Statistical Inference & Techniques

  • In this activity, students explore calculations with simple rates and proportions, and basic time series data, in the context of news coverage of an important statistical study. From 1973 to 1995, a total of 4578 US death penalty cases went through the full course of appeals, with the result that 68% of the sentences were overturned! Reports of the study in various newspapers and magazines fueled public debate about capital punishment.
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  • In this activity, students learn the true nature of the chi-square and F distributions in lecture notes (PowerPoint file) and an Excel simulation. This leads to a discussion of the properties of the two distributions. Once the sum of squares aspect is understood, it is only a short logical step to explain why a sample variance has a chi-square distribution and a ratio of two variances has an F-distribution. In a subsequent activity, instances of when the chi-square and F-distributions are related to the normal or t-distributions (e.g. Chi-square = z2, F = t2) will be illustrated. Finally, the activity will conclude with a brief overview of important applications of chi-square and F distributions, such as goodness-of-fit tests and analysis of variance.
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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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  • This activity allows students to explore the relationship between sample size and the variability of the sampling distribution of the mean. Students use a Java applet to specify the shape of the "parent" distribution and two sample sizes. The simulation then samples from the parent distribution to approximate the sampling distributions for the two sample sizes. Students can see both sampling distributions at the same time making them easy to compare. The activity also allows students to determine the probability of extreme sample means for the different sample sizes so that they can discover that small sample sizes are much more likely than large samples to produce extreme values. Keywords: sampling distribution, sample size, simulation
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  • This interactive lecture activity motivates the need for sampling. "Why sample, why not just take a census?" Under time pressure, students count the number of times the letter F appears in a paragraph. The activity demonstrates that a census, even when it is easy to take, may not give accurate information. Under the time pressure measurement errors are more frequently made in the census rather than in a small sample.
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  • This activity illustrates the convergence of long run relative frequency to the true probability. The psychic ability of a student from the class is studied using an applet. The student is asked to repeatedly guess the outcome of a virtual coin toss. The instructor enters the student's guesses and the applet plots the percentage of correct answers versus the number of attempts. With the applet, many guesses can be entered very quickly. If the student is truly a psychic, the percentage correct will converge to a value above 0.5.
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  • The purpose of this activity is to enhance students' understanding of various descriptive measures. In particular, by completing this hands-on activity students will experience a visual interpretation of a mean, median, outlier, and the concept of distance-to-mean.
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  • By means of a simple story and a worksheet with questions we guide the students from research question to arriving at a conclusion. The whole process is simply reasoning, no formulas. We use the reasoning already done by the student to introduce the standard vocabulary of testing statistical hypotheses (null & alternative hypotheses, p-value, type I and type II error, significance level). Students need to be familiar with binomial distribution tables. After the ducks story is finished, the class is asked to come up with their own research question, collect the data, do the hypotheses testing and answer their own research question. The teaching material is intended to be flexible depending of the time available. Instructors can choose to do just the interactive lecture type, interactive lecture + activity, or even add the optional material.
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  • This hands-on activity is appropriate for a lab or discussion section for an introductory statistics class, with 8 to 40 students. Each student performs a binomial experiment and computes a confidence interval for the true binomial probability. Teams of four students combine their results into one confidence interval, then the entire class combines results into one confidence interval. Results are displayed graphically on an overhead transparency, much like confidence intervals would be displayed in a meta-analysis. Results are discussed and generalized to larger issues about estimating binomial proportions/probabilities.
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  • In this hands-on activity, students count the number of chips in cookies in order to carry out an independent samples t-test to see if Chips AhoyŒ¬ cookies have a higher, lower, or different mean number of chips per cookie than a supermarket brand. First there is a class discussion that can include concepts about random samples, independence of samples, recently covered tests, comparing two parameters with null and alternative hypotheses, what it means to be a chip in a cookie, how to break up the cookies to count chips, and of course a class consensus on the hypotheses to be tested. Second the students count the number of chips in a one cookie from each brand, and report their observations to the instructor. Third, the instructor develops the independent sample t-test statistic. Fourth, the students carry out (individually or as a class) the hypothesis test, checking the assumptions on sample-size/population-shape.
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