13.3: The One Factor ANOVA Model
- Page ID
- 20922
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In ANOVA, we calculate the variance two different ways: The mean square factor (\(\mathrm{MS}_{F}\)), also known as mean square between, measures the variability of the means between groups, while the mean square within (\(\mathrm{MS}_{E}\)), also known as mean square within, measures the variability within the population. Under the null hypothesis, the ratio of \(\mathrm{MS}_{F} / \mathrm{MS}_{E}\) should be close to 1 and has \(\mathrm{F}\) distribution.
Model Assumptions
- The populations being sampled are normally distributed.
- The populations have equal standard deviations.
- The samples are randomly selected and are independent.
Test Statistic
- \(\mathrm{F}=\dfrac{\mathrm{MS}_{\text {Factor }}}{\mathrm{MS}_{\text {Error }}}\)
- \(\mathrm{df}_{\text {num }}=k-1\)
- \(\mathrm{df}_{\text{den}}=n-k\)