Is Yates's correction the same as Yates' correction?

Yes. These are possessive-spelling variants of the same statistical method in this glossary.

Does the correction always leave the conclusion unchanged?

No. It usually increases the approximate p-value and can change whether a chosen threshold is crossed.

Is Fisher's exact test merely another name for it?

No. Fisher's test uses a different reference calculation, with its own sampling interpretation.

AI Glossary / Statistics and probability / Intermediate

Yates's correction for continuity

Definition

Yates's correction for continuity is the conventional half-unit adjustment to cell deviations in a two-by-two Pearson chi-square test. It attempts to account for the discreteness of counts when using a continuous chi-square approximation. This spelling denotes the same method as “Yates' correction for continuity,” which is separately listed in the supplied glossary.

What it means

The method is encountered when comparing two binary classifications, for example experimental group and task success. It alters how far the observed table is treated as lying from the table expected under the null hypothesis of independence.

The adjustment typically makes the test less likely to reject than the uncorrected Pearson calculation. That can be useful to understand when reconciling reports, but it does not establish that the corrected result is always the most appropriate one. Choosing a method requires considering the design, available information and purpose of inference rather than treating a software default as a universal rule.

How it works

For a two-by-two table, first derive expected counts from the row and column totals under independence. Each cell's contribution to the uncorrected statistic is its squared observed-minus-expected difference divided by its expected count.

With Yates's correction, use the squared value of max(|observed − expected| − 0.5, 0) instead. Sum the four corrected contributions and use the one-degree-of-freedom chi-square reference for the approximate p-value. Keeping the adjustment no larger than the original deviation prevents overshooting the expected value. This computation assumes positive expected counts and does not replace checking whether the data support the intended independence test.

Three practical examples

1. Software reconciliation: A data team reproduces an old two-group report. It checks whether the original chi-square analysis applied the correction before attributing a discrepancy to a coding error.

2. AI user study: Researchers compare completed versus incomplete tasks between independent participant groups. They document the correction setting and report the completion-rate difference alongside the test.

3. Operational audit: A reviewer examines a pass/fail table and verifies that records represent independent units. The reviewer recognizes that continuity correction cannot repair repeated measurements incorrectly treated as unrelated observations.

Think of it this way

Think of rounding the distance between a discrete count and a smooth theoretical boundary slightly inward before judging how unusual it is. This modifies the comparison rule. It does not change the actual events, their observed proportions or the question of whether those events were collected in a valid study.

Worked example

Consider an original example with 20 independent users in each of two groups. Group A records 14 completions and six noncompletions; group B records six completions and 14 noncompletions. The row totals are 20 and 20, the column totals are 20 and 20, and the overall total is 40.

Every expected count is therefore 20 × 20/40 = 10. Each absolute deviation is four. Pearson's uncorrected statistic is 4 × 4²/10 = 6.4. Yates's correction reduces each deviation to 3.5, giving 4 × 3.5²/10 = 4.9.

The approximate corrected p-value from chi-square with one degree of freedom is 0.0269. The observed completion rates remain 70% and 30%. If a 5% test was prespecified, the corrected calculation rejects independence under the stated assumptions, but it does not quantify the probability that the interface caused the difference. The example demonstrates one table calculation, not a recommendation to choose a testing method after seeing its result.

Illustrative case study

In this fictional case, Hazel Design prepares a report on two independently assigned onboarding groups. Its analyst includes the counts, completion proportions and a clearly labeled continuity-corrected test. A reviewer reproduces the calculation and confirms that the correction was applied to cell deviations rather than to the total statistic.

The team discusses the observed size of the difference, study limitations and uncertainty rather than relying on the p-value alone. When a later study collects repeated attempts from each participant, it revises the analysis plan to account for dependence instead of applying the same simple table test without modification.

Common misconceptions and mistakes

Yates's correction is not a blanket correction for small samples, missing data or bias. It is also distinct from adding a small constant to every cell when estimating an odds ratio with a zero count. These operations have different purposes and formulas.

Do not confuse it with Yates analysis of factorial experiments. Do not use the word “exact” for the corrected chi-square p-value, because the reference remains asymptotic. The method can be conservative and is not always preferred. A nominal significance level does not automatically establish the actual false-positive rate for every finite table or sampling arrangement.

Business use

The main business benefit is better statistical communication and reproducibility. Teams often encounter historical reports, spreadsheet outputs and software packages that differ in whether they apply the correction. Naming the setting prevents avoidable disagreement about an otherwise identical analysis.

Preserve the original contingency table and clarify which population and comparison it represents. Report an interpretable effect measure and suitable uncertainty, then explain how the findings relate to the decision. A method choice that changes a threshold conclusion is a reason for careful interpretation and planning, not a reason to hide alternative calculations.

Check your understanding

Why is the expected count ten in every example cell?

Answer: Each cell's row and column totals are 20, and 20 × 20/40 = 10.

What is the corrected cell deviation?

Answer: Four minus one-half, or 3.5.

Does the corrected p-value change the observed 40-percentage-point completion difference?

Answer: No. The test calculation and the descriptive difference are separate quantities.

Related terms

Continuity correction
Odds ratio
Independence
Pearson statistic
two-by-two table
expected count
exact inference

Learn next

Next, reproduce the expected counts and corrected contributions without software. Compare the outcome with an uncorrected calculation and a method appropriate to the study's sampling design. Learn to recognize when paired or clustered observations require a different framework altogether.

Sampling design

Sources

The R documentation for chisq.test states the correction and its non-overshooting convention: https://stat.ethz.ch/R-manual/R-devel/library/stats/html/chisq.test.html

SciPy documents the corresponding continuity-correction option for the one-degree-of-freedom contingency-table test: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.contingency.chi2_contingency.html

The completion table and Hazel Design case are original teaching illustrations. This entry deliberately preserves the supplied alternate spelling; editorial navigation should cross-link the two names rather than present them as separate methods.

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