# Sampling Distributions

• ### Dancing Sampling Error

A video using dance to teach about concepts involved with sampling error and the standard error of a statistic.  This 2013 video is from the “Dancing Statistics” series developed by Lucy Irving from Middlesex University (UK) funded by a BPS Public Engagement grant and additional funding from IdeasTap.  Full credits are within the video.   The Dancing Statistics project is described at https://www.frontiersin.org/articles/10.3389/fpsyg.2015.00050/full

The video also comes with teaching notes for viewing by instructors who are logged into CAUSEweb.org.

• ### Penn State STAT 800: Introduction to Applied Statistics

This is a graduate level introduction to statistics including topics such as probabilty/sampling distributions, confidence intervals, hypothesis testing, ANOVA, and regression.  Perfect for students and teachers wanting to learn/acquire materials for this topic.

• ### Song: A Radical Approach

A song for use in helping students to understand that standard error changes with the square root of the sample size.  Music & Lyrics by Tom Toce, © 2015 Retrograde Music.  This song is part of an NSF-funded library of interactive songs that involved students creating responses to prompts that are then included in the lyrics (see www.causeweb.org/smiles for the interactive version of the song, a short reading covering the topic, and an assessment item).

• ### Song: Take Me Out to the Brew'ry

A song to help with discussion of the history of William Sealy Gosset's (a.k.a. Student) result about the t-distribution for modeling standardized means.  The lyrics were written by Lawrence Mark Lesser from The University of Texas at El Paso in 2017 and may be sung to the tune of Jack Norworth and Albert Von Tizle's 1908  standard "Take Me Out to the Ballgame."

• ### Nature of the chi-square distribution

In this activity, students learn the true nature of the chi-square and F distributions in lecture notes (PowerPoint file) and an Excel simulation. This leads to a discussion of the properties of the two distributions. Once the sum of squares aspect is understood, it is only a short logical step to explain why a sample variance has a chi-square distribution and a ratio of two variances has an F-distribution. In a subsequent activity, instances of when the chi-square and F-distributions are related to the normal or t-distributions (e.g. Chi-square = z2, F = t2) will be illustrated. Finally, the activity will conclude with a brief overview of important applications of chi-square and F distributions, such as goodness-of-fit tests and analysis of variance.
• ### Simulating the Effect of Sample Size on the Sampling Distribution of the Mean

This activity allows students to explore the relationship between sample size and the variability of the sampling distribution of the mean. Students use a Java applet to specify the shape of the "parent" distribution and two sample sizes. The simulation then samples from the parent distribution to approximate the sampling distributions for the two sample sizes. Students can see both sampling distributions at the same time making them easy to compare. The activity also allows students to determine the probability of extreme sample means for the different sample sizes so that they can discover that small sample sizes are much more likely than large samples to produce extreme values. Keywords: sampling distribution, sample size, simulation
• ### Song: Stat 51: I Will Survive

Song about the use of the 5-number summary to describe skewed data as an alternative to the mean and standard deviation. May be sung to the tune of the 1979 song "I Will Survive" by Gloria Gaynor. Lyrics written by Sheila O'Leary Weaver. The song took first place in the song category in the 2007 A-Mu-Sing competition. Musical accompaniment realization are by Joshua Lintz and vocals are by Mariana Sandoval from University of Texas at El Paso.

• ### Data Collection: State Health Facts

This site funded by the Kaiser Family Foundation provides information on health care and demographics for the 50 U.S. states. Users can use interactive maps or search by particular characteristics for each state. Tables can be created and copied and there is also direct data download (in Excel format) from this site. The site includes data on median income, gender, ethnicity, medical and drug spending, HIV/AIDS rates, and over 500 other variables at the state level
• ### **Inference for Means Activity

This activity enables students to learn about confidence intervals and hypothesis tests for a population mean. It focuses on the t-distribution, the assumptions for using it, and graphical displays. The activity also focuses on how to interpretations a confidence interval, a p-value, and a hypothesis test.

• ### Cartoon: Thoughtful Survey

A cartoon to teach about ambiguous reporting of survey information. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites.