I like to give my students a question :

If we have two class (two mean) to compare, can we use Analysis of Variance (ANOVA)?

Most of them will answer, that they should use t-Test.

And I will continue with question, so, what is ANOVA for ? They will usually answer, to determine the difference of more that two means (in this sample, is a class).

๐ , it is common miss perception or they are not carefully enough reading the material during the statistic class …. but, hey, it is not the-most-exiting class anyway. I can understand …

Well, dear my students, you should understand that the definition actually is that you can determine the difference of** two or more** mean. Not more than two. So, you can use ANOVA in determining 2 mean, actually.

Ok, in t-Test, when the result shows the significance is 0.02 (when you are comparing class A and B) with the Confidence Interval (CI) = 95, means you can tell that both class A and B are different statistically. If the class B mean is higher than class A. It proofed that class B is higher. And may be in the discussion you can conclude that class B is smarter (in this particular subject area).

Now, what if we want to compare 4 classes (class A, B, C, D) ? ย When the result of the calculation shows that between groups is significant ? Below is the result from ANOVA

In this sample, we can say that indeed the class A, B, C, and D performed differently. They are different.

But which class is performed better ? Which class is the lowest or highest ?

We dont know.

Because using ANOVA, it only tells you that there is difference between those 4 classes. That is why, when you are using ANOVA and you have significant different result, you have to perform Post-Hoc test.

There are many Post-Hoc test. If you are using SPSS, you can see many choices. Choose the one that appropriate for you. In this case, I like to use Tukey’s-b

Tukey’s -b is the one that give the easiest way to interpret the difference of our groups.

Above is the result from the calculation. Turn out that in this data sample, there are three groups.

In other case, may be it will divided into 2 groups or even 4 groups. If you curious enough, when the ANOVA result shows not significance different, if you run a post-hoc test, you will see that there is only one group. Why ? because all of them consider the same, not different.

In this case, Class D is the lowest, Class A & C in the middle, and class B have the highest average score.

And that is proven to be statistical significant different.

Easy rite ? Now after you know that they are different, with this post-hoc test you can see that 2 classes consider having the same performance, while the other 2 classes is lower/higher.

This is why I like to use Tukey-b post-hoc test.

We, the statistic users, only need statistic to withdraw meaningful interpretation of our data. Other nitty-gritty ? well … you can ignore it.

In the next level, you need to add in your decision of choosing the statistic method about

**1**. what type of method that suitable for my data

**2.** what type of method that can give meaningful interpretation of my data

**3.** above all, in choosing the statistical method, ask your self why. why do I choose this method ? can I use it ? …etc …etc…etc

happy counting …. ๐