confidence interval

简明释义

置信区间

英英释义

例句

1.The survey results showed that the mean income of the participants lies within a 95% confidence interval (置信区间) of $50,000 to $60,000.

调查结果显示，参与者的平均收入在95%的置信区间（置信区间）内为$50,000到$60,000。

2.The clinical trial reported a confidence interval (置信区间) for the effectiveness of the new drug at 90% certainty.

临床试验报告了新药有效性的置信区间（置信区间），可信度为90%。

3.The confidence interval (置信区间) for the average test score indicates a range from 75 to 85.

平均测试分数的置信区间（置信区间）显示范围为75到85。

4.In our analysis, we calculated a confidence interval (置信区间) for the proportion of voters supporting the candidate.

在我们的分析中，我们计算了支持该候选人的选民比例的置信区间（置信区间）。

5.When estimating the average height of students in a school, we found a confidence interval (置信区间) of 150 cm to 160 cm.

在估计一所学校学生的平均身高时，我们发现置信区间（置信区间）为150厘米到160厘米。

作文

Understanding statistical concepts is crucial for interpreting data accurately, especially in fields such as economics, psychology, and health sciences. One of the fundamental concepts in statistics is the confidence interval, which provides a range of values that is likely to contain the population parameter with a certain level of confidence. This concept helps researchers and analysts to make informed decisions based on sample data rather than making assumptions without evidence. A confidence interval is typically expressed as a lower and upper bound, indicating the range within which we expect the true value of the parameter to lie. For example, if a study reports a confidence interval for the mean height of a group of people as 160 cm to 170 cm, it suggests that the researchers are confident that the actual average height of the population falls within this range. The width of the confidence interval can provide insights into the precision of the estimate; a narrower interval indicates more precision, while a wider interval suggests more uncertainty. The level of confidence associated with a confidence interval is usually set at 95% or 99%. A 95% confidence interval means that if we were to take 100 different samples and compute a confidence interval for each sample, we would expect about 95 of those intervals to contain the true population parameter. This level of confidence is commonly used in research, but depending on the context, researchers may choose a different level of confidence to balance between precision and certainty. Calculating a confidence interval involves several steps, including determining the sample mean, the standard deviation, and the sample size. The formula for a confidence interval for the mean is typically given by: Confidence Interval = Sample Mean ± (Critical Value × Standard Error) Here, the critical value corresponds to the desired level of confidence and can be found using statistical tables or software. The standard error is calculated by dividing the standard deviation by the square root of the sample size. This formula illustrates how the confidence interval is influenced by the variability in the data and the size of the sample. In practice, understanding confidence intervals can significantly enhance one's ability to interpret research findings. For instance, in clinical trials, a confidence interval for the effectiveness of a new drug can inform healthcare professionals about the potential benefits and risks associated with its use. Similarly, in market research, businesses rely on confidence intervals to gauge consumer preferences and make strategic decisions. However, it is essential to recognize that a confidence interval does not guarantee that the true parameter lies within the specified range; rather, it reflects the uncertainty inherent in sample data. Misinterpretation of confidence intervals can lead to erroneous conclusions and decisions. Therefore, researchers must communicate their findings clearly and ensure that stakeholders understand what the confidence interval represents. In conclusion, the concept of confidence intervals plays a vital role in statistical analysis and decision-making across various disciplines. By providing a range of plausible values for population parameters, confidence intervals help to quantify uncertainty and guide researchers and practitioners in making informed judgments based on empirical evidence. As we continue to navigate an increasingly data-driven world, mastering the understanding of confidence intervals will undoubtedly enhance our ability to interpret and utilize data effectively.

理解统计概念对于准确解释数据至关重要，尤其是在经济学、心理学和健康科学等领域。统计学的一个基本概念是置信区间，它提供了一个可能包含总体参数的值范围，并伴随着一定的置信水平。这个概念帮助研究人员和分析师基于样本数据做出明智的决策，而不是在没有证据的情况下做出假设。置信区间通常表示为一个下限和上限，指示我们期望参数的真实值落在这个范围内。例如，如果一项研究报告某组人的平均身高的置信区间为160厘米到170厘米，这表明研究人员相信该人群的实际平均身高落在这个范围内。置信区间的宽度可以提供对估计精度的洞察；较窄的区间表示更高的精度，而较宽的区间则暗示更多的不确定性。与置信区间相关的置信水平通常设定为95%或99%。95%的置信区间意味着如果我们从100个不同的样本中计算每个样本的置信区间，我们预计大约95个区间将包含真实的总体参数。这个置信水平在研究中被广泛使用，但根据具体情况，研究人员可能会选择不同的置信水平，以在精度和确定性之间取得平衡。计算置信区间涉及几个步骤，包括确定样本均值、标准偏差和样本大小。样本均值的置信区间的公式通常给出如下：置信区间 = 样本均值 ± (临界值 × 标准误)这里，临界值对应于所需的置信水平，可以通过统计表或软件找到。标准误则通过将标准偏差除以样本大小的平方根来计算。这个公式说明了置信区间如何受到数据变异性和样本大小的影响。在实践中，理解置信区间可以显著增强人们解读研究结果的能力。例如，在临床试验中，某种新药的置信区间可以向医疗专业人员提供有关其使用潜在益处和风险的信息。同样，在市场研究中，企业依赖置信区间来评估消费者偏好并做出战略决策。然而，必须认识到，置信区间并不保证真实参数落在指定范围内；相反，它反映了样本数据固有的不确定性。对置信区间的误解可能导致错误的结论和决策。因此，研究人员必须清晰地传达他们的发现，并确保利益相关者理解置信区间所代表的内容。总之，置信区间的概念在各个学科的统计分析和决策制定中发挥着至关重要的作用。通过为总体参数提供一系列合理的值，置信区间帮助量化不确定性，并指导研究人员和从业者基于实证证据做出明智的判断。随着我们继续在一个日益数据驱动的世界中前行，掌握置信区间的理解无疑将增强我们有效解读和利用数据的能力。