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Annemarie Zand Scholten and Emiel van Loon

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.

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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).

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Syllabus

Before we get started...
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Comparing two groups
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.
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Categorical association
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.
Simple regression
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.
Multiple regression
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.
Analysis of variance
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.
Non-parametric tests
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.
Exam time!
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!

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Teaches the fundamentals of inferential statistics, which is standard in social science research
Covers a wide range of statistical tests and techniques for analyzing different types of data and research designs
Taught by experts in the field of statistics, Annemarie Zand Scholten and Emiel van Loon
Provides a practical approach to statistical analysis, with examples and exercises to help learners apply the concepts
Suited for learners with a basic understanding of statistics who want to enhance their skills in inferential analysis

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Reviews summary

Value in inferential statistics

Learners say that Inferential Statistics is a valuable, worthwhile course for gaining a deep understanding of statistics. While the course is regarded as well-structured, learners warn that it is challenging. The course is considered difficult for beginners and assumes the learner has prior experience with statistics. The course effectively teaches practical applications of statistics, demonstrating how to use R. Despite some errors and inconsistencies in the course material, students appreciate the engaging examples which make the material more understandable.
Challenging but worthwhile course, not for beginners.
"Challenging but worth it. I know substantially more than I did 7 weeks ago."
"This course is billed as a beginner's course, but the lecturers just glance over some really complicated question and are awful at explaining them."
Well-structured course with engaging examples.
"Really well structured, and the combination of the lecture, weekly quiz and datastudio R practices really helped me to thoroughly understand the topics."
"Fun examples make listening to the lectures fun and impressionable, which helps with remembering the explanations."
Practical applications of statistics taught effectively.
"This course managed to help me learn what I consider to be a very difficult topic and what I loved most about it was that it really took baby steps, showing how each calculation was made, each graph, and worked only based on concrete examples and not so much on hypothetical situations."
"Definitely the most challenging course in the Methods and Statistics in Social Sciences specialization, and the most important takeaways are: 1) a beginner's look into programming with R and most importantly 2) a guide in understanding which test to use under each specific circumstance."
Errors and inconsistencies in course material.
"I felt this course was educational and worth the effort.... BUT it was effort. The lecture progressively got more difficult to tease out the necessary nuggets of info for the exams.. Glad its over...Would not like to do it again"
"Personally, I thought it was a very discouraging course. There were many mistakes in the slides and transcripts that never got fixed after all these years."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Inferential Statistics with these activities:
Review Applied Statistics and Probability for Engineers
This book provides a solid foundation in the concepts of probability and statistics, focusing on applications in engineering and science. Reviewing this book will help familiarize you with the foundational concepts covered in this course.
Show steps
  • Read Chapters 1-5 to gain a foundational understanding of probability and statistical inference.
  • Complete the practice problems at the end of each chapter to test your comprehension.
  • Discuss the key concepts with a classmate or study group to reinforce your understanding.
Gather Resources on Statistical Hypothesis Testing
Having a curated collection of resources on statistical hypothesis testing will provide quick access to valuable information.
Show steps
  • Search for articles, videos, and online resources on statistical hypothesis testing.
  • Compile the resources in a central location, such as a shared document or online platform.
  • Categorize and organize the resources for easy retrieval.
Follow Tutorials on Statistical Software
Guided tutorials will provide step-by-step instructions on how to use statistical software, enhancing your proficiency in data analysis.
Browse courses on Statistical Software
Show steps
  • Identify statistical software tutorials aligned with the concepts covered in this course.
  • Follow the tutorials carefully, completing the exercises and examples.
  • Apply the acquired skills to your own data analysis projects.
Four other activities
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Show all seven activities
Explore Data Analysis Tools
Getting hands-on experience with data analysis tools will enhance your understanding of the techniques covered in this course.
Show steps
  • Choose a data analysis tool such as Python's Pandas library, R's dplyr package, or Microsoft Excel.
  • Follow tutorials or documentation to learn the basics of the tool.
  • Apply the tool to a small dataset to gain practical experience.
Join Study Groups or Discussion Forums
Engaging in discussions with peers will foster a deeper understanding of course concepts and provide diverse perspectives.
Show steps
  • Join online study groups or discussion forums related to inferential statistics.
  • Actively participate in discussions, ask questions, and share insights.
  • Collaborate with peers on practice problems and assignments.
Solve Practice Problems on Significance Testing
Regular practice with significance testing problems will improve your ability to apply these techniques to real-world scenarios.
Show steps
  • Find practice problems on significance testing from textbooks, online resources, or the course materials.
  • Attempt to solve the problems independently.
  • Check your solutions against provided answer keys or consult with the instructor for guidance.
  • Repeat the process with a variety of problems to reinforce your understanding.
Create a Comprehensive Study Guide
A comprehensive study guide will serve as a valuable resource for reviewing key concepts and preparing for assessments.
Show steps
  • Gather and organize lecture notes, readings, and practice problems.
  • Summarize the main concepts and formulas in a concise and logical manner.
  • Include practice questions and solved examples to reinforce your understanding.
  • Review the study guide regularly to enhance your retention and recall.

