student's distribution

简明释义

斯氏分布

英英释义

例句

1.When comparing two means, we apply the student's distribution to determine if the difference is significant.

在比较两个均值时，我们应用学生分布来判断差异是否显著。

2.The student's distribution is crucial for hypothesis testing in small sample scenarios.

在小样本情境下，学生分布对假设检验至关重要。

3.In statistics, we often use student's distribution to estimate the mean of a population when the sample size is small.

在统计学中，当样本量较小时，我们常用学生分布来估计总体的均值。

4.Many researchers prefer the student's distribution over the normal distribution for small sample sizes.

许多研究人员更喜欢在小样本量情况下使用学生分布而非正态分布。

5.The formula for calculating confidence intervals often involves the student's distribution.

计算置信区间的公式通常涉及到学生分布。

作文

In the field of statistics and probability theory, the concept of the student's distribution is fundamental for understanding various phenomena. The student's distribution (学生分布) is a type of probability distribution that is used particularly in hypothesis testing and in estimating population parameters when the sample size is small. It was first described by William Sealy Gosset under the pseudonym 'Student' in the early 20th century. The primary reason for using the student's distribution (学生分布) is that it accounts for the extra uncertainty that comes from estimating the population standard deviation from a small sample. When we have a small sample size, the sample mean can vary significantly, which makes the student's distribution (学生分布) a more accurate representation of the data compared to the normal distribution. This distribution has heavier tails, which means that it allows for more variability and extreme values, making it particularly useful in real-world situations where data may not follow a perfect normal distribution.One common application of the student's distribution (学生分布) is in the t-test, which is used to determine if there is a significant difference between the means of two groups. For instance, if a researcher wants to know whether a new teaching method is more effective than the traditional one, they might conduct a study with two groups of students: one group taught with the new method and another with the traditional approach. By applying a t-test, the researcher can use the student's distribution (学生分布) to analyze the results and draw conclusions about the effectiveness of the new method.Another important aspect of the student's distribution (学生分布) is its degrees of freedom, which are determined by the sample size. The degrees of freedom essentially reflect the number of independent pieces of information in the data. As the sample size increases, the student's distribution (学生分布) approaches the normal distribution, indicating that the estimates become more reliable as we gather more data. This property is crucial for researchers because it highlights the importance of collecting sufficient data to support their conclusions.Understanding the student's distribution (学生分布) is essential for students and professionals in fields such as psychology, medicine, and education, where research often relies on small sample sizes. Mastery of this concept enables individuals to make informed decisions based on statistical analysis and to communicate their findings effectively. In an era where data-driven decision-making is paramount, grasping the principles behind the student's distribution (学生分布) is invaluable.In conclusion, the student's distribution (学生分布) plays a critical role in statistical analysis, particularly when dealing with small samples. Its unique characteristics allow researchers to account for additional variability and uncertainty, leading to more accurate conclusions. As we continue to explore the complexities of data, the student's distribution (学生分布) remains a vital tool in the statistician's arsenal, ensuring that our interpretations of data remain robust and reliable.

在统计学和概率论领域，学生分布的概念对于理解各种现象是基础性的。学生分布是一种概率分布，特别用于假设检验和在样本量较小时估计总体参数。它最初由威廉·西利·戈塞特以“学生”的笔名在20世纪初描述。使用学生分布的主要原因是，它考虑了从小样本中估计总体标准差所带来的额外不确定性。当我们有一个小样本量时，样本均值可能会显著变化，这使得学生分布比正态分布更准确地表示数据。该分布具有更重的尾部，这意味着它允许更多的变异性和极端值，使其在数据可能不完美遵循正态分布的现实世界情境中特别有用。学生分布的一个常见应用是t检验，用于确定两组均值之间是否存在显著差异。例如，如果研究人员想知道一种新的教学方法是否比传统方法更有效，他们可能会进行一项研究，涉及两组学生：一组使用新方法，另一组使用传统方法。通过应用t检验，研究人员可以使用学生分布来分析结果并得出关于新方法有效性的结论。学生分布的另一个重要方面是其自由度，由样本大小决定。自由度基本上反映了数据中独立信息的数量。随着样本量的增加，学生分布趋近于正态分布，表明随着数据收集的增加，估计变得更加可靠。这一特性对研究人员至关重要，因为它突出了收集足够数据以支持结论的重要性。理解学生分布对于心理学、医学和教育等领域的学生和专业人士至关重要，因为这些研究通常依赖于小样本量。掌握这一概念使个人能够根据统计分析做出明智的决策，并有效地传达他们的发现。在数据驱动决策至关重要的时代，掌握学生分布背后的原则是无价的。总之，学生分布在统计分析中扮演着关键角色，特别是在处理小样本时。它的独特特性使研究人员能够考虑额外的变异性和不确定性，从而得出更准确的结论。随着我们继续探索数据的复杂性，学生分布仍然是统计学家工具箱中的重要工具，确保我们对数据的解释保持稳健和可靠。