Life-science statistics with the depth of R,
and the ease of a wizard.

Every result is validated against R. Every statistical kernel is cross-validated against R 4.6.0 (metafor 5.0.1, survival 3.8.6, MatchIt 4.7.2, mice 3.19.0, robustbase 0.99.7, gsDesign 3.10.0, pwr 1.3.0, clinfun 1.1.5, lme4 2.0.1, geepack 1.3.13, cmprsk 2.2.12, MASS 7.3.65, car 3.1.5, rms 8.1.1, e1071 1.7.17, WINS 1.5.1, dagitty 0.3.4, brant 0.3.0, vcd 1.4.13, logistf 1.26.1, and 160 further packages), most recently on 2026-08-23. Re-run an analysis in R at these versions and you get the same numbers LunaStat reports.

Known differences from R:

• Fine and Gray competing-risks models when event times are tied: LunaStat matches R's standard competing-risks package (cmprsk), which handles tied event times the Breslow way, to about 1e-12. R's general Cox function defaults to a different tie handling; refitting that way moved a coefficient by about 0.001 on a dataset with 24 tied event times out of 139, and the gap GROWS as more events share a time, so data recorded by month or year is where it matters most. Without tied event times the two agree. To reproduce LunaStat's number in R, run cmprsk::crr.
• Tipping-point analyses, which compare two proportions: LunaStat compares the two proportions with a Pearson chi-square that has no continuity correction. R's two-proportion test applies one by default, which makes R's p-value larger. Measured on the committed tipping-point example (40 of 50 observed responders in the treated arm, 10 missing, against 30 of 50 in the control arm): the correction multiplies the p-value by 1.28 to 1.88 times across the sweep, and at three missing patients counted as non-responders it moves p from 0.0367 to 0.0601 -- across 0.05. The tipping point therefore moves by one patient: four on LunaStat's uncorrected test, three on R's default. Read the whole sweep rather than the single tipping number. To reproduce LunaStat's number in R, run prop.test(successes, totals, correct = FALSE).
• Cross-tabulations with small expected counts: When any expected count in the table falls below 5, LunaStat reports Fisher's exact test instead of the chi-square. R reports the chi-square with a warning and leaves the choice to you. To reproduce LunaStat's number in R, run fisher.test(table); to see R's chi-square, run chisq.test(table).
• Blank cells in a grouping column: A blank cell in a grouping column is treated as a missing value, not as a group of its own. R treats a blank in a text column as its own group, which means the blank can become the baseline that every reported effect is compared against. LunaStat reports how many blanks it read as missing in each column. To get R's behaviour, replace the blanks with a label such as "Unknown" before running the analysis, and that group will then be modelled.
• GEE models for clustered or repeated data: LunaStat and R's geepack solve the same equations with different code. Measured: coefficients and robust standard errors agree to about one part in a thousand, and the estimated within-cluster correlation to within about 0.05. To compare, fit the same model with geeglm().
• Group-sequential boundaries: agreement to 0.005 on the z-scale: LunaStat computes the stopping boundaries by its own exact integration and R's gsDesign by its own; the two agree to within 0.005 on the z-scale and within 0.005 on the alpha spent at each look. That is the accuracy two independent solutions of the same integral share, not a disagreement about the design. To reproduce, run gsDesign with the same spending function and compare the boundary table.
• Multiple imputation: the random draw is not reproducible across languages: Predictive mean matching fills each missing value by picking one of several similar patients at random, and LunaStat's random numbers are not R's -- so the filled-in values, and any result pooled from them, will not match R's run exactly, and would not match a second R run either. Everything that is NOT random is checked exactly: the model that chooses the candidates agrees with mice to 1e-10, the candidate list itself must be identical, and the arithmetic that combines the imputations (Rubin's rules and the Barnard-Rubin degrees of freedom) agrees with mice::pool to 1e-10. To compare, run mice with the same settings and compare the pooled standard errors and degrees of freedom rather than the imputed cells.
• Mixed models (repeated measures): LunaStat and R's lme4 use different optimizers for the same mixed model, so they stop at different answers. Measured against lme4: fixed effects agree to about 1 percent, variance components to about 5 percent, and the ICC to within 0.02. To compare, fit the same model with lmer() and expect agreement at that level rather than digit for digit.
