Sampling
Distributions
This Java
applet lets you explore various aspects of sampling distributions. When
the applet begins, a histogram of a normal distribution is displayed at
the topic of the screen.
The distribution portrayed at the top of the screen is the population
from which samples are taken. The mean of the distribution is indicated
by a small blue line and the median is indicated by a small purple line.
Since the mean and median are the same, the two lines overlap. The red
line extends from the mean one standard deviation in each direction. Note
the correspondence between the colors used on the histogram and the statistics
displayed to the left of the histogram.
The second histogram displays the sample data. This histogram is initially
blank. The third and fourth histograms show the distribution of statistics
computed from the sample data. The number of samples (replications) that
the third and fourth histograms are based on is indicated by the label
"Reps=."
Basic operations
The simulation is set to initially sample five numbers from the population,
compute the mean of the five numbers, and plot the mean. Click the "Animated
sample" button and you will see the five numbers appear in the histogram.
The mean of the five numbers will be computed and the mean will be plotted
in the third histogram. Do this several times to see the distribution
of means begin to be formed. Once you see how this works, you can speed
things up by taking 5, 1,000, or 10,000 samples at a time.
Choosing a statistic
The following statistics can be computed from the samples by choosing
form the popup menu:
Mean
Standard deviation of the sample (N is used in the denominator)
Variance of the sample (N is used in the denominator)
Unbiased estimate of variance (N1 is used in denominator)
Mean absolute value of the deviation from the mean
Range
Selecting
a sample size
The size of each sample can be set to 2, 5, 10, 16, 20 or 25 from the
popup menu. Be sure not to confuse sample size with number of samples.
Comparison to a normal distribution
By clicking the "Fit normal" button you can see
a normal distribution superimposed over the simulated sampling distribution.
Changing the population distribution
You can change the population by clicking on the top histogram with the
mouse and dragging.
New
terms
The following
terms appear, and more detailed study of these topics is outside the scope
of this course.
skew 
a lack of symmetry in a distribution. A normal distribution has no
skew.
kurtosis
 a measure of the shape of a distribution. A normal distribution
has kurtosis of zero.
