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CONNECTED TEACHING OF STATISTICSPowerPoint Presentation

CONNECTED TEACHING OF STATISTICS

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### 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 = 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)

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

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