Institute for Statistics and Econometrics Economics Department Humboldt University of Berlin Spandauer Straße Berlin Germany CONNECTED TEACHING OF STATISTICS

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

Accessible from any java-equipped web server JAVA INTERFACE

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 H 0 : p = p 0 vs. H 1 : p > p 0 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)

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 APPROXIMATING THE BINOMIAL BY THE NORMAL DISTRIBUTION

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