confidence region

简明释义

置信范围

英英释义

例句

1.The size of the confidence region is influenced by the sample size; larger samples typically yield smaller regions.

置信区域的大小受样本大小的影响；较大的样本通常会产生较小的区域。

2.Researchers often visualize the confidence region in a graph to show the uncertainty in their estimates.

研究人员通常在图表中可视化置信区域，以显示他们估计中的不确定性。

3.When conducting a regression analysis, the confidence region provides insight into the reliability of the model's predictions.

在进行回归分析时，置信区域提供了对模型预测可靠性的洞察。

4.In statistical analysis, the confidence region is used to estimate the parameters of a population based on sample data.

在统计分析中，置信区域用于根据样本数据估计总体参数。

5.The confidence region can help determine if a new treatment is statistically significant compared to a control group.

通过置信区域可以帮助确定新治疗是否在统计上显著优于对照组。

作文

In the realm of statistics and data analysis, the term confidence region plays a crucial role in understanding the uncertainty associated with estimates. A confidence region is a set of values that is believed to contain the true parameter of interest with a certain probability. This concept is particularly important when making inferences about population parameters based on sample data. For instance, when conducting a survey or an experiment, researchers often collect data from a sample rather than the entire population. The confidence region provides a way to quantify the uncertainty around the estimated parameters derived from this sample data.To illustrate, consider a scenario where a researcher is interested in estimating the average height of adult males in a city. By taking a random sample of 100 adult males, the researcher calculates the sample mean and standard deviation. Using these statistics, the researcher can construct a confidence region for the average height. If the researcher decides on a 95% confidence level, it means that if the study were repeated multiple times, approximately 95% of the constructed confidence regions would contain the true average height of all adult males in the city.The mathematical formulation of a confidence region typically involves the use of a normal distribution, especially when dealing with large sample sizes. The confidence region can be visualized as an interval on a number line or as a multi-dimensional space when dealing with multiple parameters. In two dimensions, for example, the confidence region could take the shape of an ellipse, indicating the range of plausible values for two related parameters.Understanding confidence regions is essential not only for statisticians but also for professionals in various fields such as economics, biology, and engineering. It allows them to make informed decisions based on the data at hand while accounting for the inherent variability and uncertainty. For example, in clinical trials, a confidence region can help researchers determine whether a new drug is effective compared to a placebo by providing a range of possible outcomes based on the collected data.However, it is important to note that the interpretation of confidence regions requires careful consideration. A common misconception is that a confidence region provides a definitive range within which the true parameter lies. Instead, it reflects the degree of uncertainty associated with the estimate and the probability that the region contains the true value. Therefore, communicating findings that involve confidence regions should be done with clarity to avoid misinterpretation.In conclusion, the concept of confidence region is fundamental in statistical analysis, providing a framework for understanding the uncertainty surrounding estimates. As data-driven decision-making becomes increasingly prevalent in various fields, mastering the concept of confidence regions will empower researchers and practitioners to draw more reliable conclusions from their data. By effectively utilizing confidence regions, one can navigate the complexities of statistical inference and contribute to more robust findings in research and practice.

在统计学和数据分析领域，术语置信区间在理解与估计相关的不确定性方面起着至关重要的作用。置信区间是一组被认为包含真实参数的值，其置信度达到一定概率。这个概念在基于样本数据对总体参数进行推断时尤为重要。例如，在进行调查或实验时，研究人员通常从一个样本而不是整个总体中收集数据。置信区间提供了一种量化从样本数据得出的估计参数周围不确定性的方法。举例来说，考虑一个研究者希望估计一个城市成年男性的平均身高的情境。通过随机抽取100名成年男性，研究者计算出样本均值和标准差。利用这些统计数据，研究者可以构建一个置信区间来表示平均身高。如果研究者选择95%的置信水平，这意味着如果重复进行多次研究，构建的置信区间大约有95%会包含该城市所有成年男性的真实平均身高。置信区间的数学公式通常涉及使用正态分布，尤其是在处理较大样本量时。置信区间可以在数轴上可视化为一个区间，或者在处理多个参数时可视化为多维空间。例如，在二维情况下，置信区间可能呈椭圆形状，表示两个相关参数的合理值范围。理解置信区间不仅对统计学家至关重要，而且对经济学、生物学和工程等各个领域的专业人士也同样重要。它使他们能够根据手头的数据做出明智的决策，同时考虑到固有的变异性和不确定性。例如，在临床试验中，置信区间可以帮助研究者判断一种新药是否比安慰剂有效，通过提供基于收集数据的可能结果范围。然而，需要注意的是，解读置信区间需要谨慎。一个常见的误解是，置信区间提供了一个真实参数所在的确定范围。相反，它反映了与估计值相关的不确定性程度以及该区域包含真实值的概率。因此，涉及置信区间的研究结果的传播应当清晰，以避免误解。总之，置信区间的概念在统计分析中是基础，为理解估计周围的不确定性提供了框架。随着数据驱动决策在各个领域变得越来越普遍，掌握置信区间的概念将使研究人员和从业者能够从数据中得出更可靠的结论。通过有效利用置信区间，人们可以驾驭统计推断的复杂性，并为研究和实践中的更强有力的发现做出贡献。