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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 X
1
- X
2
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 π
1
- π
2
Testing the difference π
1
- π
2
9.3 Inferences about two population means
The scenario for comparing two population means
Assuming σ
1
and σ
2
are known
Not assuming σ
1
and σ
2
are known
Assuming σ
1
and σ
2
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 β
0
and β
1
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