6006499 ANOVA Introduction
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Transcript of 6006499 ANOVA Introduction
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7/28/2019 6006499 ANOVA Introduction
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bas statistics for Social Science slide 1
Analysis of Variance
(ANOVA)
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Why ANOVA?
To compare differences between group means
Example: Is there any significant difference in satisfaction
between users of the following three computer operating
systems
The variables Type Scale
Satisfaction
Operating systems
Dependent
Independent
Interval
Nominal
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Which of the following data sets indicate differences between thetwo groups?
Data 1:
Group
A B
Data 2:
Group
A B
30 21
14 28
26 14
15 31
27 16
13 1225 27
13 25
12 26
15 28
14 27
15 26
12 3017 29
Range 17 19
Mean 21.4 21.3
Range 5 5
Mean 14 27.3
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Assumptions Underlying
One-way ANOVA
1. The dependent variable is normally distributed for each
of the populations as defined by the different levels of
the factor (independent variable)
2. The variances of the dependent variable are the same forall populations
3. The cases represent random samples from the
populations and the scores on the test variable areindependent of each other
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What to expect?
Post hoc
comparison
Nosig.diffe
rence
z
Sig.diff
erence
Omega and
Eta squaresTesthypothesis
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Steps in ANOVA
1. State the null and alternative hypotheses
HO: 1 = 2 = 3HA: Not all means are equal
2. Calculate the test statistic
F-ratio3. Determine critical value
4. Make your decision
5. Make conclusion
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Step 1: State the hypotheses
HO: 1 = 2 = 3 = ..
HA: Not all means are equal
Depends on number of
groups
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Step 2: Calculate test statistic
1. Calculate sum of squares
( )
=
22
. N
X
XSSTa
( )22
.N
X
n
TSBb
j =S
SSBSSTSSWc =.
2. Determine degrees of freedom
1. = kdfa B
kNdfb W =.
1. = Ndfc T
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3. Calculate Mean Squares 4. Calculate F-ratio
Bdf
SSBMSBa =.
MSW
MSBF=
Wdf
SSWMSWb =.
Summary ANOVA table:
Source SS df MS F
Between-group SSB k-1 MSB F-ratio
Within-group SSW N-k MSW
Total SST N-1
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Step 3: Determine critical valueCritical value is based on:
n Significance level ()
o Degrees of freedom1=
kkN
df
df FF bw
Step 4: Decision
Manual:Reject HO: Fcal > Fcritical
Fail to reject HO: Fcal Fcritical
SPSS:Reject HO: sig-F<
Fail to reject HO: sig-F
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Step 5: Conclusion
Reject HO:
Significant difference between the groups
Fail to reject HO:No significant difference between the groups
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Additional Analysis I:
Post-hoc Comparison
Tukeys HSD (Honestly Significant Difference)
n
MSWqHSD
Wdfk ,,=
Criteria to determine difference:
Sig difference: Mean difference > HSD
No sig. difference: Mean difference HSD
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Additional Analysis II:
Omega SquareAmount of variance of the dependent variable attributed
to the independent variables
( )( ) NFdf
Fdf
B
B
+
=
1
1 2
Eta SquareProportion of variance of dependent variable that is
attributed to the independent variable
SST
SSB=
2