standard error

简明释义

标准误差

英英释义

例句

1.A smaller standard error 标准误差 indicates more precise estimates.

较小的标准误差 标准误差表示更精确的估计。

2.In regression analysis, the standard error 标准误差 of the regression coefficients is crucial for hypothesis testing.

在回归分析中，回归系数的标准误差 标准误差对于假设检验至关重要。

3.The standard error 标准误差 can be used to construct confidence intervals for our data.

可以使用标准误差 标准误差为我们的数据构建置信区间。

4.When conducting a survey, it's important to calculate the standard error 标准误差 to assess the reliability of the results.

在进行调查时，计算标准误差 标准误差以评估结果的可靠性是很重要的。

5.The standard error 标准误差 of the sample mean helps us understand the variability of our estimate.

样本均值的标准误差 标准误差帮助我们理解估计值的变异性。

作文

In the field of statistics, understanding the concept of standard error is crucial for interpreting data accurately. The standard error refers to the measure of the amount of variability or dispersion of a sample statistic from the population parameter it estimates. Essentially, it indicates how much the sample mean is expected to fluctuate from the true population mean due to random sampling. This concept is particularly important when conducting surveys or experiments where one seeks to draw conclusions about a larger group based on a smaller subset of data.For example, imagine a researcher is studying the average height of adult males in a city. Instead of measuring the height of every adult male, which would be impractical and time-consuming, the researcher might select a random sample of 100 men. After collecting the data, the researcher calculates the average height of this sample. However, this sample mean may not perfectly reflect the true average height of all adult males in the city. To quantify this uncertainty, the researcher computes the standard error of the sample mean.The standard error is calculated by taking the standard deviation of the sample and dividing it by the square root of the sample size. A smaller standard error indicates that the sample mean is a more accurate estimate of the population mean, while a larger standard error suggests greater variability and less reliability in the sample mean. This is why researchers often strive to increase their sample sizes; larger samples tend to yield smaller standard errors, thereby providing more trustworthy estimates of population parameters.Moreover, the standard error plays a pivotal role in hypothesis testing and confidence intervals. When researchers want to determine if their sample mean significantly differs from a hypothesized population mean, they can use the standard error to calculate a test statistic. This statistic can then be compared against critical values from statistical distributions to make informed decisions regarding the null hypothesis.Confidence intervals, another key statistical tool, rely on the standard error to provide a range of values within which the true population parameter is likely to fall. For instance, if the sample mean height of the 100 men is 175 cm with a standard error of 2 cm, a 95% confidence interval might be constructed as 175 cm ± (1.96 * 2 cm), resulting in an interval from 171.08 cm to 178.92 cm. This interval suggests that the researcher can be 95% confident that the true average height of all adult males in the city lies within this range.In conclusion, the standard error is a fundamental concept in statistics that aids researchers in understanding the precision of their sample estimates. By quantifying the uncertainty associated with sample statistics, the standard error enables more accurate interpretations of data, which is essential for making informed decisions based on statistical analysis. Whether in academic research, market surveys, or scientific studies, grasping the significance of the standard error is vital for anyone seeking to engage with data effectively.

在统计学领域，理解标准误差的概念对于准确解读数据至关重要。标准误差是指样本统计量与其估计的人口参数之间的变异性或离散度的度量。基本上，它表明由于随机抽样，样本均值预计会与真实人口均值波动多少。这个概念在进行调查或实验时尤其重要，因为研究者希望基于较小的数据子集得出关于更大群体的结论。例如，假设一位研究者正在研究某城市成年男性的平均身高。研究者可能不会测量每位成年男性的身高，因为这既不切实际也费时，因此他可能选择随机抽取100名男性的样本。在收集数据后，研究者计算该样本的平均身高。然而，这个样本均值可能并不完美地反映所有成年男性的真实平均身高。为了量化这种不确定性，研究者计算了样本均值的标准误差。标准误差的计算方法是将样本的标准偏差除以样本大小的平方根。较小的标准误差表明样本均值是对人口均值的更准确估计，而较大的标准误差则暗示着更大的变异性和对样本均值的可靠性较低。这就是为什么研究者通常努力增加样本大小的原因；较大的样本往往会产生较小的标准误差，从而提供更可信的人口参数估计。此外，标准误差在假设检验和置信区间中发挥着关键作用。当研究者想要确定他们的样本均值是否与假设的人口均值显著不同时，他们可以使用标准误差来计算检验统计量。然后，可以将该统计量与统计分布的临界值进行比较，从而对原假设做出明智的决策。置信区间，另一个关键的统计工具，依赖于标准误差提供一个值的范围，其中真实的人口参数很可能落入其中。例如，如果100名男性的样本均值身高为175厘米，标准误差为2厘米，则可以构建95%的置信区间为175厘米±（1.96 * 2厘米），结果为171.08厘米到178.92厘米。这一范围表明，研究者可以95%确定所有成年男性的真实平均身高位于此范围内。总之，标准误差是统计学中的一个基本概念，帮助研究者理解其样本估计的精确度。通过量化与样本统计量相关的不确定性，标准误差使数据的更准确解读成为可能，这对于基于统计分析做出明智决策至关重要。无论是在学术研究、市场调查还是科学研究中，掌握标准误差的重要性对于任何希望有效处理数据的人来说都是至关重要的。