• Nearest-neighbour matching: which pairs are formed: When two controls are equally close to a patient, LunaStat and R's MatchIt can pick different ones, so the individual pairs may not be identical. What the design is judged on does agree: balance after matching to within 0.05 and how many patients were kept to within 10 percent. To compare, run MatchIt with the same caliper and compare the balance table rather than the pair list.
• Ratio (1:k) matching: which controls are matched, and the weights: When each patient is matched to two or more controls, LunaStat and R's MatchIt can choose different controls, and a patient who finds fewer than k controls is weighted accordingly -- so the matched sets and their weights are not identical. What the design is judged on agrees: weighted balance after matching to within 0.06 and how many patients were kept to within 12 percent. Those bands are wider than for 1:1 matching. To compare, run MatchIt with ratio = k and the same caliper and compare the weighted balance table rather than the matched sets.
• Paired before-and-after tests when few patients changed category: When fewer than 25 patients change category between the two measurements, LunaStat reports the exact test instead of the chi-square, because the chi-square is unreliable at those counts. R does not switch on its own. To reproduce LunaStat's number in R, run binom.test(b, b + c, 0.5) on the two discordant counts; to get R's chi-square instead, turn the switch off in LunaStat.
• Robust outlier distances: LunaStat scales its robust outlier distances the way the method's original authors defined; R's robustbase uses a different published scaling. On contaminated data the two sets of distances differ by roughly 10 to 30 percent, and which points are flagged is usually the same. To compare like with like in R, rescale covMcd's distances so that their median matches the chi-square median.
• Welch t-test power: checked against a simulation, not a formula: R has no formula for the power of a Welch t-test, so LunaStat's value is checked against a simulation of the test in R -- 400,000 simulated trials per case -- and agrees to within 0.005 in power. The remaining difference is the simulation's own sampling error, not a difference in the calculation. To reproduce, simulate t.test(var.equal = FALSE) in R and compare the rejection rate.
• Propensity-score groups when a score falls exactly on a group boundary: LunaStat puts a patient into a propensity-score group by comparing their score with the group boundaries. R's MatchIt splits patients into near-equal group sizes instead. The two agree except for a patient whose score sits exactly on a boundary. Measured on a test cohort, four patients sat on a boundary and moved, and the shift in the balance measure stayed far below the 0.10 threshold that decides whether a design is usable, so the verdict cannot change. LunaStat's rule is the reproducible one: R's answer for a tied patient depends on the order the rows arrive in.
• Propensity-score groups that end up holding only one treatment arm: If a propensity-score group ends up with patients from only one arm, R's MatchIt moves patients across the boundary until it holds both. LunaStat does not. It leaves the groups where the scores put them, reports how many patients then contribute nothing, and marks the design unusable rather than letting one borrowed patient stand in for a whole arm. Measured on a 300-patient test cohort the two assignments differed by exactly one patient, and that patient carried 34 times the weight of a typical control while standing in for 26 treated patients. To see R's version, run MatchIt with method = 'subclass' and its default min.n = 1.
• Yeo-Johnson transformations: LunaStat and R's car package search for the transformation parameter with different optimizers, so the value can differ by up to 0.05. The underlying likelihood curve is checked against R's and agrees in shape. To compare, run car::powerTransform(..., family = 'yjPower').

The list above covers every deliberate difference from R that LunaStat has registered. Agreement elsewhere means agreement within the tolerance the comparator each analysis is tested against enforces: most are exact or near-exact, and a few (mixed models, GEE, robust outlier distances, transformation parameters) are checked to agree in character rather than to a fixed tolerance, because LunaStat and R solve those with different optimizers. Each of those carries its measured size in the list above.

4 further registered oracle-generation deviations exist that do not change any LunaStat number (secondary fits giving specific estimators their exact R targets); all are policed by an automated check that runs on every build.