The T Distribution
This applet allows the user to adjust the degrees of freedom of the T Distribution with a slider or manual input. The applet allows the user to fix the x and or y axes. The user immediately sees how this affects the shape of the graph.
The Weibull Distribution
This applet allows the user to adjust the alpha (rate) and the beta (scale) parameters of the Gamma distribution with a slider or manual input. The user can also indicate a model (density, hazard, or reliability).
Data Analysis
The applet in this section allows for simple data analysis of univariate data. Users can either generate normal or uniform data for k samples or copy and paste data from another source to a text box. A univariate analysis is performed for all k samples.
Correlation
The applets in this section allow you to see how different bivariate data look under different correlation structures. The Movie applet either creates data for a particular correlation or animates a multitude data sets ranging correlations from -1 to 1.
Control Charts
The applets in this section allow you to see how the common Xbar control chart is constructed with known variance. The Xbar chart is constructed by collecting a sample of size n at different times t.
The Central Limit Theorem
The applets in this section of Statistical Java allow you to see how the Central Limit Theorem works. The main page gives the characteristics of five non-normal distributions (Bernoulli, Poisson, Exponential, U-shaped, and Uniform).
Confidence Intervals
The applets in this section of Statistical Java allow you to see how levels of confidence are achieved through repeated sampling. The confidence intervals are related to the probability of successes in a Binomial experiment.
Statistical Java
This is a collection of applets regarding various topics in statistics. Topics include Central Limit Theorem, Probability Distributions, Hypothesis Testing, Power, Confidence Intervals, Correlation, Control Charts, Experimental Design, and Data Analysis.
Probability Distributions
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.
Star Library: What is the Shelf Life?
The Food and Drug Administration requires pharmaceutical companies to establish a shelf life for all new drug products through a stability analysis. This is done to ensure the quality of the drug taken by an individual is within established levels. The purpose of this out-of-class project or in-class example is to determine the shelf life of a new drug. This is done through using simple linear regression models and correctly interpreting confidence and prediction intervals. An Excel spreadsheet
Star Library: Random Rendezvous
This activity leads students to appreciate the usefulness of simulations for approximating probabilities. It also provides them with experience calculating probabilities based on geometric arguments and using the bivariate normal distribution. We have used it in courses in probability and mathematical statistics, as well as in an introductory statistics course at the post-calculus level.
Star Library: What is the Significance of a Kiss?
This article describes an interactive activity illustrating general properties of hypothesis testing and hypothesis tests for proportions. Students generate, collect, and analyze data. Through simulation, students explore hypothesis testing concepts. Concepts illustrated are: interpretation of p-values, type I error rate, type II error rate, power, and the relationship between type I and type II error rates and power. This activity is appropriate for use in an introductory college or high school
Star Library: Rectangularity
This article describes an interactive activity illustrating sampling distributions for means, properties of confidence intervals, properties of hypothesis testing, confidence intervals for means, and hypothesis tests for means. Students generate and analyze data and through simulation explore these concepts. The activity is completed in three parts. The three parts of the activity can be used in sequence or they can be used individually as “stand alone” activities. This allows the educator f
Star Library: An Unusual Episode
Dawson (1995) presented a data set giving a population at risk and fatalities for an “unusual episode” (the sinking of the ocean liner Titanic) and discussed the use of the data set in a first statistics course as an elementary exercise in statistical thinking, the goal being to deduce the origin of the data. Simonoff (1997) discussed the use of this data set in a second statistics course to illustrate logistic regression. Moore (2000) used an abbreviated form of the data set in a chapter ex
Star Library: Which Paper Towel is More Absorbent?
This group activity focuses on conducting an experiment to determine which of two brands of paper towels are more absorbent by measuring the amount of water absorbed. A two-sample t-test can be used to analyze the data, or simple graphics and descriptive statistics can be used as an exploratory analysis. Students are asked to think about design issues, and to write a short report stating their results and conclusions, along with an evaluation of the experimental design.
Star Library: Regression - Residuals - Why?
As teachers of statistics, we know that residual plots and other diagnostics are important to deciding whether or not linear regression is appropriate for a set of data. Despite talking with our students about this, many students might believe that if the correlation coefficient is strong enough, these diagnostic checks are not important. The data set included in this activity was created to lure students into a situation that looks on the surface to be appropriate for the use of linear regressi
Star Library: The Role of Probability in Discrimination Cases
An important objective in hiring is to ensure diversity in the workforce. The race or gender of individuals hired by an organization should reflect the race or gender of the applicant pool. If certain groups are under-represented or over-represented among the employees, then there may be a case for discrimination in hiring. On the other hand, there may be a number of random factors unrelated to discrimination, such as the timing of the interview or competition from other employers, that might ca
Star Library: Counting Eights: A First Activity in the Study and Interpretation of Probability
Students explore the definition and interpretations of the probability of an event by investigating the long run proportion of times a sum of 8 is obtained when two balanced dice are rolled repeatedly. Making use of hand calculations, computer simulations, and descriptive techniques, students encounter the laws of large numbers in a familiar setting. By working through the exercises, students will gain a deeper understanding of the qualitative and quantitative relationships between theoretical p
Star Library: Histogram Sorting
This activity provides students with 24 histograms representing distributions with differing shapes and characteristics. By sorting the histograms into piles that seem to go together, and by describing those piles, students develop awareness of the different versions of particular shapes (e.g., different types of skewed distributions, or different types of normal distributions), that not all histograms are easy to classify, that there is a difference between models (normal, uniform) and characte
Star Library: Breaking the Code - A Graphical Exploration Using Bar Charts
The activity begins with an explanation of the Caesar Shift for message encryption (Singh, 1999). The Caesar Shift is a translation of the alphabet; for example, a five-letter shift would code the letter a as f, b as g, … z as e. We describe a five-step process for decoding an encrypted message. First, groups of size 4 construct a frequency table of the letters in two lines of a coded message. Second, students construct a bar chart for a reference message of the frequency of letters in the Eng
