Question

What is the ANOVA?

When is the ANOVA used?

What are the components?

What are the criterion for determining (reject null hypothesis or fail to reject hypothesis)?

What does the final computed number mean?

Answer 1

Ans:

Analysis of variance (ANOVA) can determine whether the means of three or more groups are different. ANOVA uses F-tests to statistically test the equality of means.

The F-statistic is simply a ratio of two variances. Variances are a measure of dispersion, or how far the data are scattered from the mean. Larger values represent greater dispersion.

F-statistics are based on the ratio of mean squares. The term “mean squares” may sound confusing but it is simply an estimate of population variance that accounts for the degrees of freedom (DF)used to calculate that estimate.

Using the F-test in One-Way ANOVA:

To use the F-test to determine whether group means are equal, it’s just a matter of including the correct variances in the ratio. In one-way ANOVA, the F-statistic is this ratio:

F = variation between sample means / variation within the samples

ANOVA table :

Source	Sum of squares	degree of freedom	Mean square	F ratio	p-value
Treatments
Error
Total

We calculate sum of squares(SS) and df from data given,then Mean squares(MS) and F ratio is calculated fom it as below:

MS(treatements)=SS(treatments)/df(treatments)

similarly,MS(error) is calculated and we derive F statistic as below:

F=MS(treatments)/MS(error)

Decision criteria:

If F>=Fcritical,we reject null hypothesis.

If F<F critical,we fail to reject null hypothesis.