Description: Interval estimation is a statistical method that provides a range of values within which an unknown population parameter, such as the mean or proportion, is expected to lie. This approach is fundamental in statistical inference, as it allows researchers and analysts not only to estimate a point value but also to consider the inherent uncertainty in the estimation. A confidence interval is typically expressed with a confidence level, indicating the probability that the interval contains the true population parameter. For example, a 95% confidence interval suggests that if multiple samples were taken and confidence intervals calculated, approximately 95% of those intervals would include the true parameter. Interval estimation is particularly useful in situations where sample data is available and inferences about a larger population are desired, enabling researchers to make informed decisions based on data variability. This method is used across various disciplines, from medicine to economics and social sciences, and is essential for hypothesis validation and data-driven decision-making.
History: Interval estimation has its roots in the development of statistics in the 20th century, although similar concepts can be traced back to the work of statisticians like Karl Pearson and Ronald A. Fisher. Fisher, in particular, was instrumental in formalizing the theory of statistical inference in the 1920s, introducing the concept of confidence intervals in his work ‘Statistical Methods for Research Workers’ published in 1925. Over time, interval estimation has evolved and been refined, becoming an essential tool in modern statistical research.
Uses: Interval estimation is used in various fields, including medicine, psychology, economics, and social sciences. For example, in clinical trials, it can be used to estimate the effectiveness of a new treatment, providing a range of values that indicates the possible improvement in patient health. In opinion surveys, it can be applied to estimate the proportion of the population that supports a particular policy, allowing researchers to better understand public opinion.
Examples: A practical example of interval estimation is a study measuring the average height of students at a university. If a sample of 100 students is taken and the average height is found to be 170 cm with a 95% confidence interval ranging from 168 cm to 172 cm, this indicates that there is a 95% confidence that the average height of all students at the university falls within that range. Another example is in political polling, where it may be estimated that 60% of voters support a candidate, with a confidence interval ranging from 55% to 65%.
