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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.

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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
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
JAVA INTERFACE

  • Accessible from any java-equipped web server


Visualizing data
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
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
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
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
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
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
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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