An alysis o f Va riance (ANOVA)

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# An alysis o f Va riance (ANOVA) - PowerPoint PPT Presentation

An alysis o f Va riance (ANOVA). ANOVA. More than two samples Can test multiple factors at the same time Multiple-way ANOVA One factor: One-way ANOVA E.g. Are there any difference of the heights of students from class A, B, C and D? Two factors: Two-way ANOVA

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### Analysis of Variance(ANOVA)

ANOVA
• More than two samples
• Can test multiple factors at the same time
• Multiple-way ANOVA
• One factor: One-way ANOVA
• E.g. Are there any difference of the heights of students from class A, B, C and D?
• Two factors: Two-way ANOVA
• E.g. Are there any difference of the heights of students from class A, B, C and D and also between the sexes?
Assumptions for ANOVA
• Normal distribution
• Homogeneity of variances

Most important!

Otherwise, you have to use non-parametric Kruskal-Wallis test

An example (Lab 5, e.g. 6)
• Four dietary treatments applied to the snails
• Measurement: shell length
2. Test for homogeneity of variances

Ho: equal variances

Ha: unequal variances

Fmax test

1

Fmax = Varmax / Varmin

= 4.6 / 3.5

= 1.3143

Calculated Fmax < Critical F0.05(2),5,5 = 7.15

Accept Ho

Equal variances (p>0.05)

2. Test for homogeneity of variances

Ho: equal variances

Ha: unequal variances

Fmax test

2

Calculated F = 1.3143

Critical F0.05(2),5,5 = 7.15

Accept Ho

Equal variances (p>0.05)

i-1

n-1

3. One-way ANOVA

Ho: equal mean among the diets

Ha: unequal mean among the diets

Cal F > Crit F, p<0.05

Reject Ho, unequal means

In SPSS,

1. Plot a bar chart

2. One-way ANOVA

2

1

3

Only SPSS allows post-hoc Tukey test

4

a

b

a

a