Books & Videos

Table of Contents

  1. Chapter 1 Visualizing Information: First Impressions

    1. Statistics are everywhere

    2. But why learn statistics?

    3. A tale of two charts

    4. Manic Mango needs some charts

    5. The humble pie chart

    6. Chart failure

    7. Bar charts can allow for more accuracy

    8. Vertical bar charts

    9. Horizontal bar charts

    10. It’s a matter of scale

    11. Using frequency scales

    12. Dealing with multiple sets of data

    13. Your bar charts rock

    14. Categories vs. numbers

    15. Dealing with grouped data

    16. To make a histogram, start by finding bar widths

    17. Manic Mango needs another chart

    18. Make the area of histogram bars proportional to frequency

    19. Step 1: Find the bar widths

    20. Step 2: Find the bar heights

    21. Step 3: Draw your chart—a histogram

    22. Histograms can’t do everything

    23. Introducing cumulative frequency

    24. Drawing the cumulative frequency graph

    25. Choosing the right chart

    26. Manic Mango conquered the games market!

  2. Chapter 2 Measuring Central Tendency: The Middle Way

    1. Welcome to the Health Club

    2. A common measure of average is the mean

    3. Mean math

    4. Dealing with unknowns

    5. Back to the mean

    6. Handling frequencies

    7. Back to the Health Club

    8. Everybody was Kung Fu fighting

    9. Our data has outliers

    10. The butler outliers did it

    11. Watercooler conversation

    12. Finding the median

    13. Business is booming

    14. The Little Ducklings swimming class

    15. Frequency Magnets

    16. Frequency Magnets

    17. What went wrong with the mean and median?

    18. Introducing the mode

    19. Congratulations!

  3. Chapter 3 Measuring Variability and Spread: Power Ranges

    1. Wanted: one player

    2. We need to compare player scores

    3. Use the range to differentiate between data sets

    4. The problem with outliers

    5. We need to get away from outliers

    6. Quartiles come to the rescue

    7. The interquartile range excludes outliers

    8. Quartile anatomy

    9. We’re not just limited to quartiles

    10. So what are percentiles?

    11. Box and whisker plots let you visualize ranges

    12. Variability is more than just spread

    13. Calculating average distances

    14. We can calculate variation with the variance...

    15. ...but standard deviation is a more intuitive measure

    16. A quicker calculation for variance

    17. What if we need a baseline for comparison?

    18. Use standard scores to compare values across data sets

    19. Interpreting standard scores

    20. Statsville All Stars win the league!

  4. Chapter 4 Calculating Probabilities: Taking Chances

    1. Fat Dan’s Grand Slam

    2. Roll up for roulette!

    3. Your very own roulette board

    4. Place your bets now!

    5. What are the chances?

    6. Find roulette probabilities

    7. You can visualize probabilities with a Venn diagram

    8. It’s time to play!

    9. And the winning number is...

    10. Let’s bet on an even more likely event

    11. You can also add probabilities

    12. You win!

    13. Time for another bet

    14. Exclusive events and intersecting events

    15. Problems at the intersection

    16. Some more notation

    17. Another unlucky spin...

    18. ...but it’s time for another bet

    19. Conditions apply

    20. Find conditional probabilities

    21. You can visualize conditional probabilities with a probability tree

    22. Trees also help you calculate conditional probabilities

    23. Bad luck!

    24. We can find P(Black l Even) using the probabilities we already have

    25. Step 1: Finding P(Black ∩ Even)

    26. So where does this get us?

    27. Step 2: Finding P(Even)

    28. Step 3: Finding P(Black l Even)

    29. These results can be generalized to other problems

    30. Use the Law of Total Probability to find P(B)

    31. Introducing Bayes’ Theorem

    32. We have a winner!

    33. It’s time for one last bet

    34. If events affect each other, they are dependent

    35. If events do not affect each other, they are independent

    36. More on calculating probability for independent events

    37. Winner! Winner!

  5. Chapter 5 Using Discrete Probability Distributions: Manage Your Expectations

    1. Back at Fat Dan’s Casino

    2. We can compose a probability distribution for the slot machine

    3. Expectation gives you a prediction of the results...

    4. ... and variance tells you about the spread of the results

    5. Variances and probability distributions

    6. Let’s calculate the slot machine’s variance

    7. Fat Dan changed his prices

    8. There’s a linear relationship between E(X) and E(Y)

    9. Slot machine transformations

    10. General formulas for linear transforms

    11. Every pull of the lever is an independent observation

    12. Observation shortcuts

    13. New slot machine on the block

    14. Add E(X) and E(Y) to get E(X + Y)...

    15. ... and subtract E(X) and E(Y) to get E(X – Y)

