VIDEO TAPES PROGRAMS: Against All Odds
PROGRAM 1: What is Statistics?
An overview of the nature and impact of statistics using historical anecdotes and short views of contemporary applications.
PROGRAM 2: Picturing Distributions
Presenting and interpreting the distribution of a single variable. Techniques taught include stemplots, frequency tables and histograms.
PROGRAM 3: Describing Distributions: Numerical Description of Distributions Numerical measures of specific aspects of a distribution: center (mean, median), spread (percentiles, the five-number summary, boxplots, and the standard deviation). Resistance and its lack.
PROGRAM 4: Normal Distributions
Topics: density curves as smoothed histograms: mean, median, percentiles for density curves; the normal distributions (general shape, locating the mean and standard deviation, the 68-95-99.7 rule).
PROGRAM 5: Normal Calculations
Standardization and calculation of normal relative frequencies from tables; assessing normality by normal quantile plots.
PROGRAM 6: Time Series
From the distribution of a single variable we move to an examination of change over time. Topics: statistical control, inspecting time series for trend, seasonal variation cycles; smoothing by averaging, either over many units per time or over time by running medians.
PROGRAM 7: Models For Growth
Mathematical models for the overall pattern of simple kinds of growth over time. Topics: linear growth, with review of the geometry of straight lines and anintroduction to the least squares idea; exponential growth, and straightening an exponential growth curve by logarithms; prediction and extrapolation.
PROGRAM 8: Describing Relationships
Topics: scatterplots and their variations, smoothing scatterplots of response vs. explanatory variable by median trace; linear relationships, least squares regression lines, and comment on outliers and influential observations.
PROGRAM 9: Correlation
Correlation and its properties; the relationship between correlation and regression.
PROGRAM 10: Multidimensional Data Analysis
The impact of computing technology on statistics, especially graphics for displaying multidimensional data. A case study in data analysis will employ techniques discussed in previous programs.
PROGRAM 11: The Question of Causation
Association between categorical variables displayed in a two-way table; Simpson's paradox; the varied relations among variables that can underlie an observed association; how evidence for causation is obtained.
PROGRAM 12: Experimental Design
Advantages of planned datacollection over anecdotal evidence or available data. The idea of an experiment. Basic principles of design: comparison, randomization, replication.
PROGRAM 13: Blocking and Sampling: Experiments and Samples
Further principles of design: two or more factors and blocking. Introduction to sample surveys: the danger of bias, random sampling.
PROGRAM 14: Samples and Surveys: Sampling and Sampling Distributions More elaborate sample designs: stratified and multistage designs. The practical difficulties of sampling human populations. The idea of a sampling distribution.
PROGRAM 15: What is Probability?
Probability as a model for long term relative frequencies or personal assessment of chance. Sample space, basic rules of assigning probability: , , addition rule for disjoint events.
PROGRAM 16: Random Variables
Independence and the multiplication rule for independent events. Discrete and continuous random variables. Mean and variance of a random variable.
PROGRAM 17: Binomial Distributions
The law of large numbers.Addition rules for means and variances of random variables. The binomial distributions for sample counts. Normal approximation to binomial.
PROGRAM 18: The Sample Mean and Control Charts
The sampling distribution of . The central limit theorem, control charts and statistical process control.
PROGRAM 19: Confidence Intervals
The reasoning behind confidence intervals, Z-intervals for the mean of a normal distribution. Behavior of confidence intervals.
PROGRAM 20: Significance Tests
The reasoning behind significance tests illustrated by the simple case of tests on a normal mean with known standard deviation. Null and alternative hypotheses and p-values, and cautions on the limited information provided by tests.
PROGRAM 21: Inference for One Mean
Inference aboutthe mean of a single distribution, with emphasis on paired samples as the most important practical use of these procedures. The t confidence interval and test.
PROGRAM 22: Comparing Two Means
The two-sample t confidence intervals for comparing means; brief mention of the sensitivity of the corresponding procedures for variances to nonnormality and their consequent impracticality.
PROGRAM 23: Inference for Proportions
Confidence intervals and tests for a single proportion and for comparing proportions based on paired and independent samples.
PROGRAM 24: Inference for Two-Way Tables
Chi-square test for independence/equal distributions in two-way tables.
PROGRAM 25: Inference for Relationships
Inference for simple linear regression, emphasizing slope and prediction.
PROGRAM 26: Case Study
A case study that illustrates the major aspects of statistical thinking: planning data collection, analysis by graphs and informal inference, more data collection in response to partial success.