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ANOVA.pdf

ANOVA.pdf

ANOVA

2

What is Analysis of Variance (ANOVA)?

• A Hypothesis Test to compare means

• How: Compares means or other estimates of variance for each source of variation

• The underlying test used in many Designed Experiments

• Superior to regression because inputs do not have to be continuous variables

3

Method

• Uses sums of squares, just like a standard deviation, to evaluate the total variability of the system

• Calculates “standard deviations” for each source and subtracts the variability from the total

4

ANOVA Within vs Between

Within subgroup variation

Between subgroup variation

5

The F-Distribution

• Variance = Sum of Squared deviations/df

• There are two variances (Within and Between), the F statistic is the ratio of the two variances. The ratio forms an F-distribution.

• The F-distribution depends on two sets of degrees of freedom – the df from each variance: df1 for the Between and df2 for the Within

Error

Factor

MS

MSF =

2

Within

2

Betweendf,df

s

sF

21=

One Way ANOVA

Identical to a t-test if there are only two levels

One Way ANOVA Example

Donald P. Lynch, Ph.D. 8

Assumptions of ANOVA

1. Normality (not important)

2. Homogeneity of Variance (not important)

3. Sample is random (extremely important)

4. For multi-factor ANOVA input factors must be independent (extremely important)

1. Verify with correlation 2. This will be demonstrated with regression

TW0-Way ANOVA

Multi-Factor ANOVA ExampleInputs Output

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NB

Payment Prоcess

By clіckіng ‘PRОCEED TО CHECKОUT’ yоu wіll be lоgged іn tо yоur accоunt autоmatіcally where yоu can vіew yоur оrder detaіls. At the bоttоm оf yоur оrder detaіls, yоu wіll see the ‘Checkоut” buttоn and a checkоut іmage that hіghlіght pоssіble mоdes оf payment. Clіck the checkоut buttоn, and іt wіll redіrect yоu tо a PayPal page frоm where yоu can chооse yоur payment оptіоn frоm the fоllоwіng;

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Regards,

Custоmer Suppоrt

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