    16. You can also add and subtract linear transformations

    17. Jackpot!

  6. Chapter 6 Permutations and Combinations: Making Arrangements

    1. The Statsville Derby

    2. It’s a three-horse race

    3. How many ways can they cross the finish line?

    4. Calculate the number of arrangements

    5. Going round in circles

    6. It’s time for the novelty race

    7. Arranging by individuals is different than arranging by type

    8. We need to arrange animals by type

    9. Generalize a formula for arranging duplicates

    10. It’s time for the twenty-horse race

    11. How many ways can we fill the top three positions?

    12. Examining permutations

    13. What if horse order doesn’t matter

    14. Examining combinations

    15. It’s the end of the race

  7. Chapter 7 Geometric, Binomial, and Poisson Distributions: Keeping Things Discrete

    1. Meet Chad, the hapless snowboarder

    2. We need to find Chad’s probability distribution

    3. There’s a pattern to this probability distribution

    4. The probability distribution can be represented algebraically

    5. The pattern of expectations for the geometric distribution

    6. Expectation is 1/p

    7. Finding the variance for our distribution

    8. You’ve mastered the geometric distribution

    9. Should you play, or walk away?

    10. Generalizing the probability for three questions

    11. Let’s generalize the probability further

    12. What’s the expectation and variance?

    13. Binomial expectation and variance

    14. The Statsville Cinema has a problem

    15. Expectation and variance for the Poisson distribution

    16. So what’s the probability distribution?

    17. Combine Poisson variables

    18. The Poisson in disguise

    19. Anyone for popcorn?

  8. Chapter 8 Using the Normal Distribution: Being Normal

    1. Discrete data takes exact values...

    2. ... but not all numeric data is discrete

    3. What’s the delay?

    4. We need a probability distribution for continuous data

    5. Probability density functions can be used for continuous data

    6. Probability = area

    7. To calculate probability, start by finding f(x)...

    8. ... then find probability by finding the area

    9. We’ve found the probability

    10. Searching for a soul sole mate

    11. Male modelling

    12. The normal distribution is an “ideal” model for continuous data

    13. So how do we find normal probabilities?

    14. Three steps to calculating normal probabilities

    15. Step 1: Determine your distribution

    16. Step 2: Standardize to N(0, 1)

    17. To standardize, first move the mean...

    18. ... then squash the width

    19. Now find Z for the specific value you want to find probability for

    20. Step 3: Look up the probability in your handy table

    21. Julie’s probability is in the table

    22. And they all lived happily ever after

  9. Chapter 9 Using the Normal Distribution ii: Beyond Normal

    1. Love is a roller coaster

    2. All aboard the Love Train

    3. Normal bride + normal groom

    4. It’s still just weight

    5. How’s the combined weight distributed?

    6. Finding probabilities

    7. More people want the Love Train

    8. Linear transforms describe underlying changes in values...

    9. ...and independent observations describe how many values you have

    10. Expectation and variance for independent observations

    11. Should we play, or walk away?

    12. Normal distribution to the rescue

    13. When to approximate the binomial distribution with the normal

    14. Revisiting the normal approximation

    15. The binomial is discrete, but the normal is continuous

    16. Apply a continuity correction before calculating the approximation

    17. All aboard the Love Train

    18. When to approximate the binomial distribution with the normal

    19. A runaway success!

  10. Chapter 10 Using Statistical Sampling: Taking Samples

    1. The Mighty Gumball taste test

    2. They’re running out of gumballs

    3. Test a gumball sample, not the whole gumball population

    4. How sampling works

    5. When sampling goes wrong

    6. How to design a sample

    7. Define your sampling frame

    8. Sometimes samples can be biased

    9. Sources of bias

    10. How to choose your sample

    11. Simple random sampling

    12. How to choose a simple random sample

    13. There are other types of sampling

    14. We can use stratified sampling...

    15. ...or we can use cluster sampling...

