Deterministic: Definition and Examples

Statistics Definitions > Deterministic

What is Deterministic?

Deterministic (from determinism, which means lack of free will) is the opposite of a random event. It tells us that some future event can be calculated exactly, without the involvement of randomness. For example, the conversion between Celsius and Kelvin is deterministic, because the formula is not random…it is an exact formula that will always give you the correct answer (assuming you perform the calculations correctly):

Kelvin = Celsius + 273.15.

If something is deterministic, you have all of the data necessary to predict (determine) the outcome with 100% certainty. The process of calculating the output (in this example, inputting the Celsius and adding 273.15) is called a deterministic process or procedure. A few more examples:

  • Rolling a fair die: each number on a six-sided die has the same odds (1/6) of coming up.
  • Calculating what your savings account balance will be in a month (add up your deposits and the prevailing interest rate).
  • The relationship between a circumference and radius of a circle, or the area and radius of a circle.

On the other hand, a random event or process can’t be determined with an exact formula. You can ballpark it, or “hazard a good guess,” but you can’t assign probabilities to it. For example, the odds of seeing a black cat on your way to work tomorrow cannot be calculated, as the process is completely random, or stochastic. You could take a good guess (zero probability would be a good start), but it would still be just that — a guess.

Deterministic Relationships

In simple linear regression, if the response and explanatory variables have an exact relationship, then that relationship is deterministic. In other words, if you can predict with 100% certainty where a y-value is going to be based only on your x-value, then that’s a deterministic relationship.

Statistical Relationships

Most things in real life are a mixture of random and deterministic relationships. For example, weather patterns are partly random, and they can partly be forecast. When something is part random and part deterministic, it’s called a statistical relationship or probabilistic relationship. Both terms mean the same thing; Which you use is a matter of personal preference.

Related article: Deterministic Functions.

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