Glossary

Short definitions of the terms you will meet in Celeus, its results pages and its guides. Each entry links to a page that uses the term in context. For help choosing an analysis, see the method guides and the method reference.

Alpha (significance level)

The false-positive rate a test is allowed, chosen before the data are seen: the probability of rejecting the null hypothesis when it is true. It is usually 0.05, so a p-value below 0.05 is called statistically significant, and about 1 in 20 tests of a true null hypothesis will come out significant by chance alone. Lower it when many tests are run together. See Type I and type II errors and Multiple comparisons.

Assumption checks

Tests and diagnostics that ask whether the data fit what a statistical method assumes, such as normality or equal variances. A failed check does not make a result wrong by itself, but it can mean another method answers the question more reliably. Celeus runs the checks that belong to each method and shows their outcomes with the result. See Reading your results.

Audit trail

A record of what was done, by whom and when, kept so that it can be checked later. Celeus keeps two: a tamper-evident activity trail for each workspace, which records actions and never data values, and an audit log inside each run’s reproducible package, which records that run’s steps, including each prompt sent to the AI. See The audit trail.

Bonferroni correction

A way to control false positives when several tests are run together: each p-value is compared with the significance level divided by the number of tests. It is simple and always valid, but it becomes conservative as the number of tests grows. See Multiple comparisons.

Censoring

An observation is censored when its exact value is only partly known. In time-to-event data, a participant who leaves the study or reaches its end without the event is right-censored: they are known to have lasted at least that long. A measurement reported as below a detection limit is left-censored. See Kaplan-Meier and Cox regression and values below the detection limit.

Chi-square test

A test of whether two categorical variables are associated, computed from a table of counts. It compares the observed counts with the counts expected if the variables were independent, and relies on a large-sample approximation that can be poor when expected counts are small. See Chi-square vs Fisher’s exact test and the chi-square method page.

Cohen’s d

A standardized effect size for a difference in means: the difference divided by a standard deviation. Because there are several choices of standard deviation, a report should say which one was used. See Paired t-test vs Wilcoxon.

Complete-case analysis

Analysing only the rows that have no missing values in the variables the analysis uses. It is simple and unbiased when data are missing completely at random, but it discards information and can be biased otherwise. See Handle missing data.

Confidence interval

A range of values for an estimate, such as a difference in means, computed so that the procedure captures the true value in a stated share of repeated studies, usually 95%. A narrow interval means a precise estimate; a wide one means the data leave the size of the effect uncertain. See Reading your results.

Cox regression

A model for time-to-event data that relates the hazard of the event to one or more predictors without specifying the shape of the baseline hazard. Its results are hazard ratios, and it assumes proportional hazards. See Kaplan-Meier and Cox regression and the Cox method page.

De-identification

Removing or transforming the parts of a dataset that identify individuals, such as names, record numbers and exact dates. In Celeus you review the identifier scan’s findings and choose what happens to each flagged column. See The identifier scan and de-identification.

Degrees of freedom

The number of independent pieces of information left for estimating variability once the quantities a statistic depends on have been estimated. A one-sample t-test on 20 values has 19 degrees of freedom, because estimating the mean uses one up. They decide which t, F or chi-square distribution a test statistic is compared with, so the same statistic gives a different p-value at different degrees of freedom. See How to find a p-value from a test statistic.

Effect size

How large a difference or association is, as opposed to whether it is statistically significant. It can be in the original units, such as a difference in means, or standardized, such as Cohen’s d. A tiny p-value can go with a trivial effect, so report both. See Reading your results.

Eta squared

An effect size for analysis of variance: the share of the total variation in the outcome that is explained by group membership. It runs from 0 to 1, and in small samples it tends to overstate the effect. See the one-way ANOVA method page.

Expected count

In a table of counts, the number of observations a cell would hold if the row and column variables were independent: row total times column total, divided by the grand total. Small expected counts are what make the chi-square approximation unreliable. See Chi-square vs Fisher’s exact test.

False discovery rate

The expected share of false positives among the results declared significant. Controlling it, for example with the Benjamini-Hochberg procedure, keeps more power than controlling the chance of any false positive at all, at the cost of accepting a few. See Multiple comparisons.

Fisher’s exact test

A test of association in a table of counts that computes the p-value from an exact distribution instead of a large-sample approximation. It stays valid when expected counts are small. See Chi-square vs Fisher’s exact test and the Fisher’s exact method page.

