Sizu Riatto
It Didn’t Have To Be This Hard · Book 4 · Kindle

Statistics Didn’t Have to Be This Hard

The simple ideas behind averages, spread, polls, p-values and correlation that nobody explained. A reading book, not a textbook: one idea at a time, in plain English, with 107 real-life worked examples and 83 diagrams.

Buy on Amazon Kindle
Cover of Statistics Didn't Have to Be This Hard: a night sky of points rising from left to right, with the best straight line drawn through them

Home › Books › Statistics Didn’t Have to Be This Hard

What this book is

The ideas of statistics, explained slowly, from the very beginning. Which average to trust and when. What a standard deviation really measures. Where the bell curve comes from, and when not to use it. Why a poll of a thousand people can speak for millions, and what its margin of error leaves out. What a p-value is, in one sentence, and four things it isn’t. Why most alarms for rare things are false. How a correlation can mislead, and how a chart can fool you without a single false number.

It’s written for a student in a required statistics course, a new analyst, a manager handed a report, and anyone who reads the news. Every dataset is invented to make the method easy to see; every number in it was computed by program and checked a second way.

Every chapter, its worked examples, and its free calculator

The calculators are free, need no sign-up, and keep what you type in your own browser. Each one opens with the book’s own example loaded. The book is complete without them.

Part One · What You’ve Got

Chapter 1 · What a Number Is Hiding
Calculators: Percentages
Worked examples 1–4
  1. Mina's order sheet: rows, columns and kinds of data
  2. A day's drinks: counts, shares and the mode
  3. Break-ins in two towns, per 1,000 homes
  4. Three questions to ask of a 4.6-star rating
Chapter 2 · The Middle
Calculators: Mean, Median and Mode · Weighted Average
Worked examples 5–11
  1. A week of sales: the mean as fair share and balance point
  2. A founder walks into a bar: mean against median
  3. Six house prices and one mansion
  4. A shoe shop's best-selling size: the mode
  5. Ben's weighted course grade, and the final mark he needs
  6. Two classes of different sizes: the average of averages
  7. Eight waits: a long tail pulls the mean
Chapter 3 · The Spread
Calculators: Describe Your Data
Worked examples 12–16
  1. Two cities, one average temperature: the range
  2. Ben's commute: quartiles and the middle half
  3. Five waits for a bus: a standard deviation by hand
  4. Two bakers' loaves: same mean, different spread
  5. Mice and elephants: relative spread
Chapter 4 · The Shape
Calculators: Describe Your Data
Worked examples 17–22
  1. Sixty pizza deliveries in a histogram
  2. The same deliveries with three bin widths
  3. A box plot from five numbers
  4. The 1.5 × IQR fence: when is a delivery an outlier?
  5. Two rushes a day: the average customer arrives when nobody does
  6. Two branches' waits in side-by-side box plots
Chapter 5 · Where Do I Stand?
Calculators: Z-Score and Percentile
Worked examples 23–29
  1. Finishing 140th of 800: a percentile
  2. 85% on a quiz isn't the 85th percentile
  3. Ana's two exams compared by z-score
  4. Translating a standing from one exam to another
  5. A long jump against a sprint
  6. A negative z-score
  7. Can most drivers be better than average?

Part Two · Chance and the Bell Curve

Chapter 6 · Chance, Plainly
Calculators: Expected Value · Dice Lab
Worked examples 30–36
  1. Six thousand rolls of a die: small samples wobble
  2. Two dice: why seven is most likely
  3. Rain and a late train: "and", "or" and "one minus none"
  4. "1 in 30" or "3%"? Natural frequencies
  5. A raffle ticket's expected value
  6. Five heads in a row, and how common streaks are
  7. The birthday surprise
Chapter 7 · The Bell Curve
Calculators: Bell Curve Areas
Worked examples 37–43
  1. Coin flips build a bell curve
  2. A milk steamer and the 68-95-99.7 rule
  3. A legal minimum fill: setting the machine
  4. Eggs between two weights
  5. Bolts outside their tolerance
  6. The score for the top 10%
  7. Pizza times are not a bell
Chapter 8 · Why Averages Behave
Calculators: Dice Lab
Worked examples 44–48
  1. Averages of 1, 2, 5 and 25 dice: the central limit theorem
  2. Ten thousand coin flips: the law of large numbers
  3. Two maternity wards
  4. Why the best and worst schools are small
  5. The square-root law: four times the data for half the wobble

