2/13/2011

1

Lecture 6

Chapter 11

Section 11.5

One-Way ANOVA for Differences among more than two means

Frequently asked Question

Two samples are independent: the

sample selected from one population is

not related to the sam

p

le selected from

How do you differentiate “independent” and

“dependent” samples?

p

the second population.

The two samples are dependent:each

member of one sample corresponds to a

member of the other sample. Dependent

samples are also called paired samples

or matched samples.

Hypothesis Test

One Population

Population Mean,

µ

Population

Proportions, p

Arenp5and

1known1unknown

Is pop normal?

Z-test

Is pop normal?

T-test

Are

np5

and

n(1-p)5

Z-test

Hypothesis Test

One Population

Hypothesis Test

Two Populations

Sample

Independent Sample

dependent

2 MEANS2 Proportions

Check the 4

conditions

If yes

Normal?

Yes

No

STOP

Equal V2?unequal V2

V1and V2known?

Z-test Pooled Variance t-test

Z-test

Paired t-test

Yes

No

YesYe s

No

T-test

Pooled variance

Hypothesis Test

Two Population

Hypothesis Test

More than

Two Populations

Sample

Independent Sample

dependent

c MEANSc Proportions

Check the

conditions

If yes

Levene’stestFriedman Test,

Kendall

’

s

Wtest

Equal Variance unequal Variance

STOP

Chi-square

Test

Non-parametric test

One-Way ANOVA

Conditions/Assumptions:

1. Randomness and independence

2. Normality

3. Homogeneity of variance

Kendall s

W

test

,

Cochran’s Q test.

One-Way ANOVA (ANalysis Of

VAriance)

•Compare means of more than two groups

•One-way ANOVA, deals with one factor of

interest (e.g. performance, salary, etc)

•Analyzing the variation “within groups” and

“

between groups

”

between

groups

Partitioning the TOTAL Variation : SST = SSA +SSW

Total Variation

SST

df=n-1

Among Group Variation

SSA

df=c-1

Within Group Variation

SSW

df=n-c

Note: n=total number of values in all

groups

n= n1+n2+n3+…

c= number of groups

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