/ 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 - 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

### 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