A practical introduction to variation, summaries, samples, uncertainty and responsible data communication.
Educational · not faculty-reviewed6 chapters40–55 minutes estimatedEnglish content
CHAPTER 01 · Statistical Reasoning: From Data to Decisions
Data are observations with context
Key idea
A dataset is produced by decisions about units, variables, collection and inclusion. Before calculating, identify what one row represents, what each column means, how values were collected and which observations are missing.
Worked example
A table of weekly study minutes may mix self-reported estimates and timed logs. The unit, collection method and recall period affect what a comparison means.
Check your understanding
A dataset is not a neutral window into reality; collection and inclusion rules shape it.
Self-check: Which part is observation, which is interpretation, and what evidence would change the conclusion?
Reasoning: Name the claim’s scope, supporting source and one limitation before deciding how far it travels.
Limit: A dataset is not a neutral window into reality; collection and inclusion rules shape it.
CHAPTER 02 · Statistical Reasoning: From Data to Decisions
Describe distributions
Key idea
A distribution shows how values vary. Use an appropriate center and describe spread and shape. The mean is sensitive to extreme values; the median can be more robust for skewed distributions. A summary should preserve information relevant to the question.
Worked example
For values 2, 3, 3, 4, 18, the mean and median tell different stories. Displaying all points or a distribution plot can reveal the unusually high value.
Check your understanding
Do not choose a summary only because it makes a preferred result look stronger.
Self-check: Which part is observation, which is interpretation, and what evidence would change the conclusion?
Reasoning: Name the claim’s scope, supporting source and one limitation before deciding how far it travels.
Limit: Do not choose a summary only because it makes a preferred result look stronger.
CHAPTER 03 · Statistical Reasoning: From Data to Decisions
Samples and selection
Key idea
A sample is a subset observed from a broader target. How it was selected limits what can be generalized. A large sample can still be systematically unrepresentative; a small sample may be useful for a different purpose, such as early exploration.
Worked example
A voluntary online poll may describe respondents who chose to answer. It does not automatically represent everyone eligible to answer.
Check your understanding
Sample size alone does not remove selection bias.
Self-check: Which part is observation, which is interpretation, and what evidence would change the conclusion?
Reasoning: Name the claim’s scope, supporting source and one limitation before deciding how far it travels.
Limit: Sample size alone does not remove selection bias.
CHAPTER 04 · Statistical Reasoning: From Data to Decisions
Uncertainty and intervals
Key idea
An estimate is not the exact value of a broader quantity. Intervals can communicate uncertainty under stated assumptions. Their interpretation depends on the method and design; they are not guarantees about every future observation.
Worked example
Compare two plausible estimates and their uncertainty ranges before declaring a clear difference. Ask whether the design supports the comparison and whether the difference matters in practice.
Check your understanding
A confidence interval is not the probability that a fixed parameter lies in this one computed interval in the usual frequentist interpretation.
Self-check: Which part is observation, which is interpretation, and what evidence would change the conclusion?
Reasoning: Name the claim’s scope, supporting source and one limitation before deciding how far it travels.
Limit: A confidence interval is not the probability that a fixed parameter lies in this one computed interval in the usual frequentist interpretation.
CHAPTER 05 · Statistical Reasoning: From Data to Decisions
Association is not explanation
Key idea
Two variables can move together for many reasons, including a causal relationship, reverse direction, confounding, selection or coincidence. A causal claim needs a design and assumptions that address alternatives.
Worked example
If people who use a service report better outcomes, users and nonusers may differ before use. A comparison needs to address those differences before assigning an effect to the service.
Check your understanding
Correlation alone does not identify a cause.
Self-check: Which part is observation, which is interpretation, and what evidence would change the conclusion?
Reasoning: Name the claim’s scope, supporting source and one limitation before deciding how far it travels.
Limit: Correlation alone does not identify a cause.
CHAPTER 06 · Statistical Reasoning: From Data to Decisions
Communicate data honestly
Key idea
Use clear labels, units, scales, source notes, dates and a note about exclusions. Avoid truncated axes that exaggerate small differences and avoid decorative encodings that hide the actual quantity.
Worked example
A chart title should state the comparison, the vertical axis should name the measure and unit, and the note should identify the source and any transformation.
Check your understanding
This guide teaches reasoning; it is not statistical consulting for a high-stakes decision.
Self-check: Which part is observation, which is interpretation, and what evidence would change the conclusion?
Reasoning: Name the claim’s scope, supporting source and one limitation before deciding how far it travels.
Limit: This guide teaches reasoning; it is not statistical consulting for a high-stakes decision.
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