    16. ...or even systematic sampling

    17. Mighty Gumball has a sample

  11. Chapter 11 Estimating Populations and Samples: Making Predictions

    1. So how long does flavor really last for?

    2. Let’s start by estimating the population mean

    3. Point estimators can approximate population parameters

    4. Let’s estimate the population variance

    5. We need a different point estimator than sample variance

    6. Which formula’s which?

    7. Mighty Gumball has done more sampling

    8. It’s a question of proportion

    9. Buy your gumballs here!

    10. So how does this relate to sampling?

    11. The sampling distribution of proportions

    12. So what’s the expectation of Ps?

    13. And what’s the variance of Ps?

    14. Find the distribution of Ps

    15. Ps follows a normal distribution

    16. How many gumballs?

    17. We need probabilities for the sample mean

    18. The sampling distribution of the mean

    19. Find the expectation for X̄

    20. What about the the variance of X̄?

    21. So how is X̄ distributed?

    22. If n is large, X̄ can still be approximated by the normal distribution

    23. Using the central limit theorem

    24. Sampling saves the day!

  12. Chapter 12 Constructing Confidence Intervals: Guessing with Confidence

    1. Mighty Gumball is in trouble

    2. The problem with precision

    3. Introducing confidence intervals

    4. Four steps for finding confidence intervals

    5. Step 1: Choose your population statistic

    6. Step 2: Find its sampling distribution

    7. Point estimators to the rescue

    8. We’ve found the distribution for X̄

    9. Step 3: Decide on the level of confidence

    10. How to select an appropriate confidence level

    11. Step 4: Find the confidence limits

    12. Start by finding Z

    13. Rewrite the inequality in terms of μ

    14. Finally, find the value of X̄

    15. You’ve found the confidence interval

    16. Let’s summarize the steps

    17. Handy shortcuts for confidence intervals

    18. Just one more problem...

    19. Step 1: Choose your population statistic

    20. Step 2: Find its sampling distribution

    21. X̄ follows the t-distribution when the sample is small

    22. Find the standard score for the t-distribution

    23. Step 3: Decide on the level of confidence

    24. Step 4: Find the confidence limits

    25. Using t-distribution probability tables

    26. The t-distribution vs. the normal distribution

    27. You’ve found the confidence intervals!

  13. Chapter 13 Using Hypothesis Tests: Look At The Evidence

    1. Statsville’s new miracle drug

    2. So what’s the problem?

    3. Resolving the conflict from 50,000 feet

    4. The six steps for hypothesis testing

    5. Step 1: Decide on the hypothesis

    6. So what’s the alternative?

    7. Step 2: Choose your test statistic

    8. Step 3: Determine the critical region

    9. To find the critical region, first decide on the significance level

    10. Step 4: Find the p-value

    11. We’ve found the p-value

    12. Step 5: Is the sample result in the critical region?

    13. Step 6: Make your decision

    14. So what did we just do?

    15. What if the sample size is larger?

    16. Let’s conduct another hypothesis test

    17. Step 1: Decide on the hypotheses

    18. Step 2: Choose the test statistic

    19. Use the normal to approximate the binomial in our test statistic

    20. Step 3: Find the critical region

    21. SnoreCull failed the test

    22. Mistakes can happen

    23. Let’s start with Type I errors

    24. What about Type II errors?

    25. Finding errors for SnoreCull

    26. We need to find the range of values

    27. Find P(Type II error)

    28. Introducing power

    29. The doctor’s happy

  14. Chapter 14 The χ2 Distribution: There’s Something Going On...

    1. There may be trouble ahead at Fat Dan’s Casino

    2. Let’s start with the slot machines

    3. The χ2 test assesses difference

    4. So what does the test statistic represent?

    5. Two main uses of the χ2 distribution

    6. v represents degrees of freedom

    7. What’s the significance?

    8. Hypothesis testing with χ2

    9. You’ve solved the slot machine mystery

    10. Fat Dan has another problem

    11. the χ2 distribution can test for independence

    12. You can find the expected frequencies using probability

    13. So what are the frequencies?

    14. We still need to calculate degrees of freedom

    15. Generalizing the degrees of freedom

    16. And the formula is...

    17. You’ve saved the casino

  15. Chapter 15 Correlation and Regression: What’s My Line?

    1. Never trust the weather

    2. Let’s analyze sunshine and attendance

    3. Exploring types of data

    4. Visualizing bivariate data

    5. Scatter diagrams show you patterns

    6. Correlation vs. causation

    7. Predict values with a line of best fit

    8. Your best guess is still a guess

    9. We need to minimize the errors

    10. Introducing the sum of squared errors

    11. Find the equation for the line of best fit

    12. Finding the slope for the line of best fit

    13. Finding the slope for the line of best fit, part ii

    14. We’ve found b, but what about a?

    15. You’ve made the connection

    16. Let’s look at some correlations

    17. The correlation coefficient measures how well the line fits the data

    18. There’s a formula for calculating the correlation coefficient, r

    19. Find r for the concert data

    20. Find r for the concert data, continued

    21. You’ve saved the day!

    22. Leaving town...

    23. It’s been great having you here in Statsville!

  1. Appendix Leftovers: The Top Ten Things (we didn’t cover)

    1. #1. Other ways of presenting data

    2. #2. Distribution anatomy

    3. #3. Experiments

    4. Designing your experiment

    5. #4. Least square regression alternate notation

    6. #5. The coefficient of determination

    7. #6. Non-linear relationships

    8. #7. The confidence interval for the slope of a regression line

    9. #8. Sampling distributions – the difference between two means

    10. #9. Sampling distributions – the difference between two proportions

    11. #10. E(X) and Var(X) for continuous probability distributions

    12. Finding E(X)

    13. Finding Var(X)

  2. Appendix Statistics Tables: Looking Things Up

    1. #1. Standard normal probabilities

    2. #2. t-distribution critical values

    3. #3. X2 critical values