Institute for Statistics and Econometrics

Economics Department

Humboldt University of Berlin

Spandauer Straße 1

10178 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 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)

• 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