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

Jim Publishing, 2019. — 248 p.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.
Modeling 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.Recommended Citation for This Book.