ANOVA

Analysis of Variance (ANOVA)

Indian Institute of Public Health Delhi
MSc CR 2013-15

Outline of the session
• Need for Analysis of Variance
• Concept behind one way ANOVA

• Example
• Non-parametric alternative

When dependent variable is continuous
Type of
Dependent
variable

Type of
Independent
variable

Number of Groups

Continuous

Categorical

More than two

Non-parametric (Wilcoxon sign rank) Paired t – test

Not normal

Non-parametric (Wilcoxon sign rank) Independent z or t – test

Not normal

Non-parametric (Wilcoxon rank sum or Mann-Whitney U )

Not normal

Unrelated or independent Not normal

Normal

Two

z or one sample t – test

Normal

Related

Choice of Significance test

Normal

NA

Distribution of dependent variable
Normal

One

Related/
Dependent

One way ANOVA/linear regression Non-parametric (Kruskal Wallis)

Normal

Repeated ANOVA

Not normal

Non-parametric (Friedmans test)

Unrelated

Related

Background
• When you have more than two groups to compare, you can apply t-test multiple times
• But this is not done, why???
• Probability of type I error increases
• This increases as the number of comparison increases • Analysis of variance (ANOVA) is one way of dealing with this problem which tests for overall significance

One way ANOVA
• Used to compare the mean of a numerical outcome variable in the groups defined by an exposure level with two or more categories

• Method is based on how much overall variation in the outcome variables is attributable to differences between the exposure group means
• This is equal to t-test for two sample with equal variance One-Way ANOVA
Partitions Total Variation

Total variation

Variation due to treatment

• Among Groups Variation

Variation due to random sampling • Within Groups Variation

One-Way ANOVA
• Difference between the means could be due to
variability