Resource Library

The activity is designed to help students develop a better intuitive understanding of what is meant by variability in statistics. Emphasis is placed on the standard deviation as a measure of variability. As they learn about the standard deviation, many students focus on the variability of bar heights in a histogram when asked to compare the variability of two distributions. For these students, variability refers to the "variation" in bar heights. Other students may focus only on the range of values, or the number of bars in a histogram, and conclude that two distributions are identical in variability even when it is clearly not the case. This activity can help students discover that the standard deviation is a measure of the density of values about the mean of a distribution and to become more aware of how clusters, gaps, and extreme values affect the standard deviation. Key words: Variability, standard deviation

G*Power is a tool to compute statistical power analyses for many different t tests, F tests, χ2 tests, ztests and some exact tests. G*Power can also be used to compute effect sizes and to display graphically the results of power analyses.

A song for use in helping students to recognize how a change in units affects the variance (since variance is expressed in squared units).  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).

This site provides general information to students considering majors in Statistics or Actuarial Science.

A song lyric by Dennis Pearl of The Ohio State University written as a parody of the 1960 tune "Hit the Road Jack" by Percy Mayfield; made popular by Ray Charles in his 1961 recording. What to say in class before song: There are times when the mode may be preferred to the mean - especially if the concept of interest is tied to understanding the most likely situation. You might remember that Ray Charles used to sing a song about this... In a class where Bayesian and Maximum Likelihood methodology has been introduced you might add the following after the first sentence "For example when you assume a uniform non-informative prior for a parameter, then the m.l.e. coincides with the mode of the posterior distribution - and the mean of the posterior distribution may not be a good estimate." Tip for Teaching: The song takes up a bit too much class time for delivering its message. Thus, for in-class use, it is recommended to play only the first verse or three. Musical accompaniment realization and male vocals are by Joshua Lintz, female vocals are by Mariana Sandoval from University of Texas at El Paso.

This applet shows the normal or Gaussian distribution. The distribution has two parameters, the mean and the standard deviation. Click the draw button after filling in new values for the mean and the standard deviation to obtain a new diagram of the normal distribution.

This page of Statistical Java describes 11 different probability distributions including the Binomial, Poisson, Negative Binomial, Geometric, T, Chi-squared, Gamma, Weibull, Log-Normal, Beta, and F. Each distribution has its own applet in which users can manipulate the parameters to see how the distribution changes. The parameters are described on the main page as well as situations that would use each distribution. The equations of the distributions are not given. To select between the different applets you can click on Statistical Theory, Probability Distributions and then the Main Page. At the bottom of this page you can make your applet selection. This page was formerly located at http://www.stat.vt.edu/~sundar/java/applets/

(Uses JAVA)  Some basic statistical analysis tools that allow the user to input their own data or use the pre-existing data and perform the desired test (e.g ANOVA, Descriptive, t-test, chi-square, correlation and regression).

This resource defines and explains standard deviation and the normal distribution.

Use the Sample Size Calculator to determine the sample size you need in order to get results that reflect the target population as precisely as needed. You can also find the level of precision you have in an existing sample. The site also describes terms you need to know to understand confidence intervals and what they mean.