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An alysis o f Va riance (ANOVA)PowerPoint Presentation

An alysis o f Va riance (ANOVA)

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An alysis o f Va riance (ANOVA)

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Analysis of Variance(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?

- Normal distribution
- Homogeneity of variances

Most important!

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

- Four dietary treatments applied to the snails
- Measurement: shell length

1. Plot a bar chart

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

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b

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