Statistics All-in-One For Dummies

Title Page
Copyright Page
Table of Contents
Introduction
About This Book
Foolish Assumptions
Icons Used in This Book
Beyond the Book
Where to Go from Here
Unit 1 Getting Started with Statistics
Chapter 1 The Statistics of Everyday Life
Statistics and the Media: More Questions than Answers?
Probing popcorn problems
Venturing into viruses
Comprehending crashes
Mulling malpractice
Belaboring the loss of land
Scrutinizing schools
Scanning sports
Banking on business news
Touring the travel news
Surveying sexual stats
Breaking down weather reports
Using Statistics at Work
Delivering babies — and information
Posing for pictures
Poking through pizza data
Statistics in the office
Chapter 2 Taking Control: So Many Numbers, So Little Time
Detecting Errors, Exaggerations, and Just Plain Lies
Checking the math
Uncovering misleading statistics
Breaking down statistical debates
Untwisting tornado statistics
Zeroing in on what the scale tells you
Checking your sources
Counting on sample size
Considering cause and effect
Finding what you want to find
Looking for lies in all the right places
Feeling the Impact of Misleading Statistics
Chapter 3 Tools of the Trade
Thriving in a Statistical World
Statistics: More than Just Numbers
Designing Appropriate Studies
Surveys (Polls)
Experiments
Treatment group versus control group
Placebo
Blind and double-blind
Collecting Quality Data
Sample, random, or otherwise
Bias
Grabbing Some Basic Statistical Jargon
Data
Data set
Variable
Population
Statistic
Parameter
Mean (Average)
Median
Standard deviation
Percentile
Standard score
Distribution and normal distribution
Central Limit Theorem
z-values
Margin of error
Confidence interval
Hypothesis testing
p-values
Statistical significance
Correlation, regression, and two-way tables
Drawing Credible Conclusions
Reeling in overstated results
Questioning claims of cause and effect
Becoming a Sleuth, Not a Skeptic
Unit 2 Number-Crunching Basics
Chapter 4 Crunching Categorical Data
Summing Up Data with Descriptive Statistics
Crunching Categorical Data: Tables and Percents
Counting on the frequency
Relating with percentages
Two-way tables: Summarizing multiple measures
Interpreting counts and percents with caution
Practice Questions Answers and Explanations
Whaddya Know? Chapter 4 Quiz
Answers to Chapter 4 Quiz
Chapter 5 Means, Medians, and More
Measuring the Center with Mean and Median
Averaging out to the mean
Splitting your data down the median
Comparing means and medians: Histograms
Accounting for Variation
Reporting the standard deviation
Calculating standard deviation
Interpreting standard deviation
Understanding properties of standard deviation
Lobbying for standard deviation
Being out of range
Examining the Empirical Rule (68-95-99.7)
Measuring Relative Standing with Percentiles
Calculating percentiles
Interpreting percentiles
Comparing household incomes
Examining ACT Scores
Gathering a five-number summary
Exploring interquartile range
Practice Questions Answers and Explanations
Whaddya Know? Chapter 5 Quiz
Answers to Chapter 5 Quiz
Chapter 6 Getting the Picture: Graphing Categorical Data
Take Another Little Piece of My Pie Chart
Tallying personal expenses
Bringing in a lotto revenue
Ordering takeout
Projecting age trends
Raising the Bar on Bar Graphs
Tracking transportation expenses
Making a lotto profit
Tipping the scales on a bar graph
Pondering pet peeves
Practice Questions Answers and Explanations
Whaddya Know? Chapter 6 Quiz
Answers to Chapter 6 Quiz
Chapter 7 Going by the Numbers: Graphing Numerical Data
Handling Histograms
Making a histogram
An award-winning example
Creating appropriate groups
Handling borderline values
Clarifying the axes
Interpreting a histogram
Checking out the shape of the data
Measuring center: Mean versus median
Viewing variability: Amount of spread around the mean
Putting numbers with pictures
Detecting misleading histograms
Missing the mark with too few groups
Watching the scale and start/finish lines
Examining Boxplots
Making a boxplot
Interpreting a boxplot
Checking the shape with caution!
