Transcript Teachware Quantlets

CONNECTED TEACHING OF
STATISTICS
Institute for Statistics and Econometrics
Economics Department
Humboldt University of Berlin
Spandauer Straße 1
10178 Berlin
Germany
COMPUTER-ASSISTED STATISTICS
TEACHING TOOL:
MOTIVATION
• For students, Learning basic concepts of statistics
through trial and error
• For the teacher, allowing the students to work at their
own pace
• Bringing current technology into classroom instruction
• Interactive learning
JAVA INTERFACE
• Accessible from any java-equipped web server
VISUALIZING DATA
• Illustrates a variety of visual display techniques for
one-dimensional data
• Student is presented a histogram and scatterplot of
the data, can choose a variety of additional
representations/transformations of the data
RANDOM SAMPLING
• Illustrates that “arbitrary human choice” is different
from proper random sampling
• Student designates his/her own distribution, then
sees a histogram of it, along with a hypothesis test
that the data is (uniformly) randomly distributed
THE p-VALUE IN HYPOTHESIS
TESTING
• Illustrates the concept of the p-value
• For a sample from the binomial probability
distribution, testing H0: p = p0 vs. H1: p > p0
• Why do we use P(X  x) rather than P(X = x)?
• Student can experiment with the data to see the
advantages of using P(X  x) over P(X = x)
APPROXIMATING THE BINOMIAL BY
THE NORMAL DISTRIBUTION
• Illustrates that the normal distribution provides a good
approximation to the binomial distribution for large n
• Student can experiment to see that under the right
transformations, the binomial distribution is more and
more similar to the standard normal distribution as n
approaches infinity
THE CENTRAL LIMIT THEOREM
• Illustrates the Central Limit Theorem
• The student defines a distribution, then sees a
histogram of the means from a simulation of 30
samples
• Can then increase or decrease the number of
samples to see that the histogram approximates the
normal distribution for a large number of samples
THE PEARSON CORRELATION
COEFFICIENT
• Illustrates how dependence is reflected in the
formulas for the estimated Pearson correlation
coefficient , and why it’s necessary to normalize the
data
• Student sets some specifications, then sees a
scatterplot of simulated data
• Presented with three formulas for estimating the
correlation coefficient 
• Transforms the data, sees the effects these have on
the three formulas -- why one formula is better than
the others
LINEAR REGRESSION
• Illustrates the concept of linear regression
• Student sees a scatterplot and a line on one graph,
and a graph of the residuals on another
• Tries to minimize the residual sum of squares by
modifying the parameters of the line