Statistical Tests

Licklider selects the correct inferential test automatically — with broad coverage of parametric methods (t-tests, ANOVA, regression, post-hoc, etc.). Rank-based (non-parametric) methods appear in selection guidance and labels, but do not currently have a verified end-to-end public stats-engine path — see Non-Parametric Alternatives.

Overview

Choosing the wrong statistical test is one of the most common errors in published research. Licklider eliminates this risk by profiling your dataset before analysis begins, asking targeted questions about your experimental design, and applying a deterministic decision tree to select the appropriate test.

The selection process is transparent: every decision is explained in plain language alongside the technical justification, so reviewers and collaborators can audit the methodology.

Automatic Test Selection

The decision engine considers the following factors in order:

• Number of groups being compared (2 vs. 3+)
• Independence of observations (paired vs. unpaired)
• Distributional assumptions (normality, homoscedasticity)
• Sample size per group (affects power and fallback strategies)
• Presence of covariates or repeated measures

Parametric Tests

When distributional assumptions are met, Licklider applies parametric tests that maximize statistical power:

• Independent samples t-test (Welch's) — two unpaired groups, unequal variance is assumed by default
• Paired t-test — two matched samples, crossover or pre/post designs
• One-way ANOVA — three or more independent groups
• Repeated measures ANOVA — within-subject designs with multiple timepoints
• Two-way ANOVA — factorial designs with interaction terms
• Pearson correlation — linear association between continuous variables
• Linear regression — continuous outcome with one or more predictors

Non-Parametric Tests

The decision layer may reference distribution-free alternatives when assumptions are weak (e.g. Mann–Whitney, Wilcoxon, Kruskal–Wallis). Those names appear in selection metadata and documentation. They are not guaranteed to run as a dedicated rank-based engine route in the current product. Use Non-Parametric Alternatives for methodology guidance.

• Spearman correlation — monotonic association (where exposed for correlation workflows)
• Rank-based group comparisons — conceptual counterparts include Mann–Whitney, Wilcoxon, Kruskal–Wallis, Friedman; execution scope is limited — see the guidance page above

Multiple Comparisons

When a significant omnibus parametric test (e.g. ANOVA) is followed by pairwise comparisons, Licklider applies correction for familywise error rate where supported:

• Holm-Bonferroni — default for most pairwise comparisons; controls FWER with higher power than standard Bonferroni
• Tukey's HSD — all pairwise comparisons with equal group sizes
• Dunnett's test — comparisons against a single control group
• Benjamini-Hochberg — available for exploratory analyses where FDR control is more appropriate than FWER

Output Format

Every test result is reported in a structured format that matches journal submission requirements:

• Test statistic (t, F, U, χ², etc.) with degrees of freedom
• Exact p-value (not rounded to <0.05 or <0.001)
• 95% confidence interval on the mean difference or effect
• Effect size with interpretation (small / medium / large by convention)
• Sample sizes per group

Results are embedded directly in the figure legend and in a downloadable methods summary that can be pasted into a manuscript's Statistical Analysis section.