One Sample Sign Test Calