Learn Statistics

These posts form a complete introduction to statistics, taught with real nonprofit and fundraising examples. Follow them in order or jump to the section that fits where you are.

1

Describing Data

Before you analyze anything, understand what kind of data you have and what the basic summaries actually tell you.

  1. Not All Numbers Are Created Equal Levels of measurement and why they matter before you compute anything
  2. A Picture Worth a Thousand Averages Frequency distributions and histograms
  3. Where Did All That Money Go? Mean, median, and mode
  4. Two Campaigns, Same Average, Totally Different Stories Standard deviation and variance
  5. What Does It Mean to Be in the Top 10%? Percentiles and quartiles
  6. Not Everything Is a Bell Curve Skewness and kurtosis
  7. The Gift That Broke the Spreadsheet Outlier detection methods
2

Preparing and Comparing Data

Real data has gaps, errors, and hidden subgroups. Learn to handle the mess before drawing conclusions.

  1. The Donors Who Didn't Answer Missing data mechanisms (MCAR, MAR, MNAR)
  2. What Goes in the Empty Cells? Imputation methods for filling gaps
  3. What Your Retention Rate Isn't Telling You Cross-tabulations and comparing groups
3

Probability

The mathematical language of uncertainty. These distributions and theorems are the foundation for everything that comes next.

  1. The Hidden Denominator Conditional probability
  2. Why Your Prospect List Is Full of False Alarms Bayes' theorem
  3. When the Bell Curve Actually Fits The normal distribution
  4. Was That Spike Real? The binomial distribution
  5. How Many Is Too Many? The Poisson distribution
  6. The Few Who Carry Everything Power-law and Pareto distributions
  7. Why Averages Behave Better Than Individuals The central limit theorem
  8. When the Numbers Finally Settle Down The law of large numbers
  9. Which Campaign Actually Won? The beta distribution
  10. When the Full List Wasn't Enough The negative binomial distribution
4

Testing and Inference

Turn data into decisions. Hypothesis testing gives you a framework for telling signal from noise.

  1. What If Nothing Changed? Null and alternative hypotheses
  2. How Surprised Should You Be? p-values explained
  3. The Range Where the Truth Lives Confidence intervals
  4. The Two Ways to Be Wrong Type I and Type II errors
  5. Are You Looking Hard Enough? Statistical power
  6. How Many People Do You Actually Need? Sample size determination

Ready to practice?

Put these concepts to work with the interactive calculators.

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