IEU EVERYWHERE · OFFLINE PACK V1.0.0
Statistical Reasoning
Original IEU website project learning draft · all rights reserved · personal educational use. Prepared by IEU website project (educational draft; not faculty-reviewed). Not faculty-reviewed; no official academic credit.
Learning plan: read each section, complete the self-check in your own notes, then identify one remaining question. Approximate time: 25–40 minutes.
Data are observations with context
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.
Limit: A dataset is not a neutral window into reality; collection and inclusion rules shape it.
Describe distributions
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.
Limit: Do not choose a summary only because it makes a preferred result look stronger.
Samples and selection
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.
Limit: Sample size alone does not remove selection bias.
Uncertainty and intervals
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.
Limit: A confidence interval is not the probability that a fixed parameter lies in this one computed interval in the usual frequentist interpretation.
Association is not explanation
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.
Limit: Correlation alone does not identify a cause.
Communicate data honestly
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.
Limit: This guide teaches reasoning; it is not statistical consulting for a high-stakes decision.
Practice worksheet
- Write the central question in one sentence.
- Mark a supported observation and a separate interpretation.
- Name one important limitation.
- Identify one source or measurement to check next.
Further reading (internet required)
Credits and rights
IEU website project (educational draft; not faculty-reviewed) · Rights review is pending. All rights reserved; view/print for personal learning. Redistribution or adaptation requires written permission. External sources are linked and are not included in this ZIP. Internet is required to open them.
Version 1.0.0 · No ISBN, DOI or peer-review claim.