--- title: "Power and Effect Size, Decided Before the Data" description: "Plan power for a specified effect, test, variability and sampling design. Calculate sample size under stated assumptions, check sensitivity, and distinguish scientific importance from statistical sign" canonical: https://lightmysky.com/learn/science/power-and-effect-size-decided-before-the-data-mt_zYNmSWAJT8 source: https://lightmysky.com/learn/science/power-and-effect-size-decided-before-the-data-mt_zYNmSWAJT8.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Power and Effect Size, Decided Before the Data Plan power for a specified effect, test, variability and sampling design. Calculate sample size under stated assumptions, check sensitivity, and distinguish scientific importance from statistical significance. Subject: Science · Area: Scientific Inquiry · Ages 22 to 24 Page: https://lightmysky.com/learn/science/power-and-effect-size-decided-before-the-data-mt_zYNmSWAJT8 ## Ready when they can - Compute and round up sample size using a stated power formula and its assumptions - Explain why observed-effect power adds no independent evidence for the same fixed test - Explain how selecting significant results can exaggerate estimated effect magnitudes in low-power settings ## Lesson: Planning power before you collect data Power is the probability that a specified test rejects H0 at a specified true effect. Plan before collecting data using the test, significance level, variability and sampling design. As in the previous topic, distinguish assigned units from repeated readings and account for grouping. Planned power depends on assumptions and does not guarantee one study's result. For independent normal observations with known standard deviation sigma, test H0: mu = mu0 against mu > mu0. For a target shift delta = mu - mu0 > 0, use n = ceil[((z_a + z_p) sigma / delta)^2]. Ceil means round up. z_a sets the significance threshold; z_p sets target power. For alpha 0.05 and power 0.80, use rounded constants 1.645 and 0.842. Other tests and grouped designs need different calculations. *(drawing: This calculation assumes the stated normal model, known sigma, alpha 0.05 and target power 0.80.)* Under this model, more independent observations or lower variability raise power at a fixed positive effect and alpha. A larger target effect needs fewer observations at fixed power. Effect size can use original or standardized units. A small p-value does not establish practical importance. Compare the estimated magnitude and interval with a justified scientific threshold. Observed power substitutes the observed effect into a power calculation. For the same fixed test and assumptions, it is tied to the test result and adds no independent evidence. After a study, examine the estimate and interval. Later planning can still use scientifically chosen effects to assess a new design; it need not reuse the observed effect. *(drawing: The target effect is a planning choice. The estimated effect comes from the data.)* When power for a small true effect is low, selecting significant results can favor unusually large estimated magnitudes. Under common sampling models, selected magnitudes can exceed the true magnitude on average. This does not mean every significant estimate is inflated. Check uncertainty and selection risks, and seek independent replication. Choose the smallest scientifically useful effect, then vary plausible effects and variability in planning. In the stated formula, halving delta multiplies the unrounded sample size by four. Sensitivity shows dependence on assumptions, not broken arithmetic. Sizing a replication around an inflated selected estimate can give too small a sample for a more modest true effect. **Recap.** Plan for a specified effect and design. Check assumptions, round sample size up, and interpret estimates and uncertainty separately from significance. *Original lesson, questions and flashcards about power planning, written for this learning dataset.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Pseudoreplication: When n Is Smaller Than It Looks](https://lightmysky.com/learn/science/pseudoreplication-when-n-is-smaller-than-it-looks-mt_2gRWB6RTaI) - [Errors, Power and the Design of a Test](https://lightmysky.com/learn/mathematics/errors-power-and-the-design-of-a-test-mt_D7ZXbvSD0l) ## Opens up - [Researcher Degrees of Freedom and the Pre-registered Analysis Plan](https://lightmysky.com/learn/science/researcher-degrees-of-freedom-and-the-pre-registered-analysis-plan-mt_UJgZQ2AADm)