Method reference

One page for each of the 39 statistical methods Celeus runs. Not sure which one fits your question? Start with choosing a method.

Comparing groups

• Welch's t-test - Two independent groups, continuous outcome, unequal variances (default two-group test).
• Student's t-test - Two independent groups, continuous outcome, equal variances assumed.
• Paired t-test - Two paired/repeated continuous measurements, normal differences.
• Mann-Whitney U test - Two independent groups, continuous/ordinal outcome, non-normal.
• Wilcoxon signed-rank test - Two paired measurements, non-normal differences.
• One-way ANOVA - 3+ independent groups, continuous outcome, equal variances.
• Welch's ANOVA - 3+ independent groups, continuous outcome, unequal variances.
• Kruskal-Wallis test - 3+ independent groups, continuous/ordinal outcome, non-normal.
• Repeated-measures ANOVA (Greenhouse-Geisser) - Continuous outcome measured on the SAME subjects across the levels of a within-subject factor (e.g. pre / post / follow-up). Classic repeated-measures ANOVA with a sphericity correction; for unbalanced or missing data prefer the linear mixed model.
• ANCOVA (analysis of covariance) - Compare a continuous outcome across 2+ groups while adjusting for one or more covariates (e.g. a baseline/pre-treatment value, age, sex).
• Two-way ANOVA (factorial) - A continuous outcome and TWO categorical factors (2+ levels each): tests each factor's main effect and whether the two factors INTERACT (whether one factor's effect on the outcome depends on the level of the other).

Association and correlation

• Chi-squared test of association - Association between two categorical variables, adequate expected counts.
• Fisher's exact test - Association between two categorical variables, small expected counts.
• Pearson correlation - Linear association between two continuous variables.
• Spearman correlation - Monotonic association between two continuous/ordinal variables.
• McNemar's test - Two paired binary measurements on the SAME subjects (e.g. before/after, two raters on one occasion): tests whether the proportion changes.

Regression

• Linear regression - Model a continuous outcome from predictors, adjusting for covariates.
• Logistic regression - Model a binary outcome from predictors, adjusting for covariates.
• Firth penalised logistic regression - Model a binary outcome when ordinary logistic regression breaks down: a predictor that perfectly (or almost perfectly) separates the outcome, or very few events per predictor. Firth's penalised likelihood returns FINITE odds ratios with profile-likelihood confidence intervals where the ordinary fit runs off to infinity.
• Poisson regression - Model a COUNT outcome (non-negative integers, e.g. number of events) from predictors; assumes the variance equals the mean.
• Negative-binomial regression - Model a COUNT outcome when its variance exceeds its mean (overdispersion), relaxing Poisson's equal-mean-variance assumption.
• Ordinal logistic regression - Model an ORDERED categorical outcome (3+ ordered levels, e.g. low/medium/high) from predictors via proportional-odds logistic regression.
• Multinomial logistic regression - Model an UNORDERED categorical outcome with 3+ levels (e.g. treatment A/B/C, no natural order) from predictors, reporting an odds ratio per predictor for each outcome level vs a reference level.
• Factors associated with outcome (continuous outcome) - Which of 2-30 candidate factors are associated with a CONTINUOUS outcome: the full multivariable model with every candidate is the primary result, with per-factor tests (Benjamini-Hochberg adjusted), correlations and collinearity, and an exploratory LASSO layer reporting how often each factor is selected across 200 bootstrap resamples.
• Factors associated with outcome (binary outcome) - Which of 2-30 candidate factors are associated with a BINARY outcome: the full multivariable logistic model with every candidate is the primary result, with per-factor likelihood-ratio tests (Benjamini-Hochberg adjusted), correlations and collinearity, and an exploratory LASSO layer reporting how often each factor is selected across 200 bootstrap resamples.

Mixed-effects models

• Linear mixed-effects model (random intercept) - Continuous outcome with repeated or clustered measurements (multiple rows per subject or site): fixed-effect predictors plus a per-cluster random intercept.
• Mixed-effects logistic regression (random intercept) - Binary outcome with repeated or clustered measurements: odds ratios for predictors plus a per-cluster random intercept.
• Mixed-effects Poisson regression (random intercept) - Count outcome with repeated or clustered measurements: rate ratios for predictors plus a per-cluster random intercept.

Survival and censored data

• Peto-Peto generalized Wilcoxon test - Compare a censored continuous outcome across 2+ groups when detection limits overlap observed values (not rank-determinable).
• Censored regression (Tobit-style) - Model a censored continuous outcome from predictors without substituting detection limits (lognormal or gaussian error distribution).
• Kaplan-Meier (log-rank test) - Time-to-event outcome (a time column + a 0/1 event indicator): compare survival between groups (KM curves + log-rank test).
• Cox proportional-hazards regression - Time-to-event outcome (time + 0/1 event): hazard ratios for predictors, adjusting for covariates.
• Weibull accelerated failure time regression - Time-to-event outcome (time + 0/1 event): time ratios for predictors (how much they stretch or shrink expected survival time) - an accelerated failure time model that reports time ratios instead of Cox's hazard ratios and assumes Weibull-distributed event times.
• Factors associated with outcome (time-to-event outcome) - Which of 2-30 candidate factors are associated with a TIME-TO-EVENT outcome (time + 0/1 event): the full Cox model with every candidate is the primary result, with per-factor likelihood-ratio tests (Benjamini-Hochberg adjusted), correlations and collinearity, and an exploratory LASSO layer reporting how often each factor is selected across 200 bootstrap resamples.

Diagnostic accuracy and agreement

• ROC curve / AUC - How well a CONTINUOUS score/marker discriminates a BINARY gold-standard outcome: the ROC curve, area under the curve (AUC) with a DeLong confidence interval, and the Youden-optimal cutoff with its sensitivity/specificity.
• Diagnostic accuracy (2x2) - Agreement of a BINARY test against a BINARY gold standard: sensitivity, specificity, PPV, and NPV (each with a confidence interval), the 2x2 counts, and disease prevalence.
• Bland-Altman agreement - Agreement between two NUMERIC measurements of the same quantity (method comparison): bias (mean difference) and 95% limits of agreement, each with a confidence interval.
• Compare two ROC curves (DeLong) - Which of TWO continuous scores/markers better discriminates the SAME binary gold-standard outcome: each marker's ROC AUC with a DeLong confidence interval, and DeLong's test for the difference between the two correlated (paired) AUCs.

Descriptive

• Descriptive table (Table 1) - Describe the whole dataset: every variable summarised on its own terms (median [Q1, Q3] or mean (SD), chosen per variable), counts with confidence intervals for proportions, and a missingness row - optionally split by one grouping variable. No hypothesis is tested.