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Introductory Statistics, Third Edition

Chapter 1: Introduction to Statistics

1.1 Statistical Concepts

  • Populations and samples
  • Parameters and statistics
  • Inference and description
  • Why not go straight to the population?

1.2 Data

  • Data types
  • Data from more than one variable
  • Data sources

1.3 Collecting Data

  • Observational studies and experiments
  • When should we experiment, and when should we observe?
  • An advantage of experiments over observational studies
  • An advantage of observational studies over experiments

1.4 Sample Design

  • Bias
  • Making a sample random:
    • Sampling plans
    • Simple random sample
    • Systematic sample
    • Stratified sample
    • Cluster sample

1.5 Experimental Design

  • Applying treatments
  • Randomizing the groups
  • Blocking the groups
  • Placebos and control groups
  • Blinding the experiment

Chapter 2: Presenting Data

2.1 Presenting Categorical Data

  • Counting
  • Bar charts
  • Relative frequency bar charts
  • Pie charts

2.2 Presenting Numerical Data

  • Initial summary of the data
  • The histogram
  • Reading the histogram
  • Reading the histogram - the middle of the data
  • Reading the histogram - symmetry and skew
  • Manageable amounts of data: using a stem-and-leaf plot
  • Time plots

2.3 Presenting Relationships

  • Scatterplots
  • Studying scatterplots
  • Types of relationship
  • Strength of relationship
  • Relationships between one numerical variable and one categorical variable
  • Relationships between two categorical variables

Chapter 3: Measuring Data

3.1 Measures of Center

  • Mean
  • Median
  • Mode
  • Comparing the measures of center
  • Sensitive and insensitive measures
  • Outliers
  • Measures of center and pictures
  • Measuring the center of data: a conclusion

3.2 Measures of Variation

  • Range
  • The inter-quartile range
  • The five-number summary
  • Box plots
  • A closer look at variation
  • Developing a formula for variation
  • Variance and standard deviation
  • Using the mean and standard deviation

3.3 Measures of a Population

  • Population measures
  • Why population measures?

3.4 Measures of Relationship

  • Correlation
  • Interpreting correlation
  • Calculating a correlation
  • The nature of the relationship
  • Straight lines
  • Line of best fit
  • Population measures

Chapter 4: Probability

4.1 A Notion of Probability

  • Patterns in randomness
  • Relative frequency as probability
  • Probability rules: those that we have already and those that we’d like

4.2 Formalizing Probability

  • Events and outcomes
  • Special kinds of events
  • Properties of events
  • Extending the notion of probability
  • The rules of probability

4.3 Calculating Probabilities

  • A guiding example
  • Counting events
  • Examples of calculating probabilities
  • The general addition rule

4.4 Conditional Probability

  • Conditional probability
  • Decision trees
  • The general multiplication rule
  • Independence

4.5 Bayes’ Theorem

  • Relating conditional probabilities
  • Developing Bayes’ Theorem
  • Using Bayes’ Theorem
  • Full version of Bayes’ Theorem

Chapter 5: Probability Distributions

5.1 Discrete Random Variables

  • Random variables
  • Probability distributions
  • Presenting discrete random variables
  • Measures of a discrete random variable
  • Studying combinations of random variables
  • Rules for expected value and variance

5.2 The Binomial Distribution

  • Situations described by the binomial distribution
  • The sample space for the binomial distribution
  • The assumptions for the binomial distribution
  • Developing the binomial distribution
  • Getting successes in a particular order
  • The number of particular ways to get x successes
  • The binomial distribution formula
  • The expected value, variance and standard deviation
  • Different binomial distributions
  • Examples of using the binomial distribution

5.3 Continuous Random Variables

  • The probability of every outcome is zero
  • Getting a sense of probability for continuous variables
  • Probability density function - a concept
  • The probability density function
  • Measures of a continuous random variable

5.4 The Normal Distribution

  • The probability density function for normal distributions
  • Normal distribution probabilities
  • The standard normal distribution
  • The transformation formula
  • The distribution of values in the normal distribution
  • The normal distribution as an approximation to the binomial distribution

