confidence interval

简明释义

置信区间

英英释义

例句

1.The financial report included a confidence interval for projected sales, helping investors understand the potential variability.

财务报告中包含了预计销售的置信区间，帮助投资者理解潜在的变动性。

2.The survey results showed a confidence interval of ±3%, meaning the actual percentage could be slightly higher or lower.

调查结果显示，置信区间为±3%，这意味着实际百分比可能略高或略低。

3.When estimating the average height of students in a school, the confidence interval was found to be between 150 cm and 160 cm.

在估计一所学校学生的平均身高时，置信区间被发现介于150厘米到160厘米之间。

4.In a clinical trial, researchers reported a 95% confidence interval for the treatment effect, indicating they are 95% confident that the true effect lies within this range.

在临床试验中，研究人员报告了治疗效果的95%置信区间，这表明他们有95%的信心认为真实效果位于这个范围内。

5.A confidence interval can help determine how much uncertainty exists in the estimated parameters of a model.

置信区间可以帮助确定模型估计参数中存在多少不确定性。

作文

In the field of statistics, understanding the concept of a confidence interval is crucial for making informed decisions based on data. A confidence interval is a range of values that is used to estimate the true value of a population parameter. It provides a measure of uncertainty associated with a sample statistic and helps researchers understand how much they can trust their estimates. For instance, if a researcher conducts a survey to determine the average height of adult men in a city, they will collect data from a sample of men rather than measuring every single man. Based on this sample, they calculate an average height and then create a confidence interval around that average to indicate the range within which the true average height likely falls.The width of a confidence interval is influenced by several factors, including the sample size and the variability of the data. A larger sample size generally leads to a narrower confidence interval, indicating greater precision in the estimate. Conversely, if the sample size is small or if there is a lot of variability in the data, the confidence interval will be wider, suggesting more uncertainty about the true population parameter.Moreover, the level of confidence chosen by the researcher also affects the confidence interval. Common confidence levels are 90%, 95%, and 99%. A 95% confidence interval means that if the same study were repeated multiple times, approximately 95% of the calculated intervals would contain the true population parameter. This level of confidence strikes a balance between precision and reliability, making it a popular choice among researchers.Interpreting a confidence interval requires care. It does not imply that there is a 95% chance that the true parameter lies within the interval for any specific study; rather, it indicates that if we were to take many samples and construct a confidence interval for each one, 95% of those intervals would contain the true parameter. This distinction is important for avoiding misconceptions about the meaning of statistical results.The application of confidence intervals extends beyond academic research; they are widely used in various fields such as medicine, economics, and social sciences. For example, in clinical trials, researchers use confidence intervals to report the effectiveness of a new drug compared to a placebo. By providing a confidence interval for the difference in outcomes between the two groups, they can communicate the uncertainty and potential variability in the treatment effects.In conclusion, a confidence interval is a powerful statistical tool that quantifies the uncertainty surrounding an estimate. By offering a range of plausible values for a population parameter, it aids researchers in making informed conclusions and decisions based on sample data. As we continue to navigate an increasingly data-driven world, mastering the concept of confidence intervals will undoubtedly enhance our ability to interpret and leverage statistical information effectively.

在统计学领域，理解置信区间的概念对于基于数据做出明智决策至关重要。置信区间是一个值的范围，用于估计一个总体参数的真实值。它提供了与样本统计量相关的不确定性度量，并帮助研究人员了解他们的估计有多可信。例如，如果研究人员进行调查以确定某城市成年男性的平均身高，他们将从一部分男性中收集数据，而不是测量每一个男性。根据这个样本，他们计算出一个平均身高，然后创建一个置信区间，以指示真实的平均身高可能落入的范围。置信区间的宽度受多个因素的影响，包括样本大小和数据的变异性。较大的样本大小通常导致较窄的置信区间，表明估计的精确度更高。相反，如果样本大小较小或数据变异性较大，则置信区间会更宽，暗示对真实总体参数的不确定性更大。此外，研究人员选择的置信水平也会影响置信区间。常见的置信水平有90%、95%和99%。95%的置信区间意味着如果同一研究重复多次，计算出的区间大约有95%会包含真实的总体参数。这个置信水平在精确性和可靠性之间取得了平衡，使其成为研究人员的热门选择。解读置信区间需要谨慎。它并不意味着在任何特定研究中，真实参数有95%的机会位于该区间内；相反，它表示如果我们采取许多样本并为每个样本构建一个置信区间，那么95%的这些区间将包含真实参数。这一区别对于避免对统计结果的误解非常重要。置信区间的应用超越了学术研究；它们在医学、经济学和社会科学等多个领域被广泛使用。例如，在临床试验中，研究人员使用置信区间来报告新药与安慰剂相比的有效性。通过提供两组之间结果差异的置信区间，他们可以传达治疗效果的不确定性和潜在变异性。总之，置信区间是一个强大的统计工具，量化了围绕估计的不确定性。通过提供总体参数的合理值范围，它帮助研究人员基于样本数据做出明智的结论和决策。随着我们继续在一个越来越以数据驱动的世界中航行，掌握置信区间的概念无疑将增强我们有效解读和利用统计信息的能力。