Hazard ratio

The ratio of the event rates in two groups at any moment, as estimated by Cox regression. A hazard ratio of 2 means the event happens at twice the rate in one group as in the other, among those still at risk. It is a ratio of rates, not of probabilities or survival times. See Kaplan-Meier and Cox regression.

Holm correction

A step-down version of the Bonferroni correction. The p-values are sorted and compared with gradually less strict thresholds, which gives the same protection against any false positive while rejecting at least as many hypotheses as Bonferroni. See Multiple comparisons.

Identifier

A value that points to a specific person, such as a name, a medical record number, a phone number or a full date of birth. Some identify a person on their own; others do so in combination with other columns. See what the identifier scan looks for.

Interquartile range

The spread of the middle half of the data: the third quartile minus the first, usually reported with the median, the middle value. For daily ozone readings whose quartiles are 18 and 63.25 parts per billion, the interquartile range is 45.25. A few extreme values barely move it, which makes the median and interquartile range the better summary for skewed data, and it is the basis of the 1.5 times IQR fences used to flag values for checking. See Interquartile range and The IQR rule.

Kaplan-Meier estimator

A way to estimate the share of a group that is still free of the event over time, from data where some observations are censored. It is usually drawn as a step-shaped survival curve. See Kaplan-Meier and Cox regression and the Kaplan-Meier method page.

Kruskal-Wallis test

A rank-based test that compares three or more independent groups, used instead of one-way analysis of variance when a rank-based comparison fits the data or the question better. See Multiple comparisons and the Kruskal-Wallis method page.

Limit of detection

The lowest concentration a laboratory method can reliably tell apart from zero. Values below it are reported as “below the limit” rather than as a number, and are best analysed as censored values instead of being replaced with a guess such as half the limit. See Values below the detection limit.

Limited Data Set

A term from US health-privacy rules for health data that has had direct identifiers removed but keeps some details, such as dates. It is still protected health information and may be disclosed for research, public health or health care operations only under a data use agreement. Celeus treats and labels a dataset with shifted dates as a Limited Data Set, not de-identified data. Whether it legally qualifies depends on the rest of the dataset. See Shifting dates.

Linkage key

A file that maps each pseudonymous code back to the original value it replaced. In Celeus it is an optional download when you pseudonymize a column. It is not stored by Celeus or put in the reproducible package, so keep it somewhere separate and access-restricted. Without it, your original file is the only way back. See Coded stand-ins and the linkage key.

Log-rank test

A test of whether two or more survival curves differ, comparing the number of events seen in each group with the number expected if the groups had the same hazard. It is most sensitive when the hazards stay proportional over time. See Kaplan-Meier and Cox regression.

Logistic regression

A model for a yes-or-no outcome that relates the log odds of the outcome to one or more predictors. Its coefficients are usually reported as odds ratios. See Logistic regression and the logistic regression method page.

Mann-Whitney U test

A rank-based test for two independent groups, also called the Wilcoxon rank-sum test. It asks whether a value from one group tends to be larger than a value from the other, which is not the same question as whether the means differ. See t-test vs Mann-Whitney.

Missing at random

An assumption about missing data: whether a value is missing may depend on other variables that were observed, but not on the missing value itself. Multiple imputation is valid under this assumption. It cannot be proven from the data alone. See Handle missing data.

Multiple comparisons

Running many tests on the same data. Each test carries its own chance of a false positive, so the chance of at least one grows with the number of tests unless it is controlled. See Multiple comparisons.

Multiple imputation

Filling in missing values several times, each time drawing from a model of the other variables, analysing each completed dataset and pooling the results. The pooled standard errors reflect the uncertainty about the missing values. See Handle missing data.

Normality

Whether data, or a model’s residuals, follow a normal (bell-shaped) distribution. Many methods assume it, but with larger samples the t-test and related methods are fairly robust to departures from it. See t-test vs Mann-Whitney.

Null hypothesis

The default claim a statistical test assesses, usually “no difference” or “no association”. A test asks how surprising the data would be if the null hypothesis were true. Failing to reject it is not evidence that it is true. See t-test vs Mann-Whitney.

Outlier

A value far from the rest of the data. Being extreme is not a reason to remove it: a value that is impossible or mis-recorded, such as an age of 230 years, is corrected or excluded; a unit from outside the population studied is excluded under a rule written before the results are seen; and a genuine extreme value is kept, with a method that is not driven by it if needed. See How to handle outliers before a statistical test and The IQR rule.

