Sampling, Central Limit Theorem, & Standard Error
What you'll learn
- Define key statistical terms, including population, sample, parameter, and statistic, to build a foundation in statistical language and concepts.
- Identify and differentiate between various sampling methods, such as simple random sampling, stratified sampling, and cluster sampling.
- Illustrate the concept of sampling bias and explain strategies to minimize sampling error, enhancing the validity of sample-based conclusions.
- Describe the Central Limit Theorem and explain its significance in enabling normal approximation for sample means, regardless of the population distribution.
- Calculate standard error and analyze how sample size influences the precision of sample statistics.
- Evaluate the representativeness of samples in real-world applications and assess the implications of sample variability on inferential accuracy.
- Integrate sampling methods, the CLT, and standard error to form a coherent approach to statistical inference in various applied fields.
- Justify statistical conclusions drawn from sample data and reflect on the role of inferential statistics in research and decision-making.
Requirements
- A general comfort with numbers and quantitative reasoning is important, as the course involves interpreting data, calculating averages, and understanding proportions and percentages.
- Students should be able to read and interpret graphs, charts, and tables, as these are frequently used in statistical analysis to visualize data and communicate results.
- Although not a formal prerequisite, a willingness to think critically, ask questions, and explore data patterns will help students succeed and engage deeply with the course material.
Description
This course offers a foundational introduction to the principles of statistics, focusing on sampling techniques, the Central Limit Theorem (CLT), and the concept of standard error. Students will explore the process of selecting representative samples from larger populations, a crucial step in making valid statistical inferences. Various sampling methods, such as simple random sampling, stratified sampling, cluster sampling, and systematic sampling, will be covered in detail, enabling students to understand how to collect data that accurately represents a broader group. The importance of sampling in real-world applications will be emphasized, including considerations of bias and sampling error that can impact the validity of conclusions drawn from sample data.
A central focus of the course is the Central Limit Theorem, a key statistical concept that underpins much of inferential statistics. Through examples and hands-on exercises, students will learn how the CLT allows statisticians to approximate the distribution of sample means as normal, even when the population distribution is not normal. This property is foundational to many statistical methods, such as hypothesis testing and confidence interval estimation. Understanding the CLT enables students to appreciate the role of sample size, as larger samples yield distributions of sample means that are more consistently normal and provide a closer approximation of population parameters.
The course also introduces the concept of standard error, which measures the variability of a sample statistic, such as the sample mean, around the true population parameter. Students will examine how standard error reflects the precision of sample estimates and how it can be minimized through increased sample sizes. Applications of standard error in constructing confidence intervals and performing hypothesis tests will be covered, allowing students to quantify uncertainty and make informed inferences based on sample data.
Throughout the course, students will work on practical examples that demonstrate the applications of statistical concepts across various fields, such as social science research, economics, and quality control. These examples will illustrate how sampling, the CLT, and standard error are applied in real-world scenarios to draw conclusions about larger populations from sample data. By the end of the course, students will be equipped with essential statistical tools and techniques, laying the groundwork for more advanced studies in statistics and data analysis. This course is designed for students beginning their exploration of statistical methods, providing a robust introduction to the basics of data collection, analysis, and inference.
Who this course is for:
- Social Science Students interested in analyzing patterns and trends in human behavior, society, and economics.
- Business and Marketing Students looking to make data-driven decisions, understand market trends, and conduct surveys and research.
- Health and Life Sciences Students who need to interpret research findings, assess health data, and understand risk factors.
- Education Majors aiming to analyze student performance, interpret assessment data, and evaluate educational programs.
- Engineering and Computer Science Students (Introductory Level) who want to understand basic data analysis for applications in quality control, product testing, and research.
- Non-Majors and General Education Students who want to enhance their quantitative literacy, critical thinking, and ability to work with data in a range of contexts.
Instructor
- 4.4 Instructor Rating
- 58,145 Reviews
- 974,094 Students
- 163 Courses
Through working with students from many different schools, Mr. Steele has learned best practices for helping people understand accounting fast. Learning new skills and finding the best way to share knowledge with people who can benefit from it is a passion of his.
Mr. Steele has experience working as a practicing Certified Public Accountant (CPA), an accounting and business instructor, and curriculum developer. He has enjoyed putting together quality tools to improve learning and has been teaching, making instructional resources, and building curriculum since 2009. He has been a practicing CPA since 2005. Mr. Steele is a practicing CPA, has a Certified Post-Secondary Instructor (CPI) credential, a Master of Science in taxation from Golden Gate University, a Bachelor’s Degree in Business Economics with an emphasis in accounting from The University of California Santa Barbara, and a Global Management Accounting Designation (CGMA) from The American Institute of CPA (AICPA).
Mr. Steele has also authored five books that can be found on Amazon or in audiobook format on Audible. He has developed bestselling courses in accounting topics including financial accounting and QuickBooks accounting software.
In addition to working as an accountant, teaching, and developing courses Mr. Steele has helped create an accounting website at accountinginstruction, a YouTube channel called Accounting Instruction, Help, and How Too, and has developed supplemental resources including a Facebook Page, Twitter Page, and Podcasts that can be found on I-tunes, Stitcher, or Soundcloud. Mr. Steele's teaching philosophy is to make content applicable, understandable, and accessible.
Adult learners are looking for application when they learn new skills. In other words, learners want to be able to apply skills in the real world to help their lives. Mr. Steele’s formal accounting education, practical work experience, and substantial teaching experience allow him to create a curriculum that combines traditional accounting education with practical knowledge and application. He accomplishes the goals of making accounting useful and applicable by combining theory with real-world software like Excel and QuickBooks.
Many courses teach QuickBooks data entry or Excel functions but are not providing the real value learners want. Real value is a result of learning technical skills like applications, in conjunction with specific goals, like accounting goals, including being able to interpret the performance of a business.
Mr. Steele makes knowledge understandable by breaking down complex concepts into smaller units with specific objectives and using step by step learning processes to understand each unit. Many accounting textbooks cram way too much information into a course, making it impossible to understand any unit fully. By breaking the content down into digestible chunks, we can move forward much faster.
Mr. Steele also makes use of color association in both presentations and Excel worksheets, a learning tool often overlooked in the accounting field, but one that can vastly improve the speed and comprehension of learning accounting concepts.
The material is also made understandable through the application of concepts learned. Courses will typically demonstrate the accounting concepts and then provide an Excel worksheet or practice problems to work through the concepts covered. The practice problems will be accompanied by an instructional video to work through the problem in step by step format. Excel worksheets will be preformatted, usually including an answer tab that shows the completed problem, and a practice tab where learners can complete the problem along with a step by step presentation video.
Mr. Steele makes learning accounting accessible by making use of technology and partnering with teaching platforms that have a vision of spreading knowledge like Udemy.