“An ideal requirement for the capability of detection with respect to a selected state variable would be that the actual state of every observed system can be classified with certainty as either equal to or different from its basic state.”
Statistical concepts are hard enough on their own without overlaying inscrutable English.
If you want to know what a state variable is, that is in another document: IS0 11843-1:1997(E/F). Here it is: (the definition is also in French).
quantity describing the state of a system
1 Generally, a system is characterized by more than one state variable. However, depending on the scope of the investigation, only one state variable is selected for the purpose of detecting a difference between an actual state and the basic state.
2 Usually the selected state variable attains its smallest value in the basic state.
a) Concentration or amount of a substance in a mixture of substances.
b) Intensity (energy density, power density, etc.) of the energy (radiation, sound, etc.) emitted by a source.
c) Geometric change in a static system when it is distorted.
I thought you shouldn’t use the word being defined in the definition. Actually, this definition reminds me of the joke about the dictionary definition of recursion:
Recursion: see recursion.