Against All Odds
With an emphasis on “doing” statistics, this series goes on location to help uncover statistical solutions to the puzzles of everyday life. Learn how data collection and manipulation — paired with intelligent judgement and common sense — can lead to more informed decision-making.
1. What Is Statistics?—Using historical anecdotes and contemporary applications, this introduction to the series explores the vital links between statistics and our everyday world.
2. Picturing Distributions—With this program, students will see how key characteristics in the distribution of a histogram — shape, center, and spread — help professionals make decisions in such diverse fields as meteorology, television programming, health care, and air traffic control.
3. Describing Distributions—This program examines the difference between mean and median, explains the use of quartiles to describe a distribution, and looks to the use of boxplots and the five-number summary for comparing and describing data.
4. Normal Distributions—Students will advance from histograms through smooth curves to normal curves, and finally to a single normal curve for standardized measurement, as this program shows ways to describe the shape of a distribution using progressively simpler methods.
5. Normal Calculations—With this program, students will discover how to convert the standard normal and use the standard deviation; how to use a table of areas to compute relative frequencies; how to find any percentile; and how a computer creates a normal quartile plot to determine whether a distribution is normal.
6. Time Series—Statistics can reveal patterns over time. Using the concept of seasonal variation, this program shows ways to present smooth data and recognize whether a particular pattern is meaningful.
7. Models for Growth—Topics of this program include linear growth, least squares, exponential growth, and straightening an exponential growth curve by logic. A study of growth problems in children serves to illustrate the use of the logarithm function to transform an exponential pattern into a line.
8. Describing Relationships—Segments describe how to use a scatterplot to display relationships between variables. Patterns in variables (positive, negative, and linear association) and the importance of outliers are discussed.
9. Correlation—With this program, students will learn to derive and interpret the correlation coefficient using the relationship between a baseball player’s salary and his home run statistics. Then they will discover how to use the square of the correlation coefficient to measure the strength and direction of a relationship between two variables.
10. Multidimensional Data Analysis—This program reviews the presentation of data analysis through an examination of computer graphics for statistical analysis at Bell Communications Research. Students will see how the computer can graph multivariate data and its various ways of presenting it.
11. The Question of Causation—Causation is only one of many possible explanations for an observed association. This program defines the concepts of common response and confounding, explains the use of two-way tables of percents to calculate marginal distribution, uses a segmented bar to show how to visually compare sets of conditional distributions, and presents a case of Simpson’s Paradox.
12. Experimental Design—Statistics can be used to evaluate anecdotal evidence. This program distinguishes between observational studies and experiments and reviews basic principles of design including comparison, randomization, and replication.
13. Blocking and Sampling—Students learn to draw sound conclusions about a population from a tiny sample. This program focuses on random sampling and the census as two ways to obtain reliable information about a population.
14. Samples and Surveys—This program shows how to improve the accuracy of a survey by using stratified random sampling and how to avoid sampling errors such as bias.
15. What Is Probability?—Students will learn the distinction between deterministic phenomena and random sampling. This program introduces the concepts of sample space, events, and outcomes, and demonstrates how to use them to create a probability model.
16. Random Variables—This program demonstrates how to determine the probability of any number of independent events, incorporating many of the same concepts used in previous programs.
17. Binomial Distributions—This program discusses binomial distribution and the criteria for it, and describes a simple way to calculate its mean and standard deviation.
18. The Sample Mean and Control Charts—The successes of casino owners and the manufacturing industry are used to demonstrate the use of the central limit theorem. One example shows how control charts allow us to effectively monitor random variation in business and industry.
19. Confidence Intervals—This program lays out the parts of the confidence interval and gives an example of how it is used to measure the accuracy of long-term mean blood pressure. An example from politics and population surveys shows how margin of error and confidence levels are interpreted.
20. Significance Tests—This program explains the basic reasoning behind tests of significance and the concept of null hypothesis. The program shows how a z-test is carried out when the hypothesis concerns the mean of a normal population with known standard deviation.
21. Inference for One Mean—In this program, students discover an improved technique for statistical problems that involve a population mean: the t statistic for use when σ is not known. Emphasis is on paired samples and the t confidence test and interval.
22. Comparing Two Means—How to recognize a two-sample problem and how to distinguish such problems from one- and paired-sample situations are the subject of this program.
23. Inference for Proportions—This program marks a transition in the series: from a focus on inference about the mean of a population to exploring inferences about a different kind of parameter, the proportion or percent of a population that has a certain characteristic.
24. Inference for Two-Way Tables—A two-way table of counts displays the relationship between two ways of classifying people or things. This program concerns inference about two-way tables, covering use of the chi-square test and null hypothesis in determining the relationship between two ways of classifying a case.
25. Inference for Relationships—With this program, students will understand inference for simple linear regression, emphasizing slope, and prediction. This unit presents the two most important kinds of inference: inference about the slope of the population line and prediction of the response for a given x.
26. Case Study—This program presents a detailed case study of statistics at work. Operating in a real-world setting, the program traces the practice of statistics — planning the data collection, collecting and picturing the data, drawing inferences from the data, and deciding how confident we can be about our conclusions.
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