Multivariate Categorical Relationships

  • The Caesar Shift is a translation of the alphabet; for example, a five-letter shift would code the letter a as f, b as g, ... z as e. We describe a five-step process for decoding an encrypted message. First, groups of size 4 construct a frequency table of the letters in two lines of a coded message. Second, students construct a bar chart for a reference message of the frequency of letters in the English language. Third, students create a bar chart of the coded message. Fourth, students visually compare the bar chart of the reference message (step 2) to the bar chart of the coded message (step 3). Based on this comparison, students hypothesize a shift. Fifth, students apply the shift to the coded message. After decoding the message, students are asked a series of questions that assess their ability to see patterns. The questions are geared for higher levels of cognitive reasoning. Key words: bar charts, Caesar Shift, encryption, testing hypotheses

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  • This activity is an advanced version of the "Keep your eyes on the ball" activity by Bereska, et al. (1999). Students should gain experience with differentiating between independent and dependent variables, using linear regression to describe the relationship between these variables, and drawing inference about the parameters of the population regression line. Each group of students collects data on the rebound heights of a ball dropped multiple times from each of several different heights. By plotting the data, students quickly recognize the linear relationship. After obtaining the least squares estimate of the population regression line, students can set confidence intervals or test hypotheses on the parameters. Predictions of rebound length can be made for new values of the drop height as well. Data from different groups can be used to test for equality of the intercepts and slopes. By focusing on a particular drop height and multiple types of balls, one can also introduce the concept of analysis of variance. Key words: Linear regression, independent variable, dependent variables, analysis of variance

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  • This program visualizes the effects of outliers to regression lines. The user may pick up a point with the mouse and move it across the chart. The resulting regression line is automatically adjusted after each movement, showing the effect in an immediate and impressive way. The program Leverage allows one to experiment with the leverage effect. You can create a random sample of data noisy points on a line. Dragging one of the points away from the regression line immediately shows the effect, as the regression line is recalculated and moves according to the current data set. Not online: user has to download the program.

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  • This site offers links to a multitude of data tables in PDF format. Topics include national trends in injury hospitalizations, trends in health and aging, summary health statistics for the U.S. population, trends in health insurance and access to medical care for children under age 19 years, and many more.
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  • SalStat is an small application for the statistical analysis of scientific data (with a special concentration on psychology). It can already do 18 kinds of descriptive statistics, t tests (paired, unpaired and one sample), 3 kinds of correlations linear regression and point biserial tests, and single factor ANOVA (both within and between subjects). Data are entered on an easy-to-use datagrid like a spreadsheet, and all the analyses are driven by menus and dialog boxes. Output can be formatted to HTML.

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  • MacAnova is a free, noncommercial, interactive statistical analysis program for Windows 95/98/NT, Windows 3.1 with Win32s, Macintosh and Unix. MacAnova has many capabilities but its strengths are analysis of variance and related models, matrix algebra, time series analysis (time and frequency domain), and (to a lesser extent) uni-variate and multi-variate exploratory statistics.
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  • Lisp-Stat is an extensible statistical computing environment for data analysis, statistical instruction and research, with an emphasis on providing a framework for exploring the use of dynamic graphical methods. The object-oriented programming system is also used as the basis for statistical model representations, such as linear and nonlinear regression models and generalized linear models. Many aspects of the system design were motivated by the S language.
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  • ViSta constructs very-high-interaction, dynamic graphics that show you multiple views of your data simultaneously. The graphics are designed to augment your visual intuition so that you can better understand your data.

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  • This site gives the outlines and shows the lessons for psychology 340/341: Advanced Statistical Methods.
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  • A collection of applets addressing data analysis, sampling distribution simulations, and probability and inference. Some can be used individually, though others require context from the textbook.

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