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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/stanford-statistics
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课程名称：统计学导论 概述：斯坦福大学的《统计学导论》课程教授学习数据和传达洞察所需的统计思维概念。通过本课程，您将能够进行探索性数据分析，理解抽样的关键原则，并在多个背景下选择合适的显著性检验。您将获得基础技能，为进一步掌握更高级的统计思维和机器学习主题做好准备。 课程主题包括描述性统计、抽样和随机对照实验、概率、抽样分布与中心极限定理、回归、常见显著性检验、重抽样与多重比较。 课程大纲： 1. **导论和描述性统计**：本模块提供课程概述，并回顾用于可视化信息的主要工具。 2. **生成数据和抽样**：探讨抽样与实验设计的主要概念，以及评估实验有效性的方法。 3. **概率**：学习概率的定义及其基本规则，以解决简单和复杂的挑战，结合实际案例。 4. **正态近似与二项分布**：涵盖经验法则与正态近似，以及二项分布和随机变量的基础知识。 5. **抽样分布与中心极限定理**：学习大数法则与中心极限定理，以及如何区分不同类型的直方图。 6. **回归**：讲解回归分析的重要性及其解决各种统计问题的能力，包括推理与回归诊断。 7. **置信区间**：学习如何构建和解释标准情况下的置信区间。 8. **显著性检验**：探讨测试背后的逻辑，进行适当的统计测试，并讨论常见误解与陷阱。 9. **重抽样**：关注计算密集型统计推断的两种主要方法：蒙特卡洛方法与自助法，包括理论原理与应用实例。 10. **分类数据分析**：学习分类数据的重要统计分析方法，包括卡方拟合度检验、同质性检验和独立性检验。 11. **单因素方差分析（ANOVA）**：涵盖ANOVA的基本概念及其F检验的工作原理。 12. **多重比较**：探讨在大数据时代出现的重要问题，如数据探查和多重检验谬误，并探索数据可重复性和适用性挑战的应对策略。 通过这一课程，您将建立扎实的统计学基础，为日后进一步的学习和实践打下良好基础。
Name:Introduction and Descriptive Statistics for Exploring Data
Description:This module provides an overview of the course and a review of the main tools used in descriptive statistics to visualize information.
Name:Producing Data and Sampling
Description:In this module, you will look at the main concepts for sampling and designing experiments. You will learn about curious pitfalls and how to evaluate the effectiveness of such experiments.
Name:Probability
Description:In this module, you will learn about the definition of probability and the essential rules of probability that you will need for solving both simple and complex challenges. You will also learn about examples of how simple rules of probability are used to create solutions for real-life complex situations.
Name:Normal Approximation and Binomial Distribution
Description:This module covers the empirical rule and normal approximation for data, a technique that is used in many statistical procedures. You will also learn about the binomial distribution and the basics of random variables.
Name:Sampling Distributions and the Central Limit Theorem
Description:In this module, you will learn about the Law of Large Numbers and the Central Limit Theorem. You will also learn how to differentiate between the different types of histograms present in statistical analysis.
Name:Regression
Description:This module covers regression, arguably the most important statistical technique based on its versatility to solve different types of statistical problems. You will learn about inference, regression, and how to do regression diagnostics.
Name:Confidence Intervals
Description:In this module, you will learn how to construct and interpret confidence intervals in standard situations.
Name:Tests of Significance
Description:In this module, you will look at the logic behind testing and learn how to perform the appropriate statistical tests for different samples and situations. You will also learn about common misunderstandings and pitfalls in testing.
Name:Resampling
Description:This module focuses on the two main methods used in computer-intensive statistical inference: The Monte Carlo method, and the Bootstrap method. You will learn about the theoretic principles behind these methods and how they are applied in different contexts, such as regression and constructing confidence intervals.
Name:Analysis of Categorical Data
Description:This module focuses on the three important statistical analysis for categorical data: Chi-Square Goodness of Fit test, Chi-Square test of Homogeneity, and Chi-Square test of Independence.
Name:One-Way Analysis of Variance (ANOVA)
Description:This module covers the basics of ANOVA and how F-tests work on one-way ANOVA examples.
Name:Multiple Comparisons
Description:In this module, you will learn about very important issues that have surfaced in the era of big data: data snooping and the multiple testing fallacy. You will also explore the reasons behind challenges in data reproducibility and applicability, and how to prevent such issues in your own work.
Stanford's "Introduction to Statistics" teaches you statistical thinking concepts that are essential for learning from data and communicating insights. By the end of the course, you will be able to perform exploratory data analysis, understand key principles of sampling, and select appropriate tests of significance for multiple contexts. You will gain the foundational skills that prepare you to pursue more advanced topics in statistical thinking and machine learning. Topics include Descriptive Statistics, Sampling and Randomized Controlled Experiments, Probability, Sampling Distributions and the Central Limit Theorem, Regression, Common Tests of Significance, Resampling, Multiple Comparisons.
