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ASSUMPTIONS of ANOVA:
equal variances
(required for pooling)
normality
(required for test distribution)
The null hypothesis in ANOVA is always:
This implies that any combination of means are also equal
1
2
3
j
μ
=
=
=
1
2
3
(
) / 2
+
=
The alternative hypothesis in ANOVA is always
 The population means are different (at least one
mean is different from another)
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View Full Document **** Null hypothesis is tested by comparing two estimates
of the population variance (
σ
2
)
:
(MS
B
) betweengroup estimate of (
σ
2
)
AFFECTED
by whether the null is true
(MS
W
) withingroup estimate of (
σ
2
)
UNAFFECTED by whether the null is true
.
 when the null hypothesis is true
(MS
B
)
F ratio
=

=
About 1
(MS
w
)
 when the null hypothesis is not true
(MS
B
)
F ratio
=

= Much greater than 1
(MS
w
)
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View Full Document S
2
_
X
(n) estimates
σ
2
just as well as any random samples would
S
2
_
X
(n) = MS
B
will be higher than the populations
variance because the means are farther away
from each other than would be expected by
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This note was uploaded on 09/28/2010 for the course PSYCH 100A 32830420 taught by Professor Shams during the Spring '10 term at UCLA.
 Spring '10
 SHAMS

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