Description: Estimation error refers to the difference between an estimated value and the actual or true value of a variable. This concept is fundamental in statistics, as it allows for the evaluation of the accuracy and validity of estimates made from data samples. Generally speaking, an estimation error can be positive or negative, depending on whether the estimated value is greater or less than the actual value. The magnitude of the estimation error is crucial for determining the reliability of a statistical analysis and can influence decision-making in various fields, such as economics, public health, and scientific research. Furthermore, estimation error can be classified into different types, such as systematic error, which occurs consistently in the same direction, and random error, which varies unpredictably. Understanding and minimizing estimation error is essential for improving the quality of statistical inferences and ensuring that conclusions drawn from data are as accurate as possible.
History: The concept of estimation error has been present in statistics since its beginnings in the 18th century, when methods began to be developed to infer characteristics of populations from samples. With the advancement of statistical theory, especially in the 20th century, concepts such as standard error and point estimation were formalized, allowing for a better understanding and management of estimation error in statistical analysis. The work of statisticians like Karl Pearson and Ronald A. Fisher was fundamental in establishing the foundations of modern statistical inference, where estimation error became a key element for evaluating the accuracy of estimates.
Uses: Estimation error is used in various fields, such as scientific research, economics, and public health, to assess the accuracy of estimates made from samples. For example, in opinion polls, estimation error is calculated to determine the reliability of the results. In medical research, it is used to evaluate the effectiveness of treatments based on patient samples. Additionally, in the financial sector, it is applied to estimate risks and returns on investments.
Examples: A practical example of estimation error can be observed in electoral polls, where the percentage of votes a candidate will receive is estimated. If the poll indicates that a candidate will receive 55% of the votes, but in the actual election, they only receive 50%, the estimation error is 5%. Another example can be found in clinical studies, where the success rate of a new drug is estimated; if it is estimated that 80% of patients will respond positively, but only 70% do, the estimation error is 10%.
