standard error

简明释义

标准误差

英英释义

例句

1.The calculated mean has a standard error 标准误 of 0.5, indicating the precision of our estimate.

计算得出的均值的标准误 标准误为0.5，表明我们估计的精确度。

2.The standard error 标准误 of the regression coefficient was found to be significant in the analysis.

在分析中发现回归系数的标准误 标准误是显著的。

3.A smaller standard error 标准误 indicates more reliable results in statistical testing.

较小的标准误 标准误表明统计测试中的结果更可靠。

4.In our study, the standard error 标准误 helps us understand the variability of our sample mean.

在我们的研究中，标准误 标准误帮助我们理解样本均值的变异性。

5.To calculate the standard error 标准误, we need to divide the standard deviation by the square root of the sample size.

要计算标准误 标准误，我们需要将标准差除以样本大小的平方根。

作文

The concept of standard error is crucial in the field of statistics, particularly when it comes to understanding the reliability of sample estimates. In essence, the standard error measures the variability or dispersion of a sample mean from the true population mean. It provides insight into how much the sample mean would likely fluctuate if we were to take multiple samples from the same population. This is particularly important for researchers and analysts who rely on sample data to make inferences about larger groups. When conducting a study, researchers often collect data from a subset of a population rather than the entire group due to constraints such as time, cost, or accessibility. The standard error helps quantify the uncertainty associated with using this sample to estimate population parameters. A smaller standard error indicates that the sample mean is a more precise estimate of the population mean, whereas a larger standard error suggests greater variability and less reliability in the estimate.To calculate the standard error, one typically divides the standard deviation of the sample by the square root of the sample size. This formula highlights an important principle: as the sample size increases, the standard error decreases. This relationship underscores the importance of using larger samples when possible, as they tend to yield more accurate estimates of population parameters.For instance, imagine a scenario where a researcher is studying the average height of adult men in a city. If the researcher collects a sample of 30 men and calculates their average height, the standard error can help determine how close this sample mean is likely to be to the actual average height of all adult men in that city. If the standard error is relatively small, the researcher can be more confident that their sample mean is a good representation of the population mean. Conversely, a large standard error may lead the researcher to reconsider the validity of their findings or the adequacy of their sample size.Furthermore, the standard error is also essential when constructing confidence intervals. A confidence interval provides a range of values within which the true population parameter is expected to fall, with a certain level of confidence (often 95% or 99%). The width of this interval is influenced by the standard error. A smaller standard error results in a narrower confidence interval, indicating a more precise estimate, while a larger standard error leads to a wider interval, suggesting more uncertainty.In summary, the standard error is a vital statistical tool that aids researchers in assessing the precision of their sample estimates and making informed decisions based on those estimates. Understanding the implications of the standard error allows researchers to better interpret their results and communicate their findings effectively. As such, mastering the concept of the standard error is essential for anyone engaged in statistical analysis or research, as it directly impacts the credibility and reliability of their conclusions.

标准误差的概念在统计学领域至关重要，尤其是在理解样本估计的可靠性方面。实质上，标准误差衡量的是样本均值与真实总体均值之间的变异性或离散程度。它提供了关于如果我们从同一总体中抽取多个样本，样本均值可能波动多少的洞见。这对于依赖样本数据对更大群体进行推断的研究人员和分析师尤为重要。在进行研究时，研究人员通常会从总体的一个子集收集数据，而不是整个群体，这往往是由于时间、成本或可及性等限制。标准误差帮助量化使用该样本估计总体参数所带来的不确定性。较小的标准误差表明样本均值是对总体均值的更精确估计，而较大的标准误差则暗示变异性更大，估计的可靠性较低。要计算标准误差，通常将样本的标准差除以样本大小的平方根。这个公式突出了一个重要的原则：随着样本大小的增加，标准误差会减小。这种关系强调了在可能的情况下使用更大样本的重要性，因为它们往往会产生对总体参数更准确的估计。例如，想象一个研究者正在研究某城市成年男性的平均身高。如果研究者收集了30名男性的样本并计算出他们的平均身高，标准误差可以帮助确定这个样本均值与该城市所有成年男性的实际平均身高有多接近。如果标准误差相对较小，研究者可以更有信心地认为他们的样本均值很好地代表了总体均值。相反，较大的标准误差可能会导致研究者重新考虑其发现的有效性或样本大小的充分性。此外，标准误差在构建置信区间时也是至关重要的。置信区间提供了一个范围，在该范围内，预计真实的总体参数将在一定的置信水平下（通常为95%或99%）落入。这个区间的宽度受到标准误差的影响。较小的标准误差导致更窄的置信区间，表示更精确的估计，而较大的标准误差则导致更宽的区间，表明更多的不确定性。总之，标准误差是一个重要的统计工具，帮助研究人员评估他们的样本估计的精确性，并根据这些估计做出明智的决策。理解标准误差的含义使研究人员能够更好地解释他们的结果并有效地传达他们的发现。因此，掌握标准误差的概念对于任何从事统计分析或研究的人来说都是必不可少的，因为它直接影响到他们结论的可信性和可靠性。