- First refresh your memory about the meaning of the sampling distribution
of the mean by clicking the "animate" button. You will see five
scores sampled from the population at the top and float down to the sample
data graph. The mean of these five scores is shown in blue and drops down
to the graph below which is where the distribution of means is shown. Do
this a few more times and then click the 10,000 button several times to
see the distribution of means for a large number of samples. Various statistics
are shown to the left of the distribution. Compare the mean of the distribution
of means to the population mean of 16. It should be very close, but may
not match exactly because the simulated distribution of means is just an
approximation of the sampling distribution.
- Test to see if the mean the distribution of means for N=10 is equal
to the population mean (keep in mind, since this is an approximation, it
may not be exactly equal). If it is equal then the mean is an unbiased
estimate.
- Change the parent population to the "skewed distribution" and see if
the mean of the distribution of means is equal to the population mean of
8.08. If so, the mean is unbiased for this skewed distribution.
- Choose the median as the statistic. Try some simulations with the normal
distribution. If the sample median is an unbiased estimate of the population
median, then the mean of the distribution of the median
will equal the median of
the population.
- Try some simulations with the skewed distribution and check with the
median is a biased estimate.
- Choose the variance as the statistic. Estimate the distribution of the
variance and not its shape.
- Set the sample size to 5 and use the normal population. Estimate the
sampling distribution of the variance with the simulation. Note whether
the mean is equal to the population variance of 25.
- Choose the mean for one graph and the median for the other. Make the
sample size the same for both graphs and estimate the sampling distributions.
Compare the spreads of the distributions. The standard deviation of the
distributions are the standard errors of the mean and median respectively.
Which statistic has the smaller standard error? Try this with different
sample sizes. For sample size 25, note the ratio of the standard error
of the median to the standard error of the mean.
- Compare the standard errors for the mean and the median with the skewed
distribution. Try several sample sizes.
- Try different shapes of distributions and not the relative sizes of the
standard errors of the mean and median.