PSY294 Statistics for Psychology

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PSY294 Statistics for Psychology Assignment B is
due in this afternoon (Thursday 8th) Assignment
C (C1 and C2) is due in on Thursday 15th
December The project folder (P1-P6) is due in on
Friday 16th December. You should hand it in to
the School of Maths and Stats General Office in
Merz Court (5th Floor)
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PSY294 Statistics for Psychology
Two-factor experiments
A factor is a linked set of experimental
conditions we may wish to compare e.g. Level
of stimulus Different educational
methods Groups from different social
backgrounds
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PSY294 Statistics for Psychology
Two-factor experiments
We have seen how to use one-way ANOVA and two-way
related samples designs to compare responses for
a factor We need not restrict ourselves to just
one factor. Several different factors can be
studied in a single experiment. We combine
their levels to provide treatment combinations
which can be compared in either related or
unrelated samples.
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PSY294 Statistics for Psychology
Breakdown of variability
TOTAL SS
Residual SS
Between Treatments SS
Between Subjects SS
Interaction
Factor 2
Factor 1
Extent to which factors influence each other
Main effects
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PSY294 Statistics for Psychology
Two-factor experiments
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PSY294 Statistics for Psychology
Analysis step 1
Carry out a standard one-way ANOVA on the six
different groups. Sample totals
4176,4394,4229,4572,4210,5275 Grand total
G26856 Using methods of lecture 6 TSS
276414 BTSS 146017.67 RSS 130396.33 (by
subtraction)
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PSY294 Statistics for Psychology
Analysis step 1
plt0.001
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PSY294 Statistics for Psychology
Two-factor experiments
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PSY294 Statistics for Psychology
Analysis step 2
Totals for type of user are 8570, 8801, 9485
(Reg, Occ, Non-) which leads to a
between usertype SS
This sum of squares has 2 degrees of freedom
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PSY294 Statistics for Psychology
Two-factor experiments
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PSY294 Statistics for Psychology
Analysis step 3
Repeat step 2 for type of drug Totals are
12615, 14241 (Placebo, Drug)
This sum of squares has 1 degree of freedom
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PSY294 Statistics for Psychology
Analysis step 4
Finally, calculate a sum of squares for
interaction between type of user and type of
drug
146017.67 - 37734.51 73441 34842.17
(from Step 1)
(from Step 2)
(from Step 3)
This sum of squares has 5-2-12 degrees of freedom
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PSY294 Statistics for Psychology
Analysis ANOVA table
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PSY294 Statistics for Psychology
Minitab output
MTB gt ANOVA c1c2 c3 c2c3 SUBCgt residuals
c4 SUBCgt fits c5 SUBCgt means c2c3. ANOVA
reac versus usertype, drug Factor Type
Levels Values usertype fixed 3 1 2
3 Drug fixed 2 1 2
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PSY294 Statistics for Psychology
Minitab output
all comparisons are with RMS
Analysis of Variance for reac Source DF SS
MS F P Usertype 2 37735 18867 4.34
0.022 Drug 1 73441 73441 16.90
0.000 usertypedrug 2 34842 17421 4.01
0.029 Error 30 130396 4347 Total 35 276414
Type of user significant at 5 Drug v Placebo
significant at 1 Interaction significant at 5
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PSY294 Statistics for Psychology
Minitab output
Means Usertype drug N reac 1 1
6 696.00 1 2 6 732.33 2
1 6 704.83 2 2 6
762.00 3 1 6 701.67 3
2 6 879.17
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PSY294 Statistics for Psychology
Further example (related samples)

• 10 subjects are tested on a task requiring
• concentration. There are two factors
• Background noise quiet or music
• Use of stimulant none or strong coffee
• Each subject is tested under each of the
• four possible conditions