Important
- Interpretation of Results – The results section must remain purely objective, reporting only the analyses run and the statistical outcomes; all interpretation, speculation, and connections to theory must be reserved for the Discussion section,,.
- APA Formatting for Statistics – Statistical letters (such as F and p) must be italicised, whereas numbers and Greek letters (such as η) are not; failure to italicise correctly will result in a deduction of marks,.
- Reporting P-Values – Exact p-values should be reported to three decimal places unless the value is less than .001, in which case it is written as < .001; a leading zero should be omitted for values that cannot exceed 1 (e.g., .032 rather than 0.032),.
- Reporting Interactions – In a factorial ANOVA, the interaction must be reported first; if the interaction is significant, it serves as the primary focus and should be followed by simple effects analyses rather than relying solely on main effects,,.
- Placement of Tables and Figures – Tables and figures must be explicitly referred to in the text (e.g., “see Table 1”) and must appear immediately after the paragraph in which they are first mentioned,.
- Effect Sizes in ANOVA – Effect sizes (such as partial eta squared) are required when reporting the omnibus ANOVA results but are not necessary for the follow-up simple effects analyses,.
Core Concepts
- Structure of a Results Paragraph: A standard formula for reporting statistics that begins by naming the test and variables, reporting the interaction (including test statistic, degrees of freedom, p-value, and effect size), and concluding by describing the pattern of results using means,.
- Estimated Marginal Means (EMMs): A method for reporting means that corrects for unbalanced data or confounding variables; these are generally considered best practice and preferred over observed means for ANOVA reporting, though they are often similar in balanced designs,.
- Multiple Comparisons: The statistical problem wherein conducting multiple tests increases the likelihood of false positives (Type 1 errors); this is managed using corrections such as Bonferroni or Benjamini-Hochberg,.
- Effect Sizes: Quantitative measures that indicate the magnitude of an effect independent of sample size, specifically Cohen’s d for t-tests and Partial Eta Squared ($η_p^2$) for ANOVAs,.
- Main Effects: The overall effect of one independent variable on the dependent variable, averaging across the levels of any other independent variables,.
- Interactions: A statistical result indicating that the effect of one independent variable changes or depends on the level of another independent variable.
- Simple Effects Analysis: A follow-up procedure used when a significant interaction is present, involving the testing of one independent variable at each specific level of the other independent variable to understand the interaction pattern,.
- Within vs Between Subjects Variables: A classification of study design where ‘within-subjects’ means participants experience all levels of a variable, and ‘between-subjects’ means participants are assigned to only one level; this distinction dictates whether a repeated measures or independent test is used,.
- Visualisation Standards: Guidelines for figures requiring clear axes labels, units of measurement, simple legibility, and legends if multiple conditions are displayed; figures should visually support the statistical claims,.
- The “Family” of Tests: A set of statistical tests that all address the same underlying hypothesis, which is the unit of analysis when applying corrections for familywise error rates.
Theories and Frameworks
- Signal-to-Noise Ratio: A conceptual framework for understanding test statistics (like the t-statistic) where the variance explained by the model (the effect) is divided by the unexplained variance or error (the noise).
- Familywise Error Rate (FWER): A statistical control framework designed to keep the probability of making at least one Type 1 error across a “family” of related tests at 5%, often achieved via the Bonferroni correction,.
- False Discovery Rate (FDR): An alternative framework to FWER that ensures that among all significant results (discoveries), only a specific proportion (e.g., 5%) are false positives; this is often controlled using the Benjamini-Hochberg method.
Notable Individuals
- Benjamini & Hochberg: Developers of a statistical correction method that controls the False Discovery Rate, which is less conservative than Bonferroni.
- Cohen: Statistician associated with “Cohen’s d,” a standard measure for effect size in t-tests representing the difference between groups in standard deviations.
- Butler: Researcher (2020) cited in a student example regarding a study linking Tetris gameplay to increased hippocampal volume.