statistical independence

简明释义

统计独立

英英释义

例句

1.In a clinical trial, researchers must ensure that the treatment and control groups are chosen with statistical independence （统计独立性） to avoid bias.

在临床试验中，研究人员必须确保治疗组和对照组的选择具有统计独立性 （统计独立性）以避免偏差。

2.The analysis revealed that the events were not statistical independence （统计独立性）, indicating a correlation between them.

分析显示这些事件不是统计独立性 （统计独立性），表明它们之间存在相关性。

3.The two variables in the study showed statistical independence （统计独立性）, meaning changes in one did not affect the other.

研究中的两个变量表现出统计独立性 （统计独立性），这意味着一个的变化不会影响另一个。

4.To accurately model the data, we need to assume statistical independence （统计独立性） between the observations.

为了准确建模数据，我们需要假设观察值之间具有统计独立性 （统计独立性）。

5.When conducting surveys, it's important that the sample selection reflects statistical independence （统计独立性） to ensure valid results.

在进行调查时，样本选择必须反映出统计独立性 （统计独立性）以确保结果有效。

作文

In the realm of statistics, understanding the concept of statistical independence is crucial for interpreting data and making informed decisions. Statistical independence refers to a situation where the occurrence of one event does not influence the occurrence of another event. This concept is fundamental in probability theory and has wide-ranging implications in various fields such as economics, psychology, and medicine.To illustrate this concept, consider a simple example involving two dice rolls. When rolling two dice, the outcome of the first die does not affect the outcome of the second die. Therefore, we can say that the two events are statistically independent. In mathematical terms, if A and B are two independent events, then the probability of both A and B occurring together is equal to the product of their individual probabilities: P(A and B) = P(A) * P(B).The significance of statistical independence extends beyond mere calculations. In research, it helps researchers determine whether the relationships observed between variables are genuine or merely coincidental. For instance, if a study finds a correlation between ice cream sales and drowning incidents, one might be tempted to conclude that buying ice cream causes drowning. However, if we analyze the data further, we could find that both events are influenced by a third factor, such as warm weather, indicating that they are not truly independent.Moreover, statistical independence plays a vital role in hypothesis testing. Researchers often formulate null hypotheses that assume no relationship between variables. If the null hypothesis is true, then the variables are statistically independent, and any observed effect can be attributed to random chance. If the null hypothesis is rejected, it suggests that there is a significant relationship between the variables, prompting further investigation.In practical applications, understanding statistical independence is essential for data analysis and interpretation. For example, in machine learning, algorithms often rely on the assumption of independence among features when making predictions. If this assumption is violated, it could lead to inaccurate models and misguided conclusions. Therefore, data scientists must carefully assess the relationships between variables before applying certain statistical methods.In conclusion, the concept of statistical independence is a cornerstone of statistical analysis and research. It allows researchers to discern genuine relationships from spurious correlations and is integral to hypothesis testing and data interpretation. By grasping the principles of statistical independence, individuals can enhance their analytical skills and make more informed decisions based on data. As we continue to navigate an increasingly data-driven world, the importance of understanding statistical independence will only grow, reinforcing its relevance across various disciplines and applications.

在统计学领域，理解统计独立性的概念对于解读数据和做出明智决策至关重要。统计独立性是指一个事件的发生不影响另一个事件的发生。这一概念在概率论中是基础性的，并在经济学、心理学和医学等多个领域具有广泛的影响。为了说明这个概念，我们考虑一个简单的例子，涉及两个骰子的掷骰。当掷两个骰子时，第一个骰子的结果不会影响第二个骰子的结果。因此，我们可以说这两个事件是统计独立的。在数学上，如果A和B是两个独立事件，则同时发生A和B的概率等于它们各自概率的乘积：P(A和B) = P(A) * P(B)。统计独立性的意义超出了简单的计算。在研究中，它帮助研究人员确定观察到的变量之间的关系是否真实，还是仅仅偶然。例如，如果一项研究发现冰淇淋销售与溺水事件之间存在相关性，人们可能会倾向于得出购买冰淇淋导致溺水的结论。然而，如果我们进一步分析数据，可能会发现这两个事件都受到第三个因素的影响，比如温暖的天气，这表明它们并不真正独立。此外，统计独立性在假设检验中发挥着重要作用。研究人员通常会制定零假设，假设变量之间没有关系。如果零假设为真，则变量是统计独立的，任何观察到的效应都可以归因于随机机会。如果拒绝零假设，则表明变量之间存在显著关系，促使进一步调查。在实际应用中，理解统计独立性对数据分析和解读至关重要。例如，在机器学习中，算法通常依赖于特征之间独立的假设来进行预测。如果这一假设被违反，可能会导致不准确的模型和误导性的结论。因此，数据科学家必须在应用某些统计方法之前仔细评估变量之间的关系。总之，统计独立性的概念是统计分析和研究的基石。它使研究人员能够辨别真实的关系与虚假的相关性，并且在假设检验和数据解读中至关重要。通过掌握统计独立性的原则，个人可以增强其分析技能，并根据数据做出更明智的决策。随着我们继续在一个越来越以数据驱动的世界中航行，理解统计独立性的重要性只会增加，强化了其在各个学科和应用中的相关性。