This article describes an activity that illustrates contingency table (two-way table) analysis. Students use contingency tables to analyze the "unusual episode" (the sinking of the ocean liner Titanic)data (from Dawson 1995) and attempt to use their analysis to deduce the origin of the data. The activity is appropriate for use in an introductory college statistics course or in a high school AP statistics course. Key words: contingency table (two-way table), conditional distribution
This applet allows a person to add up to 50 points onto its green viewing screen. After each point is added by clicking on the screen with the mouse, a red line will appear. This red line represents a line passing through (Average x, Average y) with a slope that can be altered by clicking the Left or Right buttons. The slope of this line may also be changed by dragging the mouse either right or left. By clicking on Show Best Fit, a blue best fit line will be calculated by the computer.
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
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
This group activity illustrates the concepts of size and power of a test through simulation. Students simulate binomial data by repeatedly rolling a ten-sided die, and they use their simulated data to estimate the size of a binomial test. They carry out further simulations to estimate the power of the test. After pooling their data with that of other groups, they construct a power curve. A theoretical power curve is also constructed, and the students discuss why there are differences between the expected and estimated curves. Key words: Power, size, hypothesis testing, binomial distribution
A mathematical word processor that includes an easy-to-use computer algebra system (MuPad). Products include Scientific Wokplace, Scientific Word, Scientific Notebook, and MuPad Pro. Student version are available.
The activity is designed to help students develop a better intuitive understanding of what is meant by variability in statistics. Emphasis is placed on the standard deviation as a measure of variability. As they learn about the standard deviation, many students focus on the variability of bar heights in a histogram when asked to compare the variability of two distributions. For these students, variability refers to the "variation" in bar heights. Other students may focus only on the range of values, or the number of bars in a histogram, and conclude that two distributions are identical in variability even when it is clearly not the case. This activity can help students discover that the standard deviation is a measure of the density of values about the mean of a distribution and to become more aware of how clusters, gaps, and extreme values affect the standard deviation. Key words: Variability, standard deviation