ANOVA I

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ANOVA I
Class 13
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Schedule for Remainder of Semester    1.
ANOVA One way, Two way 2. Planned
contrasts   3. Moderated multiple
regression   4. Data management   5. Survey
design   6. Non-experimental designs   7.
Writing up research   Class assignment After
completing data analyses series.
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ANOVA
ANOVA Analysis of Variance Next 4-5 classes
focus on ANOVA One-Way ANOVA tests differences
between 2 or more independent groups. Goals
for ANOVA series 1. What is ANOVA, tasks it
can do, how it works. 2. Provide intro to SPSS
for Windows ANOVA 3. Objective you will be
able to run ANOVA on SPSS, and be able
to interpret results. Notes on Keppel
reading 1. Clearest exposition on ANOVA 2.
Assumes no math background, very intuitive 3.
Language not gender neutral, more recent eds. are.
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Basic Principle of ANOVA
Same as
Same as
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Basic Principle of ANOVA
Same as
Same as
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Population Parameters
Mean The average score, measure, or response
S 2 ? (x - X )2 n -1
? 2 ? (X - ?)2 N
Standard Deviation The positive square root of
the variance. 1 SD .34 of entire distribution
? ? (X - ?)2 N
POPULATION
SAMPLE
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Population Parameters
Mean The average score, measure, or response
? ? X N
Variance The average amount that individual
scores vary around the mean
S 2 ? (x - X )2 n -1
? 2 ? (X - ?)2 N
Standard Deviation The positive square root of
the variance. 1 SD .34 of entire distribution
S ? (x - X)2 n -1
? ? (X - ?)2 N
POPULATION
SAMPLE
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PEOPLE WHO DISCLOSE THEIR EMOTIONS ARE
EVALUATIVE DIMENSION Good Bad Beautiful
Ugly Sweet Sour POTENCY DIMENSION Strong
Weak Large Small Heavy Light ACTIVITY
DIMENSION Active Passive Fast Slow Hot
Cold
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Birth Order Means
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Birth Order Means
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Activity Ratings as a Function of Birth Order
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ANOVA Compares Between Group Differences
to Within Group Differences Within Group
Differences Comprised of ??? Between Group
Differences Comprised of ???? ANOVA Between
Group Differences

????? When Null Hyp. is true Between group
_XXXX Within group
YYYY When Alt Hyp. is true Between group
XXXXX Within group
YYYY
ANOVA 1
ANOVA gt 1
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ANOVA Compares Between Group Differences
to Within Group Differences Within Group
Differences Comprised of random error
only. Between Group Differences Comprised of
random error treatment effects
(error true differences) ANOVA Between
Group Differences
Within Group
Differences When Null Hyp. is true Between
group error Within group
error When Alt Hyp. is true Between
group error true diff.
Within group error
ANOVA 1
ANOVA gt 1
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Logic of Inferential Statistics Is the null
hypothesis supported?
Null Hypothesis Different sub-samples are
equivalent representations of same overall
population. Differences between them are
random. First Born dont differ from Last Born
re. disclosers Alternative Hypothesis Different
sub-samples do not represent the same
overall population. Instead represent distinct
populations. Differences between them are
systematic, not random. First Born DO differ
from Last Born re. disclosers
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Logic of F Ratio
  F Differences Among Treatment
Means Differences Among Subjects Treated
Alike        F XXXXXX (Experimental
Error) Experimental Error     F
Between-group Differences ?????
Differences  
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Logic of F Ratio
  F Differences Among Treatment
Means Differences Among Subjects Treated
Alike        F Treatment Effect
(Experimental Error) Experimental
Error     F Between-group Differences
Within-group Differences  
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Average Scores Around the Mean Oldest Child
AS1 individual scores in condition 1 (Oldest
1.33, 2.00) A Mean of all scores in a
condition (e.g., 3.13) (AS - A)2 Squared
deviation between individual score and condition
mean
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    Sum of Squared Deviations     Total Sum of
Squares Sum of Squared between-group deviations
Sum of
Squared within-group deviations     SSTotal
SS????? SS?????
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    Sum of Squared Deviations     Total Sum of
Squares Sum of Squared between-group deviations
Sum of
Squared within-group deviations     SSTotal
SSBetween SSWithinb
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Computing the Sums of Squares
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Birth Order and Ratings of Activity Deviation
Scores
AS Total Between Within
(AS T) (A
T) (AS A)
Level a1 Oldest Child
1.33 (-2.97) (-1.17) (-1.80)
2.00 (-2.30) (-1.17) (-1.13)
3.33 (-0.97) (-1.17) ( 0.20)
4.33 (0.03) (-1.17) ( 1.20)
4.67 (0.37) (-1.17) ( 1.54)
Level a2 Youngest Child
4.33 (0.03) (1.17) (-1.14)
5.00 (0.07) (1.17) (-0.47)
5.33 (1.03) (1.17) (-0.14)
5.67 (1.37) (1.17) ( 0.20)
7.00 (2.70) (1.17) ( 1.53)
Sum (0) (0)
(0) Mean scores Oldest 3.13 Youngest 5.47
Total 4.30
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Computing Sums of Squares from Deviation
Scores Birth Order and Activity Ratings
(continued)
SS Sum of squared diffs, AKA sum of
squares SST Sum of squares., total (all
subjects) SSA Sum of squares, between
groups (treatment) SSs/A Sum of squares,
within groups (error)
SST (-2.97)2 (-2.30)2 (1.37)2
(2.70)2 25.88 SSA (-1.17)2 (-1.17)2
(1.17)2 (1.17)2 13.61 SSs/A
(-1.80)2 (-1.13)2 (0.20)2 (1.53)2
12.27
Total (SSA SSs/A) 25.88
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Logic of F Test and Hypothesis Testing     Form
of F Test Between Group Differences Within
Group Differences   Purpose Test null
hypothesis Between Group XXXX
YYYY   Interpretation If null hypothesis is not
supported (F gt 1) then Between Group diffs are
not simply random error, but instead reflect
??????.   Result Null
hypothesis is rejected, alt. hypothesis is

therefore ___ PROVED ___
SUPPORTED
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Logic of F Test and Hypothesis Testing     Form
of F Test Between Group Differences Within
Group Differences   Purpose Test null
hypothesis Between Group Within Group Random
Error   Interpretation If null hypothesis is not
supported (F gt 1) then Between Group diffs are
not simply random error, but instead reflect
effect of the independent variable.   Result
Null hypothesis is rejected, alt.
hypothesis is supported

(BUT NOT PROVED!)