PART I
Random experiments, events, and probabilities. Sample space. Operations between events, relations between events. Three axioms. Some basic theorems. Conditional probability. Independence. Counting rules. Random variables. Discrete Random Variables and the Probability mass function. Expected value and variance. Bernoulli random variable. Binomial random variable. Expected value of a sum of random variables. Variance of a sum of independent random variables. Expected value and variance of the Binomial random variable. The Poisson random variable. Random experiments with an uncountable set of events. Continuous random variables. Density function. The Normal random variable, its shape and its density function. Expected value and variance of continuous random variables. Expected value and variance of the Normal rv. Standardization. Expected value and variance of a standardized random variable. Distribution of a standardized random variable. Distribution of a linear combination of a Normal random variable. The standardized Normal. Computing normal probabilities using the standardized Normal and "statistical tables". A random variable describes a population. A statistic as a random variable. Sampling distribution of a statistic. Sampling distribution of the sample mean. Sampling distribution of the sample proportion. Point and set estimation. Confidence interval for the population mean. Confidence interval for the population proportion. Computing the quantiles of a Normal distribution. Sum of random variables. Central Limit Theorem. The continuous Uniform distribution. Hypothesis testing. Null and alternative hypothesis. Rejection region. Critical values. First and second type error. Test level. Test for the mean when the variance is known (two tails). Test for the mean when the variance is unknown (two tails). Test for a proportion (two tails). One-tail Tests. Fisher and the p-value approach to testing. Potential Hypothesis-Testing Pitfalls and Ethical Issues. Pooled-Variance t Test for the Difference Between Two Means. Comparing the Means of Two Related Populations. Paired t Test. F-test for the Ratio of Two Variances. Chi-Square Test of independence. Chi-Square Test for differences among two or more proportions.
PART II
Introduction to statistical analysis: What is statistics all about? Detecting Patterns and Relationships Improper uses of statistics. Phases of a statistical survey Survey design and preliminary planning, Pretesting, Final survey design and planning, Data collection, Data cleaning, data-file construction, analysis, and final report. Reading the News. The educated consumer of data. Four hypothetical examples of bad reports. Planning your study. Measures, Mistakes and Misunderstandings. "Simple" measures don't exist. Defining what is being measured. 3.5 Defining a common language. How to get a good sample, research strategies. Defining a common language. Simple random sampling and other sampling methods. Difficulties and disasters in sampling. Experiments and Observational Studies. Designing a good experiment. Difficulties and disasters in experiments. Designing a good observational sxperiment. Difficulties and disasters in observational studies. Getting the Big Picture Organizing and visualizing data. Summarizing and Displaying Measurement Data. Turning data into information. Picturing data: histograms, pie charts, barplot and scatter. Numerical descriptive measures. Summary statistics. Bell-shaped Curves and Other shapes. Populations, frequency curves and proportions. Normal Curves. Percentiles and standardized scores. z-scores and familiar intervals. Well-designed statistical pictures. Pictures of categorical data. Pictures of measurements variables. Pictures of trends across time. Relationships between Measurement Variables. Statistical relationships. Strength vs. statistical significance. Correlation. Relationships can be deceiving: spurious correlations. Correlation does not imply causation. Relationships between categorical variables. Displaying relationships: Contingency tables. Statistical Significance for 2x2 tables. Measuring the strength of a relationship. Steps for assessing statistical significance. The chi-square test. Probability and long-term expectations. Probability. Relative frequency interpretation. Personal-probability interpretation. Some simple probability rules. When intuition differs from relative frequency. Revisiting personal probability. Coincidences. The gambler's fallacy. Confusion of the inverse. Using expected values to make wise decisions. Understanding the Economic news. Cost of living: The Consumer Price Index. Uses of the Consumer Price Index. Criticisms of the Consumer Price Index. Seasonal adjustments: Reporting the Consumer Price Index. Economic Indicators. Understanding and Reporting Trends over Time: what is a time series. A Time Series Plot, components of a time series, irregular Cycles and Random Fluctuations.