Career center

Learners who complete Inferential Statistics will develop knowledge and skills that may be useful to these careers:
Data Scientist
Data Scientists use statistical methods to extract insights from data. This course provides a strong foundation in inferential statistics, which is essential for making accurate inferences about data. The course covers a wide range of statistical tests and techniques that are used in data science, including hypothesis testing, regression analysis, and analysis of variance. This course can help you develop the skills needed to be successful as a Data Scientist.
Statistician
Statisticians collect, analyze, interpret, and present data. This course provides a comprehensive overview of inferential statistics, which is used to make inferences about a population based on a sample. The course covers a wide range of statistical tests and techniques, including hypothesis testing, regression analysis, and analysis of variance. This course can help you develop the skills needed to be successful as a Statistician.
Market Researcher
Market Researchers collect and analyze data to understand consumer behavior and market trends. This course provides a strong foundation in inferential statistics, which is essential for drawing accurate conclusions from data. The course covers a wide range of statistical tests and techniques that are used in market research, including hypothesis testing, regression analysis, and analysis of variance. This course can help you develop the skills needed to be successful as a Market Researcher.
Biostatistician
Biostatisticians apply statistical methods to solve problems in medicine and public health. This course provides a strong foundation in inferential statistics, which is essential for making accurate inferences about health data. The course covers a wide range of statistical tests and techniques that are used in biostatistics, including hypothesis testing, regression analysis, and analysis of variance. This course can help you develop the skills needed to be successful as a Biostatistician.
Epidemiologist
Epidemiologists investigate the causes and patterns of disease in populations. This course provides a strong foundation in inferential statistics, which is essential for understanding epidemiological data. The course covers a wide range of statistical tests and techniques that are used in epidemiology, including hypothesis testing, regression analysis, and analysis of variance. This course can help you develop the skills needed to be successful as an Epidemiologist.
Actuary
Actuaries use statistical methods to assess risk and uncertainty. This course provides a strong foundation in inferential statistics, which is essential for making accurate predictions about future events. The course covers a wide range of statistical tests and techniques that are used in actuarial science, including hypothesis testing, regression analysis, and analysis of variance. This course can help you develop the skills needed to be successful as an Actuary.
Data Analyst
Data Analysts use statistical methods to analyze data and identify trends. This course provides a strong foundation in inferential statistics, which is essential for drawing accurate conclusions from data. The course covers a wide range of statistical tests and techniques that are used in data analysis, including hypothesis testing, regression analysis, and analysis of variance. This course can help you develop the skills needed to be successful as a Data Analyst.
Software Engineer
Software Engineers design, develop, and maintain software applications. This course provides a foundation in statistical methods, which can be used to improve the quality and reliability of software. The course covers topics such as hypothesis testing, regression analysis, and analysis of variance. This course can help you develop the skills needed to be successful in software engineering.
Operations Research Analyst
Operations Research Analysts use statistical methods to solve problems in business and industry. This course provides a strong foundation in inferential statistics, which is essential for making accurate decisions about business operations. The course covers a wide range of statistical tests and techniques that are used in operations research, including hypothesis testing, regression analysis, and analysis of variance. This course can help you develop the skills needed to be successful in operations research.
Financial Analyst
Financial Analysts use statistical methods to analyze financial data and make investment recommendations. This course provides a foundation in statistical methods, which can be used to improve the accuracy of financial forecasts. The course covers topics such as hypothesis testing, regression analysis, and analysis of variance. This course can help you develop the skills needed to be successful as a financial analyst.
Business Analyst
Business Analysts use statistical methods to analyze business data and identify opportunities for improvement. This course provides a foundation in statistical methods, which can be used to improve the quality of business decisions. The course covers topics such as hypothesis testing, regression analysis, and analysis of variance. This course can help you develop the skills needed to be successful as a business analyst.
Marketing Analyst
Marketing Analysts use statistical methods to analyze marketing data and identify opportunities for growth. This course provides a foundation in statistical methods, which can be used to improve the effectiveness of marketing campaigns. The course covers topics such as hypothesis testing, regression analysis, and analysis of variance. This course can help you develop the skills needed to be successful as a marketing analyst.
Sales Analyst
Sales Analysts use statistical methods to analyze sales data and identify opportunities for improvement. This course provides a foundation in statistical methods, which can be used to improve the effectiveness of sales strategies. The course covers topics such as hypothesis testing, regression analysis, and analysis of variance. This course can help you develop the skills needed to be successful as a sales analyst.
Customer Relationship Manager
Customer Relationship Managers use statistical methods to analyze customer data and identify opportunities for improvement. This course provides a foundation in statistical methods, which can be used to improve the quality of customer service. The course covers topics such as hypothesis testing, regression analysis, and analysis of variance. This course can help you develop the skills needed to be successful as a customer relationship manager.
Teacher
Teachers use statistical methods to analyze student data and identify opportunities for improvement. This course provides a foundation in statistical methods, which can be used to improve the quality of instruction. The course covers topics such as hypothesis testing, regression analysis, and analysis of variance. This course may be useful for teachers who want to improve their understanding of statistical methods and their use in education.

