Methods

Confidence interval

A frequentist confidence interval is produced by a procedure designed to cover the fixed population parameter at a stated long-run rate under its assumptions. For a 95% procedure, about 95% of intervals from repeated applications would contain that parameter. The interpretation concerns the procedure, not a probability assigned to the parameter after observing this interval.

What does the interval show about estimation precision under the chosen procedure and model?

How it works

  1. Define the parameter, confidence level, and interval procedure. Check that the method reflects the sampling structure and outcome, rather than applying a familiar formula to every dataset.
  2. Compute the estimate and interval, then inspect whether assumptions and data problems undermine the procedure. Distinguish uncertainty about an average or effect from the much different task of predicting an individual observation.
  3. Report endpoints with units and explain which magnitudes remain compatible with the analysis. Consider practical thresholds across the interval instead of reducing interpretation to whether a null value is inside.

Evidence: (NIST/SEMATECH: Confidence Limits for the Mean, n.d.); (NIST/SEMATECH: What Are Confidence Intervals?, n.d.)

An interval for a memory-score difference

Teaching scenario

Synthetic example: A teaching worksheet supplies an invented interval from minus one to five remembered words for an average difference between two study routines. Students identify that the range includes small negative, zero, and positive differences, so its width matters to the interpretation. They must not say there is a 95% chance the fixed true difference lies between these realized endpoints, or that 95% of individuals benefit within this range. The numbers are classroom inputs, not a published finding, and are included only to practice reading an interval.

This example is constructed for learning. It does not report an observed research result.

What can you conclude?

Expresses estimation precision and the range of parameter values compatible with the interval procedure.

Evidence: (NIST/SEMATECH: Confidence Limits for the Mean, n.d.); (NIST/SEMATECH: What Are Confidence Intervals?, n.d.)

Limits and common mistakes

  • Coverage depends on the method and assumptions; an interval does not automatically account for selection bias or bad measurement.
  • A wide interval can leave consequential possibilities unresolved, even when the point estimate appears promising.

A mistake to catch

Describing a 95% frequentist interval as a 95% posterior probability for the fixed parameter, or as the spread of individual scores.

Evidence: (NIST/SEMATECH: Confidence Limits for the Mean, n.d.); (NIST/SEMATECH: What Are Confidence Intervals?, n.d.)

Sources and inspection notes

Links checked October 21, 2026. Inspection scope is stated for each source; an access date is not a publication date.

  1. NIST/SEMATECH: Confidence limits for the mean. (n.d.). https://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm

    Definition and confidence coefficient; assumptions for mean intervals Official statistical handbook. Supports repeated-sampling coverage and the fixed-parameter distinction. Opened and checked 21 October 2026.

  2. NIST/SEMATECH: What are confidence intervals? (n.d.). https://www.itl.nist.gov/div898/handbook/prc/section1/prc14.htm

    Confidence levels; one- and two-sided confidence intervals; unknown standard deviation Official statistical handbook. Supports interval construction and selected level, not an individual-person prediction interval. Opened and checked 21 October 2026.

Keep reading

Spielman, R. M., Jenkins, W. J., & Lovett, M. D. (2020). Psychology 2e. OpenStax. https://openstax.org/books/psychology-2e/pages/2-3-analyzing-findings

Nearest related OpenStax Psychology 2e reading. This is a course connection, not evidence for every specialist detail above.

Specialist reading: NIST/SEMATECH: What are confidence intervals? (n.d.). https://www.itl.nist.gov/div898/handbook/prc/section1/prc14.htm

Related methods

Try the methods · Read a study · Explore psychological measures