5. Teachware Quantlets

Nathaniel Derby
28 July 2004

Teachware quantlets comprise a basic set of interactive, illustrative examples in introductory statistics. For the student, they provide an opportunity to understand some important basic concepts in statistics through trial and error. For the teacher, they can aid instruction by allowing the students to work independently on exploratory examples at their own pace. Additionally, with a modicum of understanding of the XploRe programming language, the teacher can modify these examples to fit his/her own preferences.

Overall, these quantlets can play a key role in bringing current technology into classroom instruction -- something that is particularly crucial in beginning-level statistics classes. Statistics is often difficult for students since it requires the coordination of quantitative and graphical insights with mathematical ability. These quantlets provide a way in which this coordination can be made easier by allowing the student to develop his/her quantitative and graphical insight without getting bogged down in the mathematics (which can be learned later). That is, the underlying mathematics can be learned after the student has developed an intuitive understanding of certain concepts, which makes the learning process much easier. Moreover, these quantlets are designed for interactive learning, whereby the student actively participates in the learning process (i.e. try out different ideas and see what happens), rather than passively reads or hears about something outside of his/her control. This example of learning by doing has proven to be most effective in the learning process.

Furthermore, as statistical problems in general use mathematical formulas and data sets that grow in size and complexity, computer knowledge is essential to those who work with statistics. Learning with quantlets can give a student valuable comfort and skill with computers early on.

The teachware quantlets are part of the tware library. In order to access this, the user must call this library:

  library("tware")
After this library has been loaded, the user has a choice of the following examples:

10107 tw1d
illustrates a variety of visual display devices for one-dimensional data.
10110 twrandomsample
illustrates that gathering a random sample is different from ``just choosing some'' by allowing the user to pick his/her own sample, then rejecting or not rejecting the hypothesis that it is a random sample.
10113 twpvalue
illustrates the concept of a $ p$-value for hypothesis testing after having the user choose the parameters and an observed value for a binomial distribution.
10116 twnormalize
illustrates how the normal distribution provides a good approximation to the binomial for large $ n$ by allowing the user to transform binomial data and compare its distribution to that of the normal.
10119 twclt
illustrates the concept of the central limit theorem by showing the empirical distribution function of the averages of a large number of samples from a simulation using a user-specified underlying probability distribution.
10122 twpearson
illustrates how dependence is reflected in the formula for the estimated Pearson correlation coefficient, and why it is essential to normalize the data for the formula.
10125 twlinreg
illustrates the concept of linear regression by setting up a scatter plot and a line, and allowing the user to move the line to try to minimize the residual sum of squares.

The following pages will describe each example in detail.