Reporting Statistical Results

Core Concept: What Does Full Reporting Mean?

Reporting a statistical result is more than writing a p-value. A complete report includes: (1) the name of the test used (e.g., independent-samples t-test), (2) the test statistic with its degrees of freedom (e.g., t(48) = 2.34), (3) the exact p-value (e.g., p = .021, not just p < .05), (4) an effect size measure (e.g., Cohen d or eta-squared), and (5) the 95% confidence interval. These five elements together allow readers to judge both the statistical and practical significance of a finding independently.

Why Effect Size and Confidence Interval Are Essential

A p-value only indicates how incompatible the data are with the null hypothesis; it does not convey the size or importance of an effect. Effect size measures (Cohen d, r, eta-squared, odds ratio, etc.) express the magnitude of a difference in standardized units. The confidence interval shows the plausible range for that magnitude and makes uncertainty visible. For example, d = 0.20 is typically small and d = 0.80 large. Reporting significance alone can make trivial differences look meaningful in large samples; effect sizes prevent this misinterpretation.

Common Misuses and Misconceptions

The most frequent errors include: writing only p < .05 without the exact value; omitting effect sizes entirely; misinterpreting p-values as proof that the null is true or false; treating a non-significant result as evidence of no effect (absence of evidence is not evidence of absence); and restating table contents verbatim in the text. Writing p = .000 is incorrect; the proper form is p < .001. A common but mistaken interpretation of confidence intervals is that a specific interval has a 95% chance of containing the parameter; correctly, 95% of intervals produced by the same procedure will contain the true value.

Reporting Format and Practical Recommendations

Style guides such as APA 7th edition standardize reporting format. Group comparisons must include means and standard deviations (e.g., M = 4.32, SD = 0.87), and tables should not duplicate the text. A well-formed comparison sentence reads: The experimental group scored significantly higher than the control group, t(58) = 3.12, p = .003, d = 0.79, 95% CI [0.42, 1.16]. In regression analyses, R-squared and coefficient confidence intervals should be reported. Figures and tables should provide additional information, not merely repeat what the text already states. Researchers are advised to also consult the reporting requirements of their target journal.

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