Statistical Demonstrations
Measures of Center
- Plop
It! - Shodor
- Click in the graph region and see how the mean, median, and mode are
affected by adding data.
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.
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.
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.
Confidence Intervals
- Confidence
Interval Simulation - Lane
- Although this simulation is written for means, it does demonstrate what
the confidence level really means.
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 under 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.
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 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
- 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.