Measuring variability with IQR
Picking out the center using the median
Investigating Old Faithful’s boxplot
Denoting outliers
Making mistakes when interpreting a boxplot
Tackling Time Charts
Interpreting time charts
Understanding variability: Time charts versus histograms
Spotting misleading time charts
Watching the scale and start/end points
Simplifying excess data
Practice Questions Answers and Explanations
Whaddya Know? Chapter 7 Quiz
Answers to Chapter 7 Quiz
Unit 3 Distributions and the Central Limit Theorem
Chapter 8 Coming to Terms with Probability
A Set Notation Overview
Noting outcomes: Sample spaces
Finite sample spaces
Countably infinite sample spaces
Uncountably infinite sample spaces
Noting subsets of sample spaces: Events
Noting a void in the set: Empty sets
Putting sets together: Unions, intersections, and complements
Unions
Intersections
Complements
Probabilities of Events Involving A and/or B
Probability notation
Marginal probabilities
Union probabilities
Intersection (joint) probabilities
Complement probabilities
Conditional probabilities
Solving conditional probabilities without a formula
Solving conditional probabilities with a formula
Understanding and Applying the Rules of Probability
The complement rule (for opposites, not for flattering a date)
The multiplication rule (for intersections, not for rabbits)
The addition rule (for unions of the nonmarital nature)
Recognizing Independence in Multiple Events
Checking independence for two events with the definition
Using the multiplication rule for independent events
Including Mutually Exclusive Events
Recognizing mutually exclusive events
Simplifying the addition rule with mutually exclusive events
Distinguishing Independent from Mutually Exclusive Events
Comparing and contrasting independence and exclusivity
Checking for independence or exclusivity in a 52-card deck
Avoiding Probability Misconceptions
Predictions Using Probability
Practice Questions Answers and Explanations
Whaddya Know? Chapter 8 Quiz
Answers to Chapter 8 Quiz
Chapter 9 Random Variables and the Binomial Distribution
Defining a Random Variable
Discrete versus continuous
Probability distributions
The mean and variance of a discrete random variable
Identifying a Binomial
Checking binomial conditions step by step
No fixed number of trials
More than success or failure
Trials are not independent
Probability of success (p) changes
Finding Binomial Probabilities Using a Formula
Finding Probabilities Using the Binomial Table
Finding probabilities for specific values of X
Finding probabilities for X greater-than, less-than, or between two values
Checking Out the Mean and Standard Deviation of the Binomial
Practice Questions Answers and Explanations
Whaddya Know? Chapter 9 Quiz
Answers to Chapter 9 Quiz
Chapter 10 The Normal Distribution
Exploring the Basics of the Normal Distribution
Meeting the Standard Normal (Z-) Distribution
Checking out Z
Standardizing from X to Z
Finding probabilities for Z with the Z-table
Finding Probabilities for a Normal Distribution
Knowing Where You Stand with Percentiles
Finding X When You Know the Percent
Figuring out a percentile for a normal distribution
Doing a low percentile problem
Working with a higher percentile
Translating tricky wording in percentile problems
Normal Approximation to the Binomial
Practice Questions Answers and Explanations
Whaddya Know? Chapter 10 Quiz
Answers to Chapter 10 Quiz
Chapter 11 The t-Distribution
Basics of the t-Distribution
Comparing the t- and Z-distributions
Discovering the effect of variability on t-distributions
Using the t-Table
Finding probabilities with the t-table
Figuring percentiles for the t-distribution
Picking out t*-values for confidence intervals
Studying Behavior Using the t-Table
Practice Questions Answers and Explanations
Whaddya Know? Chapter 11 Quiz
Answers to Chapter 11 Quiz
Chapter 12 Sampling Distributions and the Central Limit Theorem
Defining a Sampling Distribution
The Mean of a Sampling Distribution
Measuring Standard Error
Sample size and standard error
Population standard deviation and standard error
Looking at the Shape of a Sampling Distribution
Case 1: The distribution of X is normal
Case 2: The distribution of X is not normal — Enter the Central Limit Theorem
Averaging a fair die is approximately normal
Averaging an unfair die is still approximately normal
Clarifying three major points about the Central Limit Theorem
Finding Probabilities for the Sample Mean
The Sampling Distribution of the Sample Proportion
Finding Probabilities for the Sample Proportion
Practice Questions Answers and Explanations
Whaddya Know? Chapter 12 Quiz
Answers to Chapter 12 Quiz
Unit 4 Guesstimating and Hypothesizing with Confidence
Chapter 13 Leaving Room for a Margin of Error
Seeing the Importance of that Plus or Minus
Finding the Margin of Error: A General Formula
Measuring sample variability
Calculating margin of error for a sample proportion
Reporting results
Calculating margin of error for a sample mean
Being confident you’re right
Determining the Impact of Sample Size
Sample size and margin of error
Bigger isn’t always (that much) better!
Keeping margin of error in perspective
Practice Questions Answers and Explanations
Whaddya Know? Chapter 13 Quiz
Answers to Chapter 13 Quiz
Chapter 14 Confidence Intervals: Making Your Best Guesstimate
Not All Estimates Are Created Equal
Linking a Statistic to a Parameter
Getting with the Jargon
Interpreting Results with Confidence
Zooming In on Width
Choosing a Confidence Level
Factoring In the Sample Size
Counting On Population Variability
Calculating a Confidence Interval for a Population Mean
Case 1: Population standard deviation is known
Case 2: Population standard deviation is unknown and/or n is small
Figuring Out What Sample Size You Need
Determining the Confidence Interval for One Population Proportion
Creating a Confidence Interval for the Difference of Two Means
Case 1: Population standard deviations are known
Case 2: Population standard deviations are unknown and/or sample sizes are small
Estimating the Difference of Two Proportions
Spotting Misleading Confidence Intervals
Practice Questions Answers and Explanations
Whaddya Know? Chapter 14 Quiz
Answers to Chapter 14 Quiz
Chapter 15 Claims, Tests, and Conclusions
Setting Up the Hypotheses
Defining the null
What’s the alternative?
