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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/inferential-statistics
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课程名称：推论统计 课程概述： 推论统计主要关注基于样本中发现的关系对人群的推断。通过推论统计，我们能够判断数据中各组之间的差异是否足够显著，从而支持在整体人群中存在组间差异的假设。本课程将从显著性检验的基本原理开始，包括抽样和检验统计分布、p值、显著性水平、检验的功效及I型和II型错误。接下来，我们将学习适用于不同数据类型和研究设计的大量统计检验和技术，对于每一种统计检验，我们将讨论其工作原理、适用的数据和设计，以及如何解读结果。同时，您还将学习如何使用免费的软件执行这些检验。 课程大纲： 1. **比较两个组**： 本模块回顾统计假设检验，并讨论如何比较两个组在分类或定量因变量上的差异，采用适合独立组和相关组的不同检验方法。 2. **分类关联**： 本模块探讨分类变量之间的关联，主要讨论卡方检验，以判断两个分类变量在总体中是否存在关系。 3. **简单回归**： 本模块介绍如何使用简单（线性）回归分析描述两个定量变量之间的关联，帮助判断总体中是否存在实际关系。 4. **多元回归**： 本模块探讨如何使用多个预测变量来描述或预测定量结果变量，尤其适用于心理和社会变量之间的复杂关系。 5. **方差分析**： 本模块讨论方差分析技术，比较多个组在定量因变量上的差异，分析多个独立变量的影响。 6. **非参数检验**： 本模块介绍非参数检验方法，这些方法在分布形状假设不成立时依然有效，适用于有序分类变量的情况下。 7. **考试时间！**： 在最后一个模块，学生将进行复习并参加期末考试。提供了实践考试以帮助备考，期末考试与实践考试结构相同，但需要遵循诚实守信的原则。 通过本课程的学习，您将掌握推论统计的基本概念、方法及其在实际数据分析中的应用。
Part: 1
Title:Comparing two groups
Description:In this second module of week 1 we dive right in with a quick refresher on statistical hypothesis testing. Since we're assuming you just completed the course Basic Statistics, our treatment is a little more abstract and we go really fast! We provide the relevant Basic Statistics videos in case you need a gentler introduction. After the refresher we discuss methods to compare two groups on a categorical or quantitative dependent variable. We use different test for independent and dependent groups.
Part: 2
Title:Categorical association
Description:In this module we tackle categorical association. We'll mainly discuss the Chi-squared test that allows us to decide whether two categorical variables are related in the population. If two categorical variables are unrelated you would expect that categories of these variables don't 'go together'. You would expect the number of cases in each category of one variable to be proportionally similar at each level of the other variable. The Chi-squared test helps us to compare the actual number of cases for each combination of categories (the joint frequencies) to the expected number of cases if the variables are unrelated.
Part: 3
Title:Simple regression
Description:In this module we’ll see how to describe the association between two quantitative variables using simple (linear) regression analysis. Regression analysis allows us to model the relation between two quantitative variables and - based on our sample -decide whether a 'real' relation exists in the population. Regression analysis is more useful than just calculating a correlation coefficient, since it allows us assess how well our regression line fits the data, it helps us to identify outliers and to predict scores on the dependent variable for new cases.
Part: 4
Title:Multiple regression
Description:In this module we’ll see how we can use more than one predictor to describe or predict a quantitative outcome variable. In the social sciences relations between psychological and social variables are generally not very strong, since outcomes are generally influences by complex processes involving many variables. So it really helps to be able to describe an outcome variable with several predictors, not just to increase the fit of the model, but also to assess the individual contribution of each predictor, while controlling for the others.
Part: 5
Title:Analysis of variance
Description:In this module we'll discuss analysis of variance, a very popular technique that allows us to compare more than two groups on a quantitative dependent variable. The reason we call it analysis of variance is because we compare two estimates of the variance in the population. If the group means differ in the population then these variance estimates differ. Just like in multiple regression, factorial analysis of variance allows us to investigate the influence of several independent variables.
Part: 6
Title:Non-parametric tests
Description:In this module we'll discuss the last topic of this course: Non-parametric tests. Until now we've mostly considered tests that require assumptions about the shape of the distribution (z-tests, t-tests and F-tests). Sometimes those assumptions don't hold. Non-parametric tests require fewer of those assumptions. There are several non-parametric tests that correspond to the parametric z-, t- and F-tests. These tests also come in handy when the response variable is an ordered categorical variable as opposed to a quantitative variable. There are also non-parametric equivalents to the correlation coefficient and some tests that have no parametric-counterparts.
Part: 7
Title:Exam time!
Description:In this final module there's no new material to study. We advise you to take some extra time to review the material from the previous modules and to practice for the final exam. We've provided a practice exam that you can take as many times as you like. The final exam is structured exactly like the practice exam, so you know what to expect. Please note that you can only take the final exam twice every seven days, so make sure you are fully prepared. Please follow the honor code and do not communicate or confer with others while taking this exam or after. In the open questions of the exam (i.e. those that are not multiple choice) you should report your answers to 3 decimal places, and use 5 decimal places in your calculations. Good luck!
Inferential statistics are concerned with making inferences based on relations found in the sample, to relations in the population. Inferential statistics help us decide, for example, whether the differences between groups that we see in our data are strong enough to provide support for our hypothesis that group differences exist in general, in the entire population. We will start by considering the basic principles of significance testing: the sampling and test statistic distribution, p-value, significance level, power and type I and type II errors. Then we will consider a large number of statistical tests and techniques that help us make inferences for different types of data and different types of research designs. For each individual statistical test we will consider how it works, for what data and design it is appropriate and how results should be interpreted. You will also learn how to perform these tests using freely available software. For those who are already familiar with statistical testing: We will look at z-tests for 1 and 2 proportions, McNemar's test for dependent proportions, t-tests for 1 mean (paired differences) and 2 means, the Chi-square test for independence, Fisher’s exact test, simple regression (linear and exponential) and multiple regression (linear and logistic), one way and factorial analysis of variance, and non-parametric tests (Wilcoxon, Kruskal-Wallis, sign test, signed-rank test, runs test).