Part Three · From a Few to Everyone

Chapter 9 · Who Got Asked
Calculators: Random Sample Picker
Worked examples 49–54
  1. Oat milk and the 7am queue: a biased sample
  2. The 1936 Literary Digest poll
  3. Bomber damage and survivorship bias
  4. Star ratings: who writes reviews
  5. Two wordings, two answers
  6. A survey with a 20% response rate
Chapter 10 · The Margin of Error
Calculators: Margin of Error
Worked examples 55–60
  1. Where a poll's margin of error comes from
  2. Why population size hardly matters
  3. Sample size for a chosen margin
  4. Is a four-point lead real?
  5. The margin on a subgroup
  6. A hundred polls of a 50:50 town
Chapter 11 · Confidence Intervals
Calculators: Confidence Interval
Worked examples 61–66
  1. Battery life: a confidence interval for an average
  2. Gosset's small samples and the t multiplier
  3. A hundred intervals: what "95% confident" means
  4. 90%, 95% and 99% intervals
  5. Two coffee blends: overlapping intervals
  6. How many waits to time

Part Four · Is It Real?

Chapter 12 · Is It Just Luck?
Calculators: Is It Just Luck?
Worked examples 67–71
  1. Fisher's eight cups of tea
  2. Sixty heads in a hundred flips
  3. One-sided and two-sided p-values
  4. A die that rolls too many sixes
  5. Two teaching methods: a shuffle test
Chapter 13 · What a p-Value Is (and Isn't)
Calculators: A/B Test
Worked examples 72–77
  1. An A/B test of a checkout button
  2. A thousand ideas: how many "significant" results are false
  3. A million visitors: significant but trivial
  4. Twenty customers: not significant, possibly big
  5. Twenty flavours: multiple comparisons
  6. Peeking at a test every day
Chapter 14 · False Alarms and Base Rates
Calculators: Base Rate and False Alarms · A/B Test (power)
Worked examples 78–83
  1. A "99% accurate" fraud alert
  2. A second, independent check
  3. A spam filter whose alarms can be trusted
  4. A smoke alarm's two settings: two kinds of error
  5. The power of a test
  6. The prosecutor's fallacy

Part Five · Two Things at Once

Chapter 15 · Correlation
Calculators: Correlation and Best-Fit Line
Worked examples 84–89
  1. Temperature and iced drinks: a scatter plot and r
  2. A correlation by hand
  3. r²: how much temperature explains
  4. One odd point makes a correlation
  5. A strong curved pattern with r near zero
  6. Entrance tests and restricted range
Chapter 16 · What Causes What
Calculators: Correlation and Best-Fit Line
Worked examples 90–94
  1. Ice cream, sunburn and sunshine: a confounder
  2. Fire engines and damage: reverse causation
  3. Two rising trends, and their yearly changes
  4. Two delivery firms: Simpson's paradox
  5. A randomized garden trial
Chapter 17 · Drawing the Line
Calculators: Correlation and Best-Fit Line
Worked examples 95–100
  1. Taxi fares: slope and intercept
  2. Least squares you can see
  3. Predicting inside and outside the data
  4. A child's growth extrapolated to age 40
  5. Ordering ice from a regression line
  6. Two tests: regression to the mean

Part Six · Using It

Chapter 18 · How Charts Fool You
Calculators: Chart Check
Worked examples 101–106
  1. A bar chart with a cut-off axis
  2. Pictures that grow in two directions
  3. "Doubles the risk": relative and absolute
  4. Percent or percentage points?
  5. Maps of counts against rates
  6. A cherry-picked starting point
Chapter 19 · Ten Questions for Any Statistic
Worked examples 107–107
  1. One survey headline, start to finish