Significance Testing Principles

  • 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 article describes an interactive activity illustrating general properties of hypothesis testing and hypothesis tests for proportions. Students generate, collect, and analyze data. Through simulation, students explore hypothesis testing concepts. Concepts illustrated are: interpretation of p-values, type I error rate, type II error rate, power, and the relationship between type I and type II error rates and power. This activity is appropriate for use in an introductory college or high school statistics course. Key words: hypothesis test on a proportion, type I and II errors, power, p-values, simulation
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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 group activity focuses on conducting an experiment to determine which of two brands of paper towels are more absorbent by measuring the amount of water absorbed. A two-sample t-test can be used to analyze the data, or simple graphics and descriptive statistics can be used as an exploratory analysis. Students are asked to think about design issues, and to write a short report stating their results and conclusions, along with an evaluation of the experimental design. Key words: Two-sample t-test

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  • In this handout, students are asked to compare the ages of terminated employees to the ages of retained employees. Students will use the comparison to decide if the data supports the conclusion of age discrimination.
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  • The ICPSR provides access to a large repository of social science and political data. Data sets can be constructed and downloaded for use in most popular statistical packages.
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  • This applet simulates experiments using 2 x 2 contingency tables. You specify the population proportions and the sample size and examine the effects on the probability of rejecting the null hypothesis.
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  • This applet lets you explore the effect of violations of the assumptions of normality and homogeneity of variance on the type I error rate and power of t tests (and two-group analysis of variance).
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  • This case study addresses the question: "Will a smiling person accused of a crime be treated more leniently than one who is not smiling? If so, does the type of smile make a difference?" It concerns the following concepts: quantile/boxplots, contrasts among means, Dunnett's test, and Bonferroni correction.
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  • This case study assesses the question, "Do physicians discriminate against overweight patients?" This study indicates that, at least in one respect, they do. Concepts: t-test, means, boxplots
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