Sampler Overview. Statistical Demonstration Software Copyright 2007 by Clifford H. Wagner

Transcription

1 Sampler Overview Statistical Demonstration Software Copyright 2007 by Clifford H. Wagner Introduction The philosophy behind Sampler is that students learn mathematics and statistics more thoroughly when concepts are presented in pictures as well as symbols. Sampler presents bold data and colorful graphics that are easily viewed on a personal monitor or on a large projection screen. At start up, the Sampler window has five pull down menus, 12 push buttons (6 currently active, 6 currently disabled), two sliders (one active, one disabled), a text panel, and a graphics panel (see Figure 1). Figure 1. The initial Sampler window

2 If the user pushes the Start/Resume button on the extreme left, Sampler will generate four samples, each of size 1000, from a standard normal population. The text panel will show the sample data and a sample summary for each sample as it is generated, and the graphics panel will show a histogram of each sample (see Figure 2; note that a different set of menus, buttons, and sliders is now active). An experienced user usually will change settings before pushing the Start/Resume button. Figure 2. The fourth sample from a standard normal population Special Features 1. Sampler simulates multiple random samples from a specified population and shows graphical illustrations of population distributions, sample data histograms, sample means histograms, and sample variances histograms. The graphical user interface is easy to use and all graphics and text are bold, legible, and easily viewed by a large audience. 2. All graphs use a horizontal z scale that shows position in terms of standard deviations from a mean. One can easily see the significance of Chebyshev s Theorem, and also see when the Central Limit Theorem does or does not apply, and when a chi-square distribution does or does not fit the sample variances distribution. One can also see that, with this scaling, there is only one graph for an exponential distribution. This is also true for logistic populations with a mean of Sampler allows the user to draw a distribution function. It can have as many modes or be as skewed as the user likes (see Figure 3).

3 Figure 3. The Hand-Drawn Population is a unique feature of Sampler. 4. Sampler provides geometric, negative binomial, and triangular distributions; these are not available in some prominent mathematics and statistics programs. 5. The Bernoulli family of distributions (Bernoulli, binomial, geometric, and negative binomial) have a CHANGE THETA slider for adjusting the success probability. The user can watch the distribution graph change shape as the slider is moved. 6. Sampler provides chi-square goodness of fit tests to see how well a normal or chisquare distribution fits a distribution of sample means or sample variances. Outline of the Menu System Population Chi-Square, Continuous Uniform, Erlang, Exponential, Gamma, Logistic, Lognormal, Normal, Student s t, Triangular Bernoulli, Binomial, Discrete Uniform, Geometric, Hypergeometric, Negative Binomial, Poisson Hand-Drawn...

4 Sample Sample Size, Number of Samples Display Show Sample Means, Show Sample Means, Show Sample Variances Show Goodness of Fit Table Change Data Precision > (with submenu), Change Data Font Size > (with submenu) Clear All Help Getting Started, Special Features Data Displays, Graph Displays Push Buttons, Sliders Continuous Populations, Discrete Populations, Hand-Drawn Populations, Sample Menu Choices, Display Menu Choices Program Requirements, FAQs About Sampler Push Buttons START/RESUME (a black triangle pointing to the right) starts the process of selecting random samples according to the current population and the current settings for sample size and number of samples. PAUSE (two vertical lines) pauses the sampling process. While paused, the user can adjust the sampling speed, and change most of the display menu choices. RESET (a counterclockwise arrow) stops the current sampling process and clears the sampling data and graph from the screen. CHANGE POPULATION PARAMETER(S) (a black triangle pointing to the left) allows the user to change the parameter(s) of the current population. CHANGE SAMPLE SIZE/NUMBER OF SAMPLES (n) allows the user to change the sample size and/or the number of samples. SHOW SAMPLE DATA (x) is equivalent to choosing SHOW SAMPLE DATA from the DISPLAY MENU.

5 SHOW SAMPLE MEANS button (x-bar) is equivalent to choosing SHOW SAMPLE MEANS from the DISPLAY MENU. SHOW SAMPLE VARIANCES button (s²) is equivalent to choosing SHOW SAMPLE VARIANCES from the DISPLAY MENU. SHOW REFERENCE DISTRIBUTION (a bell shaped curve) draws the current reference distribution in the graph display. SHOW GOODNESS OF FIT TABLE (chi-square) is equivalent to choosing SHOW GOODNESS OF FIT TABLE from the DISPLAY MENU. ZOOM IN (arrows pointing inward) shows more detail in the graph display. ZOOM OUT (arrows pointing outward) shows less detail in the graph display. Sliders SET SAMPLING SPEED The right slider controls the rate at which random samples are chosen. The default setting is FAST (+). PAN LEFT/RIGHT After samples have been chosen, the left slider allows the user to pan the graph LEFT or RIGHT. CHANGE THETA Before samples have been chosen, if the current population is a member of the Bernoulli family (Bernoulli, binomial, geometric, or negative binomial), the left slider allows the user to change the success probability THETA. The function graph changes accordingly as the user moves this slider.