Tolerance and Precision
Control the level of acceptable tolerance in student responses when compared with blank answers
Tolerance and Precision
When comparing math expressions to determine correctness of math,numeric and unit blanks the MathMatize math engine employs a combination of symbolic and numeric techniques. Numeric methods are ultimately limited in their precision by the constraints of floating point numbers. When testing student responses for correctness against a constant answer MathMatize allows content creators to specify tolerance in a number of ways. The tolerance can be set as:
- a maximum allowed absolute difference,
- as a minimum number of decimal places that need to match,
- exact agreement to a given number of significant digits,
- agreement to at least a given number of significant digits, or
- a maximum allowed percentage difference.
Unit blanks only allow tolerance to be specified as an absolute or percentage difference.
When an exact response is requested, i.e. when tolerance is set to zero,
MathMatize will consider two expressions to be equal when:
- the relative error is less than 1 part in 1 trillion, or
- the absolute error is less than 1x1015.
If for any reason a stricter bound is required to determine exactness, e.g. for answers smaller than 1x10-10, the blank tolerance can be set accordingly. The effect of setting different tolerance values on the correctness of a response can be tested here: MathMatize Formula Tester.
NOTE: If symbolic/numeric comparison fails to yield a positive match, MathMatize will attempt a case insensitive string comparison between the response and the provided answer.
See also: