ANOVA

ANOVA

• Developed by Fisher
• Studied Agriculture and crop output with different fertilizers 
• Needed test that could evaluate differences between three or more means
• Why- problems with applying the Student's t test

One- ANOVA

• Examines one factor at a time, tests for differences among levels of the factor

Fixed Effects or Model I One-way ANOVA

• the levels of the factor are specifically chosen by the investigator

Random effects or Model II One-way ANOVA

• the levels of the factor are randomly chosen by the investigator

Mechanics of One-way ANOVA

• Statistical hypothesis
• Formulae
• Critical values and decisions to reject/ not reject the null hypothesis

Formulae

• Focus in on analysis of variance- comparison between 2 types of variance
• Numerator= among group variance (variation among the grand mean and the sample means)
• Denominator= within group variance (sum of the variation within each sample-around each sample mean)

Results of ANOVA

• No difference between among group variance and within group variance
• There is no difference among means
• Stop all testing and write the results section
• Differences exists between among group variance and within group variance
• There is a difference among means
• Follow with a multiple comparisons test to determine which means are different from each other

Example of an ANOVA

1. State the biological question
2. Translate into statistical hypotheses
3. State the alpha level
4. State the statistical test
5. State the assumption of the test
6. Calculate the observed test statistic
7. Find the degrees of freedom and critical value
8. Compared the observed and critical value 
9. Interpret the results