Statistics for dummies
(Book)

Introduction: -- About this book -- Foolish assumptions -- Beyond the book -- Where to go from here -- Part 1: Getting Started With Statistics: -- 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 -- Study 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 -- Taking Control: So Many Numbers, So Little Time: -- Detecting errors, exaggerations, and just plain lies: -- Checking the math -- Uncovering misleading statistics -- Looking for lies in all the right places -- Feeling the impact of misleading statistics -- Tools Of The Trade: -- Thriving in a statistical world -- Statistics: more than just numbers -- Designing appropriate studies: -- Surveys (polls) -- Experiments -- 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 -- Part 2: Number-Crunching Basics: -- Crunching Categorical Data: -- Summing up data with descriptive statistics -- Crunching categorical data: tables and percent's: -- Counting on the frequency -- Relating with percentages -- Two-way tables: summarizing multiple measures -- Interpreting counts and percent's with caution -- 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 -- Being out of range -- Examining the empirical rule (68-95-99-7) -- Measuring relative standing with percentiles: -- Calculating percentiles -- Interpreting percentiles -- Gathering a five-number summary -- Exploring interquartile range -- 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 -- Going By The Numbers: Graphing Numerical Data: -- Handling histograms: -- Making a histogram -- Interpreting a histogram -- Putting numbers with pictures -- Detecting misleading histograms -- Examining boxplots: -- Making a boxplot -- Interpreting a boxplot -- Tackling time charts: -- Interpreting time charts -- Understanding variability: time charts versus histograms -- Spotting misleading time charts -- Part 3: Distributions And The Central Limit Theorem: -- Coming To Terms With Probability: -- Set notation overview: -- Noting outcomes: sample spaces -- Noting subsets of sample spaces: events -- Noting a void in the set: empty sets -- Putting sets together: unions, intersections, and complements -- Probabilities of events involving A and/or B: -- Probability notation -- Marginal probabilities -- Union probabilities -- Intersection (joint) probabilities -- Complement probabilities -- Conditional probabilities -- Understanding and applying the rules of probability: -- Complement rule (for opposites, not for flattering a date) -- Multiplication rule (for intersections, not for rabbits) -- 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 -- Random Variables And The Binomial Distribution: -- Defining a random variable: -- Discrete versus continuous -- Probability distributions -- 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 -- 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 -- Translating tricky wording in percentile problems -- Normal approximation to the binomial -- 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 -- Sampling Distributions And the Central Limit Theorem: -- Defining a sampling distribution -- 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: Distribution of X is normal -- Case 2: Distribution of X is not normal-enter the central limit theorem -- Finding probabilities for the sample mean -- Sampling distribution of the sample proportion -- Finding probabilities for the sample proportion --

Part 4: Guesstimating And Hypothesizing With Confidence:

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

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

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 H

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

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

Testing for an average difference (the paired t-test)

Comparing two population proportions

Part 5: Statistical Studies And The Hunt For A Meaningful Relationship:

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

Selecting the sample

Carrying out a survey

Interpreting results and finding problems

Experiments: 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

Selecting the 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

Making informed decisions

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

Interpreting the regression line

Putting it all together with an example: the regression line for the crickets

Making proper predictions:

Checking the conditions

Staying in-bounds

Explaining the relationship: correlation versus cause and effort

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

Examining all groups-a joint distribution

Comparing groups with conditional distributions

Checking independence and describing dependence:

Checking 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

Part 6: Part Of Tens:

Ten Tips For The Statistically Savvy Sleuth:

Pinpoint misleading graphs:

Pie charts

Bar graphs

Time charts

Histograms

Uncover biased data

Search for a margin of error

Identify nonrandom samples

Sniff out missing sample sizes

Detect misinterpreted correlations

Reveal confounding variables

Inspect the numbers

Report selective reporting

Expose the anecdote

Ten Surefire Exam Score Boosters:

Know what you don't know, and then do something about it

Avoid "yeah-yeah" traps:

Yeah-Yeah Trap #1

Yeah-Yeah Trap #2

Make friends with formulas

Make an "if-then-how" chart

Figure out what the question is asking

Label what you're given

Draw a picture

Make the connection and solve the problem

Do the math-twice

Analyze your answers

Appendix:

Z-table

T-table

Binomial table

Index