They are experiments which are designed in such a way as to provided maximum information about the effects on the dependent variable of explanatory (independent) variables, separately as well as their interactions, with the smallest number of experimental subjects. Latin squares and Graeco-Latin squares are some of the better known examples.
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Counting statistics experiments are useful in math. This is what helps with numbers.
A factor in statistics can be defined as a variable which will affect the results of an experiment. This is mainly an aspect which is independent.
It depends on what the experiment is designed to do!
Statistics is used to design the experiment (what type of data needs to be obtained and how much), then statistics is used to analyze the data (make inferences and draw conclusions).
The matched subject because the experiment involves pairs which halves the df.