Nazarov StatExcel L4-ANOVA

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Microarray CenterMicroarray Center

ANALYSIS IN EXCELANALYSIS IN EXCEL

Lecture 4Lecture 4

Statistical data analysis in Excel. 4. ANOVA

31-10-2011

drdr.. PetrPetr NazarovNazarov

[email protected]@crp--sante.lusante.lu


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INTRODUCTION TO ANOVA

Why ANOVA?

Means for more than 2 populationsWe have measurements for 5conditions. Are the means for these

IfIf wewe wouldwould useuse pairwisepairwise comparisons,comparisons,whatwhat willwill bebe thethe probabilityprobability ofof gettinggetting error?error?

NumberNumber ofof comparisonscomparisons:: 10!3!2

!552

==C

conditions equal?

Validation of the effects

We assume that we have severalfactors affecting our data. Whichfactors are most significant? Which

ProbabilityProbability ofof anan errorerror:: 11((00..9595))1010 == 00..44

Statistical data analysis in Excel. 4. ANOVA 22

http://easylink.playstream.com/affymetrix/ambsymposium/partek_08.wvx

ANOVAexample from Partek


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INTRODUCTION TO ANOVA

Meaning

H0: 1= 2= 3

Ha: not all 3 means are equal

6

8

10

12

14

ression

level

mm11

mm22mm33


0

2

4

FL

FL

FL

FL

FL

FL

FL

NY

NY

NY

NY

NY

NY

NY

N

C

N

C

N

C

N

C

N

C

N

C

Measures

De


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SINGLE-FACTOR ANOVA

Example

12

14

2

4

6

8

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De

pression

level

mm11

mm22mm33


0

FL FL FL FL FL FL FL NY

NY

NY

NY

NY

NY

NY

NC

NC

NC

NC

NC

NC

Measures

SSESSTRSST +=


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SINGLE-FACTOR ANOVA

Example

ANOVA tableA table used to summarize the analysis of variance computations and results. It containscolumns showing the source of variation, the sum of squares, the degrees of freedom, themean square, and the Fvalue(s).

In Excel use:

Tools Data Analysis ANOVA Single Factor

Lets perform for dataset 1: good healthLets perform for dataset 1: good health

depression.xls

ANOVA

SSTRSSTR


-

Between Groups 78.53333 2 39.26667 6.773188 0.002296 3.158843Within Groups 330.45 57 5.797368

Total 408.9833 59

SSESSE


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MULTI-FACTOR ANOVA

Factors and Treatments

FactorAnother word for the independentvariable of interest.

Factorial experimentAn experimental design that allows statisticalconclusions about two or more factors.

TreatmentsDifferent levels of a factor.

depression.xls

Factor 1:Factor 1: HealthHealth

good healthgood health

bad healthbad health

Factor 2:Factor 2: LocationLocation

FloridaFlorida

New YorkNew York

North CarolinaNorth Carolina


Depression = + Health + Location + HealthLocation +

Interaction

The effect produced when the levels of one factor interact withthe levels of another factor in influencing the response variable.


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MULTI-FACTOR ANOVA

2-factor ANOVA with rReplicates: Example

depression.xls

1.1. Reorder the data into format understandable for ExcelReorder the data into format understandable for Excel

Factor 1:Factor 1: HealthHealth

Factor 2:Factor 2: LocationLocation

Florida New York North Carolina

Good health 3 8 10

7 11 7

7 9 3

3 7 5

7 7 8

3 8 11

bad health 13 14 10

2.2. Use ToolsUse Tools Data AnalysisData Analysis ANOVA: TwoANOVA: Two--factor with replicatesfactor with replicates


17 15 1517 12 18

11 13 13

17 11 11


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MULTI-FACTOR ANOVA

2-factor ANOVA with rReplicates: Example

Health

Location

ANOVA

Source of Variation SS df MS F P-value F crit

Sample 1748.033 1 1748.033 203.094 4.4E-27 3.92433

Columns 73.85 2 36.925 4.290104 0.015981 3.075853

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Error

F

. . . . .

Within 981.2 114 8.607018

Total 2829.2 119

150

200

250

F


0

2

4

6

8

Health Location Interaction Error

0

50

100

Health Location Interaction Error


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Nazarov StatExcel L4-ANOVA

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