Chapter 6: Sampling Distributions

6.1 The Behavior of Samples

  • Populations of samples
  • Sampling distributions

6.2 Sampling Distribution of the Mean

  • A concrete example
  • Properties of the sampling distribution of the mean

6.3 Sampling Distribution of the Proportion

  • The population proportion
  • Sampling from the population
  • Describing the sampling distribution of the proportion

6.4 Sampling Distributions and Inference

  • Using one sample to make a conjecture about the population
  • What sort of population would that sample come from?
  • Inference
  • Estimation: a concept
  • Estimation: a method
  • The nature of estimates
  • Testing: a concept
  • Testing: a method

Chapter 7: Estimation

7.1 The Philosophy of Estimation

  • Estimating a population parameter
  • Imprecision and uncertainty
  • Confidence intervals
  • Estimation assertions

7.2 The Methodology of Estimation

  • Using sampling distributions to construct a confidence interval
  • So what is confidence?
  • Using the standard normal distribution
  • Different confidence intervals

7.3 Confidence Interval for the Mean, σ Known

  • Levels of significance and critical values
  • The confidence interval for the population mean
  • Constructing the confidence interval for the population mean
  • Determining a suitable sample size for a confidence interval

7.4 Confidence Interval for the Mean, σ Unknown

  • The t-distributions
  • Applying the t-distribution to statistical estimation
  • The confidence interval for the mean, σ unknown
  • Constructing the confidence interval for the population mean

7.5 Confidence Interval for the Proportion

  • The sampling distribution of the proportion
  • The z-score approach
  • The confidence interval for π

Chapter 8: Hypothesis Testing

8.1 The Philosophy of Hypothesis Testing

  • Making a hypothesis about a population parameter
  • The null hypothesis and alternative hypothesis
  • To reject or not reject

8.2 The Basic Methodology of Hypothesis Testing

  • Claims become hypotheses
  • Assuming the null hypothesis is true
  • A sample as evidence
  • Testing versus estimation

8.3 Completing the Methodology of Hypothesis Testing

  • The test statistic
  • Levels of significance, critical values, and the region of rejection
  • Step-by-step guide to conducting a hypothesis test

8.4 Considerations in Hypothesis Testing

  • Uncertainty in testing
  • Type I and Type II errors
  • How likely are the errors?
  • Using bigger samples
  • Power

8.5 Hypothesis Testing for Population Parameters

  • Testing the Mean
  • Is σ known or unknown?
  • Hypothesis testing the mean when σ is known
  • Hypothesis testing the mean when σ is unknown
  • Hypothesis testing the proportion

8.6 The P-value Approach to Hypothesis Testing

  • How likely is the sample?
  • Step-by-step guide to the P-value approach

Chapter 9: Comparing populations

9.1 Dealing with two population parameters

  • The distribution of X1 - X2
  • Comparing sampling distributions
  • Sampling distributions and inference
  • Independent samples

9.2 Inferences about two population proportions

  • The scenario for comparing two population proportions
  • Estimating the difference π1 - π2
  • Testing the difference π1 - π2

9.3 Inferences about two population means

  • The scenario for comparing two population means
  • Assuming σ1 and σ2 are known
  • Not assuming σ1 and σ2 are known
  • Assuming σ1 and σ2 are equal
  • A summary of the different methods

9.4 Inferences about mean differences

  • The mean difference
  • The scenario for studying the mean difference
  • Inferences about the mean difference

Chapter 10: Regression

10.1 Revisiting relationships

  • Association
  • Scatterplots
  • Correlation
  • Line of best fit

10.2 Regression fundamentals

  • The regression line
  • Explained and unexplained variation
  • Residuals
  • Prediction intervals

10.3 The simple linear regression model

  • The situation described by the model
  • The assumptions of the model
  • Inferences about β0 and β1
  • Predicting values and estimating means

10.4 Multiple regression

  • The effect of multiple explanatory variables
  • The multiple regression model
  • The sample regression equation
  • Interpreting the coefficients of a multiple regression model
  • Measuring explained variation: the adjusted coefficient of determination
  • Inferences in multiple regression

Appendix 10A: The F-distribution