ANOVA

Analysis Of Variance
-is a statistical test used to determine if more than two population means are equal. The test uses the F-Distribution (probability distribution) function and information about the variances of each population (within) and grouping populations (between) to help decide if variability between and within each populations are significantly different.
Methods of ANOVA to test the hypothesis:
1. Know the purpose of the analysis of variance test. 
2. Know the difference between the within-sample estimate of the variance and the between-sample estimate of the variance and how to calculate them.
3. Know the properties of an F-Distribution.
4. Know how sum of squares relate Analysis of Variance.
5. Know how to construct an ANOVA table.
6. Know how to interpret the data in the ANOVA table against the Null hypothesis.
7. Know the procedure for testing the null hypothesis that the mean for more than two populations are equal. 
Step 1: Formulate hypothesis.
Null Hypothesis: μ=μ...
Alternative Hypothesis: Not all means are equal
Step 2: Select the F-Statistics Test for equality of more than two means.
Step 3: Obtain or decide on a significance level for alpha.
Step 4: Compute the test statistics from the ANOVA Table.
Step 5: Identify the Critical Region: The region of rejection of the null hypothesis is obtained from the F-Table with alpha and degree of freedom [(k-1)(n-k)].
Step 6: Make a decision and Summarize the results.





by: Oscar Pepin B. Marfil