Gathering Good Evidence (Data)
Compiling the Evidence: The Test Statistic
Gathering sample statistics
Measuring variability using standard errors
Understanding standard scores
Calculating and interpreting the test statistic
Weighing the Evidence and Making Decisions: p-Values
Connecting test statistics and p-values
Defining a p-value
Calculating a p-value
Making Conclusions
Setting boundaries for rejecting 
Testing varicose veins
Assessing the Chance of a Wrong Decision
Making a false alarm: Type I errors
Missing out on a detection: Type II errors
Practice Questions Answers and Explanations
Whaddya Know? Chapter 15 Quiz
Answers to Chapter 15 Quiz
Chapter 16 Commonly Used Hypothesis Tests: Formulas and Examples
Testing One Population Mean
Handling Small Samples and Unknown Standard Deviations: The t-Test
Putting the t-test to work
Relating t to Z
Handling negative t-values
Examining the not-equal-to alternative
Drawing conclusions using the critical value
Testing One Population Proportion
Comparing Two (Independent) Population Averages
Case 1: Difference of two population means when population standard deviations are known
Case 2: Difference of two population means when population standard deviations are unknown
Testing for an Average Difference (The Paired t-Test)
Comparing Two Population Proportions
Practice Questions Answers and Explanations
Whaddya Know? Chapter 16 Quiz
Answers to Chapter 16 Quiz
Unit 5 Statistical Studies and the Hunt for a Meaningful Relationship
Chapter 17 Polls, Polls, and More Polls
Recognizing the Impact of Polls
Getting to the source
Surveying what’s hot
Impacting lives
Behind the Scenes: The Ins and Outs of Surveys
Planning and designing a survey
Clarifying the purpose of your survey
Defining the target population
Choosing the type and timing of the survey
Designing the introduction with ethics in mind
Formulating the questions
Selecting the sample
A good sample represents the target population
A good sample is selected randomly
A good sample is large enough for the results to be accurate
Carrying out a survey
Collecting the data
Following up, following up, and following up
Interpreting results and finding problems
Organizing and analyzing
Drawing conclusions
Practice Questions Answers and Explanations
Whaddya Know? Chapter 17 Quiz
Answers to Chapter 17 Quiz
Chapter 18 Experiments and Observational Studies: Medical Breakthroughs or Misleading Results?
Boiling Down the Basics of Studies
Looking at the lingo of studies
Observing observational studies
Examining experiments
Designing a Good Experiment
Designing the experiment to make comparisons
Fake treatments — the placebo effect
Standard treatments
No treatment
Selecting the sample size
Limiting small samples to small conclusions
Defining sample size
Choosing the subjects
Making random assignments
Controlling for confounding variables
Respecting ethical issues
Collecting good data
Analyzing the data properly
Interpreting Experiment Results
Making appropriate conclusions
Overstating the results
Taking the results one step beyond the actual data
Generalizing results to people beyond the scope of the study
Making informed decisions
Practice Questions Answers and Explanations
Whaddya Know? Chapter 18 Quiz
Answers to Chapter 18 Quiz
Chapter 19 Looking for Links: Correlation and Regression
Picturing a Relationship with a Scatterplot
Making a scatterplot
Interpreting a scatterplot
Quantifying Linear Relationships Using the Correlation
Calculating the correlation
Interpreting the correlation
Examining properties of the correlation
Working with Linear Regression
Figuring out which variable is X and which is Y
Checking the conditions
Calculating the regression line
Finding the slope
Finding the y-intercept
Interpreting the regression line
Interpreting the slope
Interpreting the y-intercept
Putting it all together: The regression line for the crickets
Making Proper Predictions
Checking the conditions
Staying in-bounds
Regression Analysis: Understanding the Output
Residing with Residuals
Explaining the Relationship: Correlation versus Cause and Effect
Practice Questions Answers and Explanations
Whaddya Know? Chapter 19 Quiz
Answers to Chapter 19 Quiz
Chapter 20 Two-Way Tables and Independence
Organizing a Two-Way Table
Setting up the cells
Figuring the totals
Interpreting Two-Way Tables
Singling out variables with marginal distributions
Calculating marginal distributions
Graphing marginal distributions
Examining all groups — a joint distribution
Calculating joint distributions
Graphing joint distributions
Comparing groups with conditional distributions
Calculating conditional distributions
Graphing conditional distributions
Checking Independence and Describing Dependence
Checking for independence
Comparing the results of two conditional distributions
Comparing marginal and conditional to check for independence
Describing a dependent relationship
Cautiously Interpreting Results
Checking for legitimate cause and effect
Projecting from sample to population
Making prudent predictions
Resisting the urge to jump to conclusions
Practice Questions Answers and Explanations
Whaddya Know? Chapter 20 Quiz
Answers to Chapter 20 Quiz
Appendix: Tables for Reference
The Z-Table
The t-Table
The Binomial Table
Index
EULA