Definition : Analysis of variance (ANOVA) uses F-tests to statistically assess the equality of means when you have three or more groups. When we come across a problem when we need to compare more than two means then we perform Analysis of variance (ANOVA).
Assumptions for ANOVA Test.
ANOVA Test is based on the test statistics F (or variance ratio), now for validity of the F-test in ANOVA are as follows,
- The observation are independent.
- Parent population from which observation are taken is normal, and
- Various treatment and environmental effects are additive in nature.
Below is the example,
Question: The following table shows the lives (in hours) of four batches of electric lamps.
Perform an analysis of variance or one way classification of these data and show that significance test does not reject their homogeneity.
Null hypothesis, Ho : mb1=mb2=mb3=mb4 ## mbi implies mean of batch i i=1,2,3,4
Alternative hypothesis, Ha : Atleast two means are different
I will answer several common questions about how to perform Analysis of Variance (ANOVA) in SPSS.
- How to manage data in SPSS?
- How do we treat Batch?
Firstly, enter all the observations in one column either row or column wise like here I have entered data row wise
Secondly, there are four batches of bulbs. If you have entered the data row wise then put the corresponding batch number to the very next column say batch.
Note: you can also enter data column wise and put the corresponding batch number in the very next column.
Select the “observation” and put it in the dependent column, and “batch” in the factor column.
You will get the desired result.
p-value for Analysis of Variance (ANOVA) is 0.123, indicates that we do not have enough evidence to reject Null hypothesis at 0.05 level of significance. Hence we may accept null hypothesis i.e the treatment means are equal. This test is statistically insignificant.
Note: here the interpretation is made on the basis of p-value.