Nemenyi test

Imagine you and your friends are racing to see who can run the fastest. Everyone runs and we write down how long it takes for each person to run. But then, we need to figure out who is the fastest runner of them all, right?

That's where the Nemenyi Test comes in. It's a way to find out if there's a big enough difference between the times to say that someone is faster than the others in a reliable way.

Here's how it works:

First, we take all the race times and put them in order from fastest to slowest. Then, we draw a graph with each person's time on it.

Next, we draw lines between the points on the graph. These lines represent the differences between the times. We draw a line only between the people who were close enough in time to be compared to each other.

Once we have all the lines drawn, we can see very clearly who was the fastest runner. The person who has the longest line going up from their time on the graph is the person who ran the fastest.

But, we don't just want to know who won. We also want to know if the difference between the fastest runner and the others is big enough that we can be sure it wasn't due to chance.

To do this, we use some math. We compare the difference in time between each person to a standard that tells us what differences would be due to chance. If the difference between the fastest runner and the others is bigger than this standard, we say that it wasn't due to chance and that the fastest runner really is faster than the others.

And that's how the Nemenyi Test works! It helps us figure out who is the best at something by using math and comparing the differences between everyone's performance.