamples t Test

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Testing Hypotheses About 2 Related MeansThe
Paired-Samples t Test

• Comps Review

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Hypothesis Testing Terminology

• Null hypothesis no difference
• New treatment produces SAME results
• College grads work same as pop 40 hr/wk
• Alternative hypothesis null is false
• New treatment changes the cure rate
• College grads do no work 40 hr/wk

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Rejecting the Null

• If the observed sig. level is small, lt.05, you
  REJECT the NULL
• When you reject the null, the confidence interval
  does not include 0
• You can also test at the .01 level, and/or do a
  99 CI

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Paired t Test

• For when you have 2 measurements, or observations
  under 2 conditions, or studies with pairs of
  subjects or measurements matched in some way
• Testing the null that the average difference b/w
  a pair is 0
• Chapter example endorph.sav

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Why Use a Paired Test?

• Makes it easier to detect true differences when
  they exist
• Do not have to stick to before/after, can compare
  wife/husband, siblings, etc.
• Do not use without a true pair
• Evaluating difference the sign tells you the
  direction of the change

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First Step Check Data
DIFF Stem-and-Leaf Plot Frequency Stem
Leaf 1.00 0 . 3 4.00 1
. 0127 5.00 2 . 00458 1.00
3 . 0 Stem width 10.00 Each leaf
1 case(s)
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Second Step Run Test

• You can use a one-sample t test if you just use
  the difference
• If you have before/after scores, then use the
  paired-samples t test
• Your mean difference, t value and 2-tailed
  significance will all be the same!
• Usually easier just to use the paired-sample t
  test

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Paired-Sample t Test
Analyze?CompareMeans?Paired-Samples T Test
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Third Step Make a Decision
Based on the 2-tailed significance level, we
REJECT the NULL hypothesis of no difference NULL
also stated mean difference 0 two means are
equal The sig. is lt.0005, but, COULD WE BE WRONG?
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For APA-Style Write-ups

• Paired-Samples t Test
• Green Lesson 22

Green also discusses effect size indices d
for one-sample d or ?2 for paired-samples