# Anova Formula

F = Anova Coefficient

MST = Mean sum of squares due to treatment

MSE = Mean sum of squares due to error.

SST = Sum of squares due to treatment

p = Total number of populations

n = The total number of samples in a population.

SSE = Sum of squares due to error

S = Standard deviation of the samples

N = Total number of observations.

### Solved Examples

**For reference please go through the below-mentioned example:**

**Question 1: **The following data is given:

Types of Animals | Number of animals | Average Domestic animals | Standard Deviation |

Dogs | 5 | 12 | 2 |

Cats | 5 | 16 | 1 |

Hamsters | 5 | 20 | 4 |

Calculate the Anova coefficient.

**Solution:**

Construct the following table:

Animal name | n | x | S | $S^{2}$ |

Dogs | 5 | 12 | 2 | 4 |

Cats | 5 | 16 | 1 | 1 |

Hamster | 5 | 20 | 4 | 16 |

p = 3

n = 5

N = 15

x̄ = 16

SST = ∑n (x−x̄)^{2}

SST= 5(12−16)^{2}+5(16−16)^{2}+11(20−16)^{2
}= 160

MST = $\frac{SST}{p−1}$

MST = $\frac{160}{3−1}$

MST = 80

SSE = ∑ (n−1)$S^{2}$

SSE = 4$\times$4 + 4$\times$1 + 4$\times$16

SSE = 84

MSE= $\frac{SSE}{N−p}$

MSE=$\frac{8415}{38415−3}$

MSE = 7

F = $\frac{MST}{MSE}$

F = $\frac{80}{84}$

F = 11.429