P-value

The probability of results at least as extreme as those observed, if the null hypothesis were true. A small p-value means the data would be unusual under the null hypothesis. It is not the probability that the null hypothesis is true, and it says nothing about the size of an effect. See Reading your results.

Paired t-test

A test of whether the mean difference between two paired measurements, such as before and after on the same participants, is zero. Pairing removes the variation between participants from the comparison. See Paired t-test vs Wilcoxon and the paired t-test method page.

PHI

Protected health information: health information that can be linked to an individual, as defined by US health-privacy rules. Names, record numbers, contact details and dates finer than a year are typical examples. See The identifier scan and de-identification and What we send to the AI.

Post-hoc test

A follow-up comparison run after an overall test, such as analysis of variance, has found a difference, to see which groups differ from which. Because it makes several comparisons, it needs a correction for multiple comparisons. See Multiple comparisons.

Power

The probability that a study detects an effect of a given size, if that effect is real. It depends on the sample size, the variability of the data and the significance level. Celeus reports the smallest effect the study could reliably have detected (for the tests where this can be calculated), rather than a power value computed from the observed effect. See Reading your results.

Proportional hazards

The assumption behind Cox regression that the hazard ratio between groups stays constant over time. When it does not hold, a single hazard ratio can mislead, and the assumption should be checked. See Kaplan-Meier and Cox regression.

Pseudonymize

Replace every value in a column with a code. In Celeus the codes look like subj-001 and are assigned in order of first appearance, so the same value always gets the same code within that column and the code is not derived from the value. The new version holds only the codes. See Coded stand-ins and the linkage key.

Reproducible package

The zip file every finished Celeus run produces: the analysis plan, results, methods text, audit log, session information, pinned package versions and an R script that re-runs the analysis. See The reproducible package.

Safe Harbor

One of the two methods US health-privacy rules give for de-identifying health data: removing a defined list of identifier types, such as names, geographic detail smaller than a state and dates finer than a year. Celeus’s identifier scan checks columns against those categories. A scan is not a legal determination, because a dataset can still fail Safe Harbor for reasons a column scanner cannot see. See What this is not.

Sample size

The number of independent units, such as participants, plots or samples, that an analysis uses, usually written n. Repeated measurements of one unit do not add to it. It sets how precisely an effect is estimated and how likely a real effect is to be detected: the standard error of a mean shrinks with the square root of n, so going from 25 to 100 units halves it. Plan it before collecting data, from the smallest effect worth detecting. See Power and Standard error of the mean.

Seed

The starting number for a computer’s random number generator. With the same seed, a step that uses randomness, such as multiple imputation, produces the same result every time. Celeus records the seed of every run. See Determinism and reproducibility.

Standard deviation

How spread out the individual observations are around their mean, in the data’s own units, computed for a sample with n minus 1 in the denominator. In a worked example of 100 quiz score changes, the mean is 2.13 points and the standard deviation 12.80 points. It describes the data, not how precisely the mean is known; that is the standard error. See Standard deviation.

Standard error

How precisely a statistic, usually a mean, is estimated: how much it would vary across repeated samples. For a mean it is the standard deviation divided by the square root of the sample size, so a standard deviation of 12.80 points over 100 units gives a standard error of 1.28 points. Use it, or better a confidence interval, to describe precision, never to describe how variable the units are. See Standard error of the mean.

Student’s t-test

A test of whether two independent groups have the same mean, assuming the two groups have equal variances. When that assumption is doubtful, Welch’s version is the safer choice. See t-test vs Mann-Whitney and the Student’s t-test method page.

Variance

The average squared distance of the values from their mean, with n minus 1 in the denominator for a sample: the standard deviation squared. Its units are squared, so a standard deviation of 12.80 points is a variance of about 164 squared points, which is why papers report the standard deviation instead. Variance stays in the working, because variances of independent quantities add and analysis of variance compares them. See Variance and Homogeneity of variance.

Welch correction

An adjustment to the t-test, and to one-way analysis of variance, that estimates each group’s variance separately and adjusts the degrees of freedom, so the test no longer assumes equal variances. It loses little when the variances are in fact equal. See t-test vs Mann-Whitney and the Welch t-test method page.

Wilcoxon signed-rank test

A rank-based test for paired measurements that asks whether the differences within pairs are centred on zero. It is an alternative to the paired t-test when the differences are far from normal. See Paired t-test vs Wilcoxon and the Wilcoxon signed-rank method page.