2^k factorial experiment design

[physea]

Hello!

In this webpage:
https://onlinecourses.science.psu.edu/stat503/node/35

it describes the 2^k factorial experiment design. I understand that k is the number of factors that we are investigating (in this case two, a and b), 2 are the levels of each factor (+/-) and 2^k=4 is the number of the all possible combinations of these factors (null, a, b, ab).

However, I don't understand what he means with "You can see that we have 3 observations at each of 4 = 2k combinations for k = 2. So we have n = 3 replicates." What are these three observations for each combination and why they are called replicates?

What happens in k=3 etc situations with these replicates?

thanks!

 

[DrClaude]

The replicates are simply the number of times the experiment was performed. For each of the $2^k$ combinations, the reaction was carried out 3 times and the yield measured each time.