Two sample t-tests can validate a hypothesis containing only two groups at a time. For samples involving three or more groups, the t-test becomes tedious, as you have to perform the tests for each combination of the groups. Also, the possibility of a type-1 error increases in this process. In such cases, you can use ANOVA.
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.
To understand how ANOVA is applied, let’s go over a simple case:
A test was conducted at a workplace, and the feedback on the three e-commerce platforms was recorded in a data set, which is as follows:
| Amazon | Flipkart | Snapdeal |
| 7.5 | 7 | 5 |
| 8.5 | 9.5 | 7.5 |
| 6 | 10 | 8.5 |
| 10 | 6 | 3 |
| 8.5 | 7.5 | 6 |
| 8 | 8.5 | 5 |
| 8 | 10 | 7 |
| 6 | 6.5 | |
| 9.5 | 6.5 | |
| 10 | 9 | |
| 6.5 | 10 |
To begin with, create a null hypothesis (Ho) for your ANOVA test. In this case, your null hypothesis will be: ‘All the platforms are equally popular’. The alternate hypothesis Ha, thus, becomes ‘At least one of the platforms has different popularity from the rest’. Now you represent this information as:
H0:μ1=μ2=μ3….=μk (where k is the number of different populations or groups or treatment levels. In your case, it’s 3). By writing this, you suggest that the ‘mean’ of the different populations will be the same, which is your null hypothesis. If the statement above is proved at the end of your test, it will imply that all the platforms are equally popular. If not, then you accept your alternative hypothesis Ha
The test statistic that we use here is called the F-statistic, which helps us in comparing the variances. In order to understand the computations, please check the following link containing three videos.
Once the computations have been done and F-statistic has been obtained, you compute the necessary p-value for this and then compare against the given standard value of 0.05. And then on the basis of this comparison, you either reject or fail to reject the null hypothesis.
Now that you’re familiar with the concept of ANOVA, please go ahead and try to answer the following questions.
Now go and ahead and answer the next question where you discuss when it is appropriate to choose ANOVA over independent t-tests.
You can also go through this link for a short summary of the ANOVA process and this link for an example.