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

Description

Learn Statistics Without Fear! Build a solid foundation in data analysis. Be confident that you understand what your data are telling you and that you can explain the results to others! I'll help you intuitively understand statistics by using simple language and deemphasizing formulas. This guide starts with an overview of statistics and why it is so important. We proceed to essential statistical skills and knowledge about different types of data, relationships, and distributions. Then we move to using inferential statistics to expand human knowledge, how it fits into the scientific method, and how to design and critique experiments. Learn the fundamentals of statistics. Why is the field of statistics so vital in our data-driven society? Interpret graphs and summary statistics. Find relationships between different types of variables. Understand the properties of data distributions. Use measures of central tendency and variability. Interpret correlations and percentiles. Use probability distributions to calculate probabilities. Learn about the normal and binomial distributions in depth. Grasp the differences between descriptive and inferential statistics. Use data collection methodologies properly and understand sample size considerations. Design and critique scientific experiments—whether it's your own or another researcher's. Free access to downloadable datasets to follow along with the examples. 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 an Experiment 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 References About the Author