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