Introduction to Statistics - An Intuitive Guide for Analyzing Data and Unlocking Discoveries

Prepare for an Adventure!
The Importance of Statistics
Draw Valid Conclusions
Avoid Common Pitfalls
Make an Impact in Your Field
Protect Yourself with Statistics
Statistics versus Anecdotal Evidence
A scientific study of the weight loss supplement
How Statistics Beats Anecdotal Evidence
Organization of this Book
Data Types, Graphs, and Finding Relationships
Quantitative versus Qualitative Data
Continuous and Discrete Data
Continuous data
Histograms: Distributions
Scatterplots: Trends
Time Series Plots
Discrete data
Bar Charts
Qualitative Data: Categorical, Binary, and Ordinal
Categorical data
Binary data
Ordinal data
Next Steps
Histograms in More Detail
Central Tendency
Variability
Skewed Distributions
Identifying Outliers
Multimodal Distributions
Identifying Subpopulations
Comparing Distributions between Groups
Histograms and Sample Size
Boxplots vs. Individual Value Plots
Individual Value Plots
Boxplots
Using Boxplots to Assess Distributions
Example of Using a Boxplot to Compare Groups
Two -Way Contingency Tables
Cautions About Graphing
Manipulating Graphs
Drawing Inferences About a Population Requires Additional Testing
Graphing and Philosophy
Automatic versus Manual Graph Scales
When You Should Change Graph Scales
Don’t Limit Yourself by Always Using Automatic Scaling
Summary and Next Steps
Summary Statistics and Relative Standing
Percentiles
Special Percentiles
Calculating Percentiles Using Values in a Dataset
Definition 1: Greater Than
Definition 2: Greater Than or Equal To
Definition 3: Using an Interpolation Approach
Measures of Central Tendency
Mean
Median
Comparing the mean and median
Mode
Finding the mode for continuous data
Which One to Use?
Measures of Variability
Why Understanding Variability is Important
Example of Different Amounts of Variability
Range
The Interquartile Range (IQR) . . . and other Percentiles
Using other percentiles
Variance
Population variance
Sample variance
Example of calculating the sample variance
Standard Deviation
Which One to Use?
Comparing Summary Statistics between Groups
Correlation
Interpreting Correlation Coefficients
Examples of Positive and Negative Correlation Coefficients
Graphs for Different Correlation Coefficients
Discussion about the Scatterplots
Interpreting our Height and Weight Correlation Example
Pearson’s Measures Linear Relationship
Correlation Does Not Imply Causation
How Strong of a Correlation is Considered Good?
Summary and Next Steps
Probability Distributions
Discrete Probability Distributions
Types of Discrete Distribution
Binomial and Other Distributions for Binary Data
Assumptions for Using Probability Distributions for Binary Data
Binomial Distribution
Geometric Distribution
Negative Binomial Distribution
Hypergeometric Distribution
Modelling Flu Outcomes Over Decades
How long until my first case of the flu on average?
How often will I catch the flu?
Continuous Probability Distributions
How to Find Probabilities for Continuous Data
Characteristics of Continuous Probability Distributions
Example of Using the Normal Probability Distribution
Example of Using the Lognormal Probability Distribution
Normal Distribution in Depth
Parameters of the Normal Distribution
Mean
Standard deviation
Population parameters versus sample estimates
Properties of the Normal Distribution
The Empirical Rule
Standard Normal Distribution and Standard Scores
Calculating Z-scores
Using a Table of Z-scores
Why the Normal Distribution is Important
Summary and Next Steps
Descriptive and Inferential Statistics
Descriptive Statistics
Example of Descriptive Statistics
Inferential Statistics
Pros and Cons of Working with Samples
Populations
Subpopulations
Population Parameters versus Sample Statistics
Tools for Inferential Statistics
Hypothesis tests
Confidence intervals (CIs)
Regression analysis
Properties of Good Estimates
Sample Size and Margins of Error
Sampling Distributions of the Mean
Confidence Intervals and Precision
Example: Sample Statistics and CIs for 10 Observations
Example: Sample Statistics and CIs for 100 Observations
Random Sampling Methodologies
Simple Random Sampling
Stratified Sampling
Cluster Sampling
Example of Inferential Statistics
Summary and Next Steps
Statistics in Scientific Studies
Step 1: Research Your Study Area
Define Your Research Question
Literature Review
Step 2: Operationalize Your Study
Variables: What Will You Measure?
Types of Variables and Treatments
Measurement Methodology: How Will You Take Measurements?
Create a Sampling Plan: How Will You Collect Samples for Studying?
Design the Experimental Methods
Step 3: Data Collection
Step 4: Statistical Analysis
Step 5: Writing the Results
Summary and Next Steps
Experimental Methods
Types of Variables in Experiments
Dependent Variables
Independent Variables
Causation versus Correlation
Confounding Variables
Example of Confounding in an Experiment
Why Determining Causality Is Important
Causation and Hypothesis Tests
True Randomized Experiments
Random Assignment
Comparing the Vitamin Study With and Without Random Assignment
Flu Vaccination Experiment
Drawbacks of Randomized Experiments
Quasi-Experiments
Pros and Cons of Quasi-Experiments
Observational Studies
When to Use Observational Studies
Accounting for Confounders in Observational Studies
Matching
Multiple Regression
Vitamin Supplement Observational Study
Using Multiple Regression to Statistically Control for Confounders
Raw results
Adjusted results
Evaluating Experiments
Hill’s Criteria of Causation
Strength
Consistency
Specificity
Temporality
Biological Gradient
Plausibility
Coherence
Experiment
Analogy
Properties of Good Data
Reliability
Test-Retest Reliability
Internal Reliability
Inter-rater reliability
Validity
Data Validity
Face Validity
Content Validity
Criterion Validity
Discriminant Validity
Experimental Validity
Internal Validity
Single Group Studies
Multiple Groups
External Validity
Relationship Between Internal & External Validity
Checklist for Good Experiments
Review
Wrapping Up and Your Next Steps
Review of What You Learned in this Book
Next Steps for Further Study
My Other Books
Hypothesis Testing: An Intuitive Guide
Regression Analysis: An Intuitive Guide
References
Recommended Citation for This Book
Index
About the Author