In quantitative research, the error is the probability that the actual value lies outside the given range. If you took a sample of 100 people and took their average height, you could assume their average height is the same as that of the population (if you sampled correctly). This assumption would be correct to a degree of accuracy. The standard deviation of your statistics gives you a clue. For a standard bell curve, 96% of the population lies within two standard deviations. You can then state in a published paper that the average population height is “x” +/- 2SDs, with p<0.05. 0.05 is your error value. 0.05, or 5%, is usually the accepted value in medical research.
NB. This only refers to type 1 errors. For type 2 errors the calculation method is different, and the accepted margin of error is 20%.