statistical assumption

简明释义

统计假定

英英释义

例句

1.The results of the ANOVA test can be misleading if the statistical assumption 统计假设 of homogeneity of variances is violated.

如果方差齐性这个 统计假设 统计假设 被违反，ANOVA测试的结果可能会产生误导。

2.The statistical assumption 统计假设 of linearity is crucial for accurate linear regression modeling.

线性假设 统计假设 统计假设 对于准确的线性回归建模至关重要。

3.In order to apply the t-test, you must ensure that the statistical assumption 统计假设 of independent samples holds true.

为了应用t检验，您必须确保独立样本的 统计假设 统计假设 成立。

4.Before conducting the regression analysis, we need to check the validity of the statistical assumption 统计假设 that the residuals are normally distributed.

在进行回归分析之前，我们需要检查残差正态分布的有效性，即 统计假设 统计假设。

5.Researchers must carefully evaluate the statistical assumption 统计假设 of normality before applying parametric tests.

研究人员在应用参数检验之前，必须仔细评估正态性 统计假设 统计假设。

作文

In the realm of statistics, the concept of statistical assumption plays a crucial role in the analysis and interpretation of data. A statistical assumption refers to a condition or premise that is accepted as true for the purposes of statistical modeling and hypothesis testing. These assumptions are foundational because they determine the validity of the results obtained from statistical methods. Without adhering to these assumptions, the conclusions drawn from data analysis may be misleading or incorrect.For instance, when conducting a linear regression analysis, one of the primary statistical assumptions is that the relationship between the independent and dependent variables is linear. If this assumption is violated, the model may not accurately predict outcomes, leading to erroneous interpretations. Additionally, another common statistical assumption is that the residuals, or the differences between observed and predicted values, are normally distributed. This is important because many inferential statistics rely on the normality of residuals to make valid inferences about the population from which the sample is drawn.Moreover, the independence of observations is also a key statistical assumption. In many statistical tests, it is assumed that the data points are independent of one another. If this assumption is violated, such as in cases where data points are correlated, the results may be biased, and the significance tests may yield unreliable results. Therefore, it is essential for researchers to check whether their data meets these statistical assumptions before proceeding with any analysis.Another important aspect to consider is the impact of violating statistical assumptions. When assumptions are not met, researchers may need to apply transformations to their data, use different statistical methods, or even collect new data altogether. For example, if the assumption of homoscedasticity, which states that the variance among the residuals should be constant across all levels of the independent variable, is violated, researchers might consider using weighted least squares regression instead of ordinary least squares regression.In practice, checking statistical assumptions can involve various diagnostic tests and visualizations. Tools such as Q-Q plots, scatter plots, and residual plots can help identify whether the assumptions hold true. By employing these methods, researchers can ensure that their analyses are robust and the conclusions drawn are credible.In conclusion, understanding and adhering to statistical assumptions is vital for anyone engaging in statistical analysis. These assumptions provide the framework within which valid conclusions can be drawn. Ignoring them can lead to flawed analyses and misinterpretations of data, which can have significant implications in fields ranging from social sciences to healthcare. Therefore, it is imperative for statisticians and researchers alike to familiarize themselves with these assumptions and rigorously test their data against them to uphold the integrity of their findings.

在统计学领域，统计假设的概念在数据分析和解释中发挥着至关重要的作用。统计假设是指在统计建模和假设检验中被接受为真实的条件或前提。这些假设是基础性的，因为它们决定了从统计方法获得的结果的有效性。如果不遵循这些假设，从数据分析中得出的结论可能会误导或不正确。例如，在进行线性回归分析时，主要的统计假设之一是自变量与因变量之间的关系是线性的。如果这个假设被违反，模型可能无法准确预测结果，从而导致错误的解释。此外，另一个常见的统计假设是残差，即观察值与预测值之间的差异，应该服从正态分布。这一点很重要，因为许多推断统计依赖于残差的正态性，以对样本所抽取的人群做出有效的推断。此外，观察值的独立性也是一个关键的统计假设。在许多统计检验中，假设数据点彼此独立。如果这个假设被违反，例如在数据点相关的情况下，结果可能会有偏差，显著性检验可能会产生不可靠的结果。因此，研究人员在进行任何分析之前，检查他们的数据是否符合这些统计假设是至关重要的。另一个需要考虑的重要方面是违反统计假设的影响。当假设未得到满足时，研究人员可能需要对数据进行变换，使用不同的统计方法，甚至重新收集数据。例如，如果违反了同方差性假设，即残差的方差应在所有自变量水平上保持恒定，研究人员可能会考虑使用加权最小二乘回归，而不是普通最小二乘回归。在实践中，检查统计假设可以涉及各种诊断测试和可视化工具。像Q-Q图、散点图和残差图这样的工具可以帮助识别假设是否成立。通过使用这些方法，研究人员可以确保他们的分析是稳健的，得出的结论是可信的。总之，理解并遵循统计假设对于任何参与统计分析的人来说都是至关重要的。这些假设提供了有效得出结论的框架。忽视它们可能导致分析缺陷和数据误解，这在社会科学到医疗保健等领域可能产生重大影响。因此，统计学家和研究人员都应该熟悉这些假设，并严格测试他们的数据，以维护研究结果的完整性。