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Analysis of variance

Compares the variation due to specific sources with variation among individuals who should be similar. The test whether several populations have the same mean by comparing how far apart the sample means are against how much variation there is w/in the samples

1

ANOVA F test

Tests the null hypothesis that all the populations being compared have the same mean

2

Conditions for ANOVA

Independent SRS from each population; that each population has Normal distribution; and that all populations have the same standard deviation

3

Mean squares

The measure of variation in the numerator and denominator of F

4

One-way analysis of variance (ANOVA)

The simplest form of ANOVA , this compares the means of several populations

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Test statistic for Analysis of Variance is F=

Observed variation in the sample means / over expected variation in the sample means population means are equal

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Observed variation

Variation among sample means

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Expected variation

Variation among individuals within samples

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ANOVA us robust but check for normality, a.e.

Outliers and skewness

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Unequal variance- ANOVA is robust if

The sample sizes are equal and no sample is very small
Check
Largest s/ smallest s< 2

10

Lack of random allocation or independent SRSs - ANOVA is NoT robust

Poorly collected data