Data Presentation

  • In these activities designed to introduce sampling distributions and the Central Limit Theorem, students generate several small samples and note patterns in the distributions of the means and proportions that they themselves calculate from these samples. Outside of class, students generate samples of dice rolls and coin spins and draw random samples from small populations for which data is given on each individual. Students report their sample means and proportions to the instructor who then compiles the results into a single data file for in-class exploration of sampling distributions and the Central Limit Theorem. Key words: Sampling distribution, sample mean, sample proportion, central limit theorem

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  • JChart2D is a minimalistic charting library published under the OSI approved GNU LESSER GENERAL PUBLIC LICENSE. It is designed for displaying multiple traces consisting of tracepoints. JChart2D is centered around a single configurable swing widget: the Chart2D. It is a JComponent that one can add to a java swing user interface. Therefore basic knowledge of java awt and swing and the information provided on this site is helpful. JChart2D is intended for engineering tasks and not for presentations. It's specialty is run time - dynamic precise display of data with a minimal configuration overhead.

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  • 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

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  • This article describes an interactive activity illustrating sampling distributions for means, properties of confidence intervals, properties of hypothesis testing, confidence intervals for means, and hypothesis tests for means. Students generate and analyze data and through simulation explore these concepts. The activity is completed in three parts. The three parts of the activity can be used in sequence or they can be used individually as "stand alone" activities. This allows the educator flexibility in utilizing the activity. Part I illustrates the sampling distribution of the sample mean. Part II illustrates confidence intervals for the population mean. Part III illustrates hypothesis tests for the population mean. This activity is appropriate for use in an introductory college or high school AP statistics course. Key words: sampling distribution of a sample mean, confidence interval for a mean, hypothesis test on a mean, simulation, random rectangles
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  • This activity provides students with 24 histograms representing distributions with differing shapes and characteristics. By sorting the histograms into piles that seem to go together, and by describing those piles, students develop awareness of the different versions of particular shapes (e.g., different types of skewed distributions, or different types of normal distributions), that not all histograms are easy to classify, that there is a difference between models (normal, uniform) and characteristics (skewness, symmetry, etc.). Key words: Histogram, shape, normal, uniform, skewed, symmetric, bimodal
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  • 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.

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  • 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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  • Residual plots and other diagnostics are important to deciding whether or not linear regression is appropriate for a set of data. Many students might believe that if the correlation coefficient is strong enough, these diagnostic checks are not important. The data set included in this activity was created to lure students into a situation that looks on the surface to be appropriate for the use of linear regression but is instead based (loosely) on a quadratic function. Key words: regression, residuals
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  • 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

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