Chapter 8: Probability and Sampling Error
Student Resources
I use the 4 “P’s” framework to help you learn the material in this chapter: Prepare, Practice, Participate, and Perform. To increase the chances to succeed in this course, I strongly encourage you to complete all four “P’s” for each chapter.
1 Prepare
1.1 Chapter Overview
This chapter introduces the fundamental concepts of probability and sampling error—essential foundations for statistical inference. You’ll learn about sampling distributions, the Central Limit Theorem, and how confidence intervals allow us to make inferences about populations from sample data in movement science research.
1.2 Multimedia Resources
The following table provides access to video and slide resources for this chapter. Click the links to open them in an overlay for better viewing on all devices.
| Resource | Description | Link |
|---|---|---|
| Long Video Overview | A detailed video explaining probability, sampling distributions, the Central Limit Theorem, and confidence intervals in movement science research. | 🔗 Watch Video |
| Slide Overview PDF | PDF slides that serve as an overview of this chapter. Read these before the textbook to introduce the main concepts and vocabulary. | 🔗 Download PDF |
| Slide Deck HTML | Interactive HTML slides for class. During class, the instructor controls the presentation; after class, review at your own pace. | 🔗 Open Slides |
| Slide Deck PDF | PDF version of the slide deck for download and offline viewing. | 🔗 Download PDF |
1.3 Read the Chapter
Read (Furtado, 2026, p. Ch8) and (Weir & Vincent, 2021, p. Ch.7) to understand probability, sampling distributions, and the foundations of statistical inference.
To succeed in this course, you must read the textbook chapters assigned for each topic. This is the only way to learn the material in depth.
Once done, proceed to the next section to practice what you learned.
2 Practice
Practicing what you learned in the chapter is essential to mastering the material. Below are some resources to help you practice the material in this chapter.
2.1 Frequently Asked Questions
Probability is the likelihood that a particular event will occur, expressed as a number between 0 (impossible) and 1 (certain). In statistics, we use probability to quantify uncertainty and make predictions about populations based on sample data.
A sampling distribution is the distribution of a statistic (like the sample mean) across all possible samples of the same size from a population. It shows how sample statistics vary due to random sampling variability.
The Central Limit Theorem (CLT) states that the sampling distribution of the mean approaches a normal distribution as sample size increases, regardless of the population’s shape. This is fundamental to statistical inference because it allows us to use normal probability to make inferences about means.
The standard error (SE) is the standard deviation of a sampling distribution. It measures how much sample statistics (like means) vary from sample to sample. Larger samples have smaller standard errors, meaning more precise estimates.
Standard deviation (SD) measures variability among individual scores in a dataset. Standard error (SE) measures variability among sample statistics (like means) across different samples. SE = SD/√n, so it decreases as sample size increases.
Sampling error is the natural variability that occurs when we use a sample to estimate a population parameter. Even with random sampling, sample statistics won’t exactly equal population parameters—this difference is sampling error.
The CLT is crucial because it allows us to: - Use normal probability for inference even when populations aren’t normal - Calculate confidence intervals and conduct hypothesis tests - Predict the accuracy of sample estimates Most statistical inference relies on the CLT.
Standard error is affected by: - Sample size (n): Larger samples → smaller SE (more precise estimates) - Population variability (σ): More variable populations → larger SE The formula SE = σ/√n shows both relationships.
A confidence interval is a range of plausible values for a population parameter, calculated from sample data. A 95% confidence interval means that if we repeated our sampling many times, about 95% of the intervals would contain the true population parameter.
A 95% CI of [50, 60] cm means: “We are 95% confident that the true population mean falls between 50 and 60 cm.” It does NOT mean there’s a 95% probability the true mean is in this interval—the parameter is fixed, not random.
The sample mean is unbiased (centers on the true population mean) and efficient (has smaller variability than other estimators). The Central Limit Theorem guarantees its sampling distribution is normal for moderate to large samples.
With larger samples: - The sampling distribution becomes more normal (CLT) - The standard error decreases (SE = σ/√n) - Estimates become more precise (narrower confidence intervals) This is why larger samples are more powerful.
2.2 Test your Knowledge
Take this low-stakes quiz to test your knowledge of the material in this chapter. This quiz is for practice only and will help you identify areas where you may need additional review.
3 Participate
This section includes activities and discussions that will be completed during class time. Your active participation is essential for deepening your understanding of the material.
During class, we will:
- Calculate sampling distributions and standard errors
- Apply the Central Limit Theorem to movement science data
- Construct and interpret confidence intervals
- Discuss the relationship between probability and statistical inference
4 Perform
4.1 Apply Your Learning
Now that you’ve prepared, practiced, and participated, it’s time to demonstrate your mastery of the material through assignments and assessments.
I strongly encourage you to complete the previous “Ps” (Prepare, Practice, Participate) before attempting any assignments or assessments associated with this chapter.