Statistical Demonstrations
Section 2.4 - Measures of Center
- Plop It! - Shodor
- Click in the graph region and see how the mean, median, and mode are affected
by adding data.
Section 3.2 - Simulation
- Birthday
Simulator - Holmes
- What is the chance that in a group of people, 2 or more will share the
same birthday? Repeat the process several times for groups of n = 10, 20,
25, and 50.
- Monty
Hall Problem -
- A prize lies behind one of three doors and a pig behind the other
two. You pick one door and are shown a pig behind another door. You're then
asked whether you want to stick with
your
original
door
or switch to the other unopened door. What should you do? Run the simulation
several times by sticking with your original choice and several times with
switching and compare the results. You can also change the number of doors
and run the simulation several times with the switch or stay policy.
- Chutes & Ladders - Jones
- How many moves does an average game of Chutes & Ladders take? Perform this
simulation several times, recording the number of moves for each time. Then
find the average number of moves per game.
- Simulation Project - Jones
- This is a project that I wrote for a course I took in 2002. It explains
the whole process of simulation and has five different simulations.
Section 3.2 - Law of Large Numbers
- Binomial
Coin Experiment - Siegrist
- Set the update size to 10 to speed up the process and then click the fast
forward icon. Notice how the observed probabilities (red) approach the theoretical
probabilities (blue) as the sample size increases. You can also change the
number of coins or the probability of flipping a head. Almost any applet
at the Virtual Laboratory
in Probability and Statistics can be used to demonstrate
the same concept.
Section 5.5 - Sampling Distributions
- Sampling
Distribution - Lane
- Sample from a normal, uniform, skewed, or custom distribution and see how
the sample mean, median, variance, standard deviation, and range behave.
According to the central limit theorem, no matter what the original distribution
looks like, the sampling distribution of the means should become more normal
as the sample size increases.
Section 6.2 - Confidence Intervals
- Confidence
Interval Simulation - Lane
- Although this simulation is written for means, it does demonstrate what
the confidence level really means.
Section 9.2 - Correlation
- Guessing
Correlations - Marden
- You are given four different scatterplots and correlation coefficients
and asked to match them.
- Scatter,
Correlation, and Regression - Stark
- Turn on the regression line and then use the slider for r. Move it towards
1 and then towards -1. Notice how the closer the correlation coefficient
is to 1 or -1, the closer the data is to the regression line. The little
red square in the middle is the centroid, notice how the regression line
always passes through the centroid. Check the "use added points" box
and then add some points to the graph. Notice how points close to the line
don't influence the graph much, but those far away and on the edges have
a lot of leverage.
- Regression
by Eye - Lane (also in Chapter 8 - Regression)
- Try to guess the correlation (five choices are given). Click "Show
r" to find out if you're right. Then try to draw the line that best
fits the data by clicking and dragging the mouse to create the line. The
Mean Square Error (MSE) is shown and is a measure of how well the line fits
the data. The smaller the mean square error, the better your line. You can
ask it to show you the minimum MSE as a target and when you think you've
gotten as good as you can get, click the box and see what the actual regression
line is.
Section 9.3 - Regression
- Regression -
West & Ogden
- This applet allows you to see the influence of points with high leverage
on the regression equation. It is limited to four points and then one that
you add. The regression equation and value of r is given in black for the
original four points and then the new equation and correlation coefficient
are given in red for the five points once you click and add one. Click on
different spots on the graph and see how points close to the line don't make
much difference, but values away from the line, especially those towards
the maximum or minimum x values, exert a lot of leverage.
- Linear
Regression - Stanton
- Start clicking on the graph on the left and it will add a regression line
for you. The green lines drawn between the points and the lines are the residuals
and a graph of residuals vs x values are given on the graph to the right.
Try making several patterns and notice how the residuals look. If the data
has a nice linear pattern, then the residuals should look random. Now try
making an exponential or quadratic curve and notice the patterns that appear
in the residuals.
- Regression
by Eye - Lane (also under Chapter 7 - Correlation)
- Try to guess the correlation (five choices are given). Click "Show
r" to find out if you're right. Then try to draw the line that best
fits the data by clicking and dragging the mouse to create the line. The
Mean Square Error (MSE) is shown and is a measure of how well the line fits
the data. The smaller the mean square error, the better your line. You can
ask it to show you the minimum MSE as a target and when you think you've
gotten as good as you can get, click the box and see what the actual regression
line is.
Additional Resources and Demonstrations
- Statistical
Demonstration Java Applets - Suess
- Many of the applications I've singled out above come from this list.
- Virtual Laboratory in Probability
and Statistics - Siegrist
- This site at the University of Alabama,
Huntsville, has integrated explanations and applications to
many topics in statistics.
- Project InterActivate -
Shodor Educational Foundation
- This site has more than just statistical applications and simulations.
There are activities and tools for
the students and most contain explanations and questions to ask. Many of
these are geared for younger ages.
- MathTools -
Math Forum
- This site contains a database of applications, tools, lesson plans, discussions,
and stories for most areas of mathematics.