Reading your results

A results page puts the computed numbers first and the explanations after them. Everything above the AI interpretation is computed by Celeus’s engine by fixed rules, so the same run always shows the same numbers and the same wording. This page explains how to read each part.

The headline result

The headline line gives:

• n - the number of observations the analysis used, after any missing-data handling and population filter.
• The estimate - the size and direction of the effect the test measures, for example a difference in means, an odds ratio or a hazard ratio. Its label says which.
• The 95% confidence interval - the range of effect sizes compatible with your data at the 95% level. A narrow interval means a precise estimate; a wide one means the data pin the effect down only loosely.
• The p-value - how surprising data like yours would be if there were truly no effect. A small p-value is evidence against “no effect”. It is not the probability that the effect is real, and it says nothing about how large or important the effect is.
• The effect size - a standardized measure of magnitude, such as Cohen’s d, which lets you judge whether an effect is large enough to matter, independent of sample size.
• The seed - the fixed random seed the run used, so it can be repeated exactly.

Read the estimate and its interval first, then the p-value. A result can be statistically significant and too small to matter, or not significant and still compatible with an important effect when the interval is wide.

A descriptive analysis, such as a Table 1, has no p-value and says so.

Assumption checks

Every test relies on assumptions, such as normally distributed residuals, equal variances or proportional hazards. Celeus checks the ones that matter for the chosen test against your data and marks each as passed or to check.

A failed check does not invalidate a result by itself. It is a signal to look at the suggested alternative test, which the flags and the suitability panel point to. For some tests the alternative has already run beside the main one, as described next.

Pre-specified sensitivity analysis

For a few tests, Celeus fixes a second test in advance and runs it in the same run when your data depart from an assumption the main test relies on, and the second test’s own suitability grade for your data is higher than the main test’s:

• Welch’s or Student’s t-test, with the Mann-Whitney U test beside it, when the outcome fails the normality check.
• One-way ANOVA or Welch’s ANOVA, with the Kruskal-Wallis test beside it, when the outcome fails the normality check.
• Poisson regression, with negative binomial regression beside it, when the counts vary more than a Poisson model expects.

The test you configured stays the primary result. It is set by your study design and is never chosen from your data’s test results, so the second test cannot replace it after the fact. The second test is labelled pre-specified sensitivity: the rule that pairs the two was fixed before any result existed, and the configure step tells you before the run that it will happen.

The results page shows both tests with their roles, and one line on whether their p-values land on the same side of the significance level. Agreement means both tests point the same way at the significance level; it is reassuring, not proof that the assumption does not matter. Disagreement does not mean one test is right: a rank test answers a related but different question (whether values in one group tend to be larger than in another), so report both and read the difference as a sign that the conclusion depends on the assumption or on the question each test asks. The reproducible package records both tests, each with its own seed, and its script recomputes both.

When your data meet the assumption, nothing extra runs and the results page shows the single test. Paired t-tests and Pearson correlations are not paired this way: the signed-rank test’s own symmetry assumption tends to fail on exactly the data that would trigger it, and a failed normality check is not a sound reason to report Spearman beside Pearson. For those, the flags and the suitability panel still point to the alternative, and running it is your choice.

Warning flags

Flags are rule-based cautions raised from the run itself: a failed assumption, low statistical power, many rows dropped for missing data, a p-value close to the threshold. They are computed by the engine, not the AI, and they travel with the reproducible package, so a reviewer sees what you see.

Some flags come with a one-click follow-up, such as re-running with a different test or a different missing-data strategy. Every run stays in the record. Choose the test from the assumptions, not from the p-value you prefer.

When a non-significant result comes from a small study, a power flag says what size of effect the study could reliably have detected. That distinguishes “no effect” from “too little data to tell”.

With very small groups or very few pairs, a rank test such as Mann-Whitney or Wilcoxon signed-rank, computed exactly, may not be able to give a p-value below the significance level at all, however large the difference. The results page then notes that the design “cannot reach the significance level”. The analysis still ran correctly and the result is valid: a p-value above the level here is not evidence of no difference. Report the estimate with its confidence interval.

Suitability and the method decision

The suitability panel grades the chosen test and its alternatives from the assumption checks on your data: Recommended, Suitable, Use with caution or Not appropriate. The same data always get the same grade.

The method decision panel records how your choice compares with what Celeus’s advisor would have ranked first for this data. Choosing a suitable method that was not ranked first is a normal decision. If the advisor would not have suggested the method at all, the panel says so, and you should be ready to explain why it fits your design. When a pre-specified sensitivity test ran, the panel lists both tests with their roles, and the suitability panel says that the higher-graded test was run beside the primary rather than suggesting you run it.

What this means

The what this means card gives plain-language sentences computed from the results by fixed rules. They describe associations in this dataset, not causes, and they are not advice about any individual patient.

The AI interpretation

If you asked for one, the interpretation is written by the AI from the computed results and is marked as AI-written. It builds on the numbers above and never replaces them: if the two ever disagree, the numbers are right. Use it as a reading aid, and read the flags and assumption checks yourself.

Before you confirm

The verify before accepting banner asks you to check what was analyzed, the numbers and the flags. Confirming records on the run who reviewed it and when, and unlocks the package download. See Export results and the reproducible package.

Celeus analyzes research data. Its results describe your dataset; they are not a basis for diagnosing or treating an individual patient.