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CONNECTED TEACHING OF STATISTICS

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.

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CONNECTED TEACHING OF STATISTICS

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  1. CONNECTED TEACHING OF STATISTICS Institute for Statistics and Econometrics Economics Department Humboldt University of Berlin Spandauer Straße 1 10178 Berlin Germany

  2. 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

  3. JAVA INTERFACE • Accessible from any java-equipped web server

  4. 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

  5. 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

  6. THE p-VALUE IN HYPOTHESIS TESTING • Illustrates the concept of the p-value • For a sample from the binomial probability distribution, testing H0: p = p0vs. 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)

  7. 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

  8. 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

  9. 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

  10. 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

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