The F-Distribution and Hypothesis tests
One Way (Single-Factored) ANOVA
ANOVA – Analysis of variance
- The Chi-Square distribution’s “goodness of fit” showed if there is a
significant difference in one observation from multiple categories.
- ANOVA tells us if there is a difference in the “goodness of fit”
between multiple categories and multiple observations within that
category.
- ANOVA measures the amount of variance between multiple means.
- The closer the variances are to 0, the closer the categories are to being
the same.
The ANOVA method
Given a table of information, the ANOVA method is as follows:
1) Find the null and alternative hypotheses
2) Compute all row totals
3) Compute grand total of all data
4) Complete ANOVA table to get the F-Value (test Statistic)
5) Obtain F* (critical value) from F-Distribution table
6) If F-Value > F*, we reject the null hypothesis
ANOVA Table – Allows us to compute the F-Value
Source of
Variation
Sum of
Squares
Degrees of
Freedom
Mean square F-Value
Factor of the
experiment
1) 4) 7) 9)
Error 2) 5) 8)
Total 3) 6)
How to compute each cell:
