Statistics for the Behavioral Sciences (5th ed.) Gravetter

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Statistics for the Behavioral Sciences (5th ed.)
Gravetter Wallnau

• Chapter 10 The t Test for Two Independent
  Samples

University of GuelphPsychology 3320 Dr. K.
HennigWinter 2003 Term
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Once or Twice?Within Subjects Design

• If the subjects are used more than once or
  matched, this design is called aWithin Subjects
  Design or a Repeated Measures Design.Advantages
  of Repeated Measures Designs
• They take fewer participants.
• They typically have more statistical power (like
  a matched t-test).
• Disadvantages of Repeated Measures Designs
• You have to worry about practice effects and
  carryover effects. We will return to this.

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?
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Between vs. within designs

• Between-subjects
• comparison of separate groups (men cf. women
  ethnicity1 cf. ethnicity2 married cf.
  unmarried) or matched groups
• between-subjects/repeated measures
• two data sets from the same sample (patients
  before therapy cf. after drug use Grade 9 cf.
  grade 11 time1 cf. time2)

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Figure 10-2 (p. 310)Do the achievement scores
for children taught by method A differ from the
scores for children taught by method B? In
statistical terms, are the two population means
the same or different? Because neither of the two
population means is known, it will be necessary
to take two samples, one from each population.
The first sample will provide information about
the mean for the first population, and the second
sample will provide information about the second
population.
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Table 10-1 (p. 316) Three major differences
mean difference of the two samples, different ns
and thus pooled variance (Sp2)
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Logic and proceduret statistic for
independent-measure design

• H0 ?1 - ? 2 0
• H1 ?1 - ? 2 ltgt 0
• overall t formula
• the independent-measures t uses the difference

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Reminder

• The means of two groups are compared relative to
  a sample distribution of
• means (is M1 different from the population ??)
• sample variances (proved mean all s2 ?2)
• mean differences (is the difference between two
  sample means, ?M1-M2, different?)

Sample n (M ?)..
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2
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Sample 1 (M ?)
1 2 3 4 5
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t-statistic (contd.)

• (Review) standard error measures how accurately
  the sample statistic represents the population
  parameter
• single sample the amount of error expected for
  a sample mean
• independent measures formula amount of error
  expected when you use the mean difference (M1-M2)
• Recall
• now we want to know the total error, but

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t-statistic (contd.)

• But, what if the size of the two samples is not
  the same (n1ltgtn2)?
• Recall
• we now have two SS and df values, thus

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• Example 10.1 (n 10 for both groups) A list of
  40 pairs of nouns (e.g., dog/bicycle, grass/door)
  are given two (independent) groups for 5 min.
• group 1 is asked to memorize
• group 2 uses mental imagery to aid memorization
  (e.g., dog riding a bicycle) a Tx effect

group 2
group 1
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Computational proceduret-test for means of two
independent samples

• Step 1. State hypotheses and select alphaH0 ?1
  - ? 2 0H1 ?1 - ? 2 ltgt 0? .05
• Step 2. Determine dfdf df1 df2 (n1 - 1)
  (n2-1) 99 18
• Step 3. Obtain data calculate t

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(contd.)

• Step 3a. For the two samples, A and B, of sizes
  n1 and n2 respectively, calculate
• Step 3b. Estimate the variance of the source
  population
• Step 3c. Estimate the sd of the sampling
  distribution of sample-mean differences
• Step 3d. Calculate t as

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Example (contd.)

• Step 3a.
• Step 3b.
• Step 3c.
• Step 3d.
• Step 4. Make a decision. Table lookup df 18

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Table look up for df 18
Obtained value of t is three times greater than
would be expected by chance (the standard error)
t 3.00 The Tx moved the mean from M 22 to M
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Figure 10-4 (p. 318)The t distribution with df
18. The critical region for ? .05 is
shown.Two things are important significance and
effect size
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Calculating effect sizeTwo methods (Cohens d or
r2)

• Cohens d mean difference/sd
• the distance between the two means is slightly
  more than 1 sd, thus d should be slightly larger
  than 1.00
• Can also calculate variance accounted for by Tx
  

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Calculating r2 directlyTx contribution to
variabilityTx variability/ total
variability180/540 .333 33.3
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Final comparison