This tutorial allows introductory statistics students see the relationship between the sample size and the variability of the sampling distribution of the mean. The tutorial combines a printable student handout with step by step use of a sampling distribution applet. The applet shows sample means of various sample sizes and from various populations in a graphical format, along with a graph of the (theoretical) sampling distribution. The tutorial also provides review material on standard scores and the Central Limit Theorem as well as solutions to the student handouts and follow up questions.
Type of Material:
A tutorial integrated with a simulation.
This material can be used as an out of class tutorial to help students develop a feeling for how sample size affects the variabliltiy of a sampling distribution. It could also be used as a laboratory assignment in a computer lab where students work through the tutorial.
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Identify Major Learning Goals:
The primary learning goal of the tutorial is to illustrate the connection between sample size and the variability of the sampling distribution.
Target Student Population:
This tutorial would work well for students in an introductory undergraduate or graduate course.
Prerequisite Knowledge or Skills:
In order to effectively use this tutorial, students must first have a knowledge of distributions, variability, calculating z-scores and using a table of the standard normal distribution to obtain probabilities, and basic statistical notation. It would also be helpful for students to have been introduced to the concept of the standard error of the mean.
Evaluation and Observation
A detailed tutorial that includes an applet that visually displays the sampling distribution of a sample mean.
The content is restricted to one aspect of the relationship between sample size and sampling distributions: variability. However, there are at least two other aspects that are very important: shape and center. These aspects will be helpful to understand in order to completely and correctly answer the questions in the tutorial that ask for comparisons of sampling distributions for different sample sizes.
The tutorial starts with samples of 100 and then works down to smaller sample sizes. This is the opposite order of what an instructor would typically use. This order might be OK, but something rather important is missing: the student is not encouraged to try samples of size n=1. Indeed, the applet does not support n=1.
Potential Effectiveness as a Teaching Tool
The directions are explicit and clear. A student should be able to use the applet quite easily. The step-by-step questions build on one another and are designed to help the student see the connection between sample size and variability in the sampling distribution. The applet allows for an overlay of the sample data, the sampling distribution, and the population distribution.
A primary concern is that there is no option available to overlay the sampling distributions for different sample sizes. Such an option would be powerful in helping students make the desired connection. As it currently is, students must remember what the previous sampling distribution looked like. Also, it would be good to include questions that ask for the explicit calculation of the standard deviation of the sampling distribution.
Another primary concern is that the applet is hard-wired to one very specific context or example. Teachers aren't able to use different initial values for the mean and standard deviation which limits this tutorial's effectiveness. Also,
students only have a few sample size options to select from. Finally, the tutorial and applet assume the population is normally distributed which is often not valid when collecting real data.
Ease of Use for Both Students and Faculty
The tutorial and applet have clear instructions and are easy to use.
The size of the text and the graphics of the applet can be quite small on many screens and may be difficult to read. This could be especially problematic if demonstrating the applet for students is on a classroom projector.