Psychology 203 Examining Main Effects and Interactions

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Psychology 203Examining Main Effects and
Interactions
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Announcement

• Laboratory 5 Impression Formation Trait Order.
  The repeated measures lab.
• Data for lab book does not have to be from 2005

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Quizz 2 format for next week

• 70 questions
• Multiple choice (1 from 4)
• Duration 1 hr

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Format for the Exam

• 2 hrs duration
• 2 Sections
• Section 1 80 multiple choice questions
• Simple formulas (not provided)
• Tables (F, t, chi square provided)
• Section 2 10 short answer questions
• Each question in each section weighted equally
• Each section weighted equally

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Things you will need to know

• How to look up statistics tables
• Formulae s2, z, sd, ss, F, d, t, chi square, df
• Laboratory work
• Content of text Gravetter Wallnau.

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Two-Way DesignANOVA Summary Table
Sums of Squared Deviations about a mean
Sums of squared deviations of factor level means
from grand mean
Source SS df MS F
Between Factor A SSA a - 1 MSA
MSA/MSW Factor B SSB b - 1 MSB
MSB/MSW A x B SSAxB (a - 1)(b -
1) MSAxB MSAxB/MSW Within SSW
ab(ncell - 1) MSW Total SST N - 1
Average of the sum of the squared deviations for
each group
Where a number of levels of Factor A b
number of levels of Factor B N total number of
observations (subjects) across all cells ncell
number of observations in each cell
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Two-Way DesignANOVA Summary Table
Degrees of freedom
Lose 1 Degree of freedom for each variance
estimate to be made from SS for factor levels
and interaction
Lose 1 degree of freedom per group based on
numbers (n) in the groups
Source SS df MS F
Between Factor A SSA a - 1 MSA
MSA/MSW Factor B SSB b - 1 MSB
MSB/MSW A x B SSAxB (a - 1)(b -
1) MSAxB MSAxB/MSW Within SSW
ab(ncell - 1) MSW Total SST N - 1
Sum of all deviations must add to zero Provides
unbiased estimate of population variance
Where a number of levels of Factor A b
number of levels of Factor B N total number of
observations (subjects) across all cells ncell
number of observations in each cell
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Two-Way DesignANOVA Summary Table
Mean of the Summed Squared Deviations about the
Mean
Source SS df MS F
Between Factor A SSA a - 1 MSA
MSA/MSW Factor B SSB b - 1 MSB
MSB/MSW A x B SSAxB (a - 1)(b -
1) MSAxB MSAxB/MSW Within SSW
ab(ncell - 1) MSW Total SST N - 1
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Interpreting Two-Way DesignsInteractions vs
Main Effects

• The effect of one factor differs across levels of
  the other factor(s)
• Interactions take interpretative precedence over
  main effects

No main effects but interaction present
2 main effects no interaction
Case II
o
x
b2
o
o
b2
x
o
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Main Effects
b2
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Plotting the Results for each condition
The effect of exercise depends on the time it is
taken
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Other forms of interaction
1 main effect of a interaction averaging within
b will give roughly the same means for b1 b2.
Averaging within a will show the main effect of a
1 main effect of b interaction averaging
within a would give roughly same means for a1
a2 . Averaging within b will show the main effect
of b
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Data from the Sternberg Laboratory
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Effect Size (Eta Squared) for a 2 Factor Anova

• For Factor A
• For Factor B
• For AxB

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Are all the groups different?

• The F test is an omnibus test that does not tell
  us where the differences lie
• We could compare each group with a standard
  t-test but this is inefficient and does not use
  all the data
• Usually we formally compare between individual
  groups using special types of t-tests
• Planned (a priori) and unplanned (post hoc)
  comparisons

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The Scheffe (post hoc) Test

• Similar to Tukeys HSD but VERY conservative.
• Step 1 Determine the SS between treatments for
  the two groups being compared
• Step 2 Calculate the SS for the comparison grps
  then MSbetween using the df for the effect (a-1,
  b-1, (a-1)(b-1)) note this makes the numerator
  smaller)
• Step 3 Compute F ratio and examine F table with
  appropriate degrees of freedom (k-1, whatever the
  DF is for the MS within treatments (N-k or )

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An Alternative Scheffe Test

• Apply the above formula (sw2 MSwithin) from the
  ANOVA table.
• Consult F table and find critical F for the
  effect dfa-1, b-1,or (a-1)(b-1) and dfN-k
  (where k is the number of groups)
• Calculate F (k-1) critical F
• If FgtF then reject Ho

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Scheffe Test