/ latin /. v., learn thoroughly

Introductory Statistics

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