Reading list

We've selected ten books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Inferential Statistics.
Provides a comprehensive overview of statistical methods, covering topics such as probability, inference, and regression. It valuable resource for students and researchers who want to learn more about the foundations of statistics.
Provides a comprehensive overview of statistical learning methods, including regression, classification, and clustering. It valuable resource for students and researchers who want to learn more about the theoretical foundations of statistical learning.
Provides a comprehensive overview of statistical inference, covering topics such as estimation, hypothesis testing, and confidence intervals. It valuable resource for students and researchers who want to learn more about the foundations of statistical inference.
Provides an introduction to statistical learning methods, including regression, classification, and clustering. It valuable resource for students and researchers who want to learn more about the practical application of statistical methods.
Provides an introduction to statistical methods commonly used in social research, including descriptive statistics, inferential statistics, and regression analysis. It valuable resource for students and researchers in social sciences who want to learn more about statistical methods.
Provides an introduction to statistical methods commonly used in business and economics, including descriptive statistics, inferential statistics, and regression analysis. It valuable resource for students and researchers in business and economics who want to learn more about statistical methods.
Provides a free and open-source introduction to statistical methods, including descriptive statistics, inferential statistics, and regression analysis. It valuable resource for students and researchers who want to learn more about statistical methods.
Provides an introduction to Bayesian data analysis, a powerful statistical method that allows researchers to incorporate prior knowledge into their analyses. It valuable resource for students and researchers who want to learn more about Bayesian methods.
Provides an introduction to statistical methods commonly used in psychology, including descriptive statistics, inferential statistics, and regression analysis. It valuable resource for students and researchers in psychology who want to learn more about statistical methods.
Provides an introduction to statistical methods commonly used in the biological and health sciences, including descriptive statistics, inferential statistics, and regression analysis. It valuable resource for students and researchers in the biological and health sciences who want to learn more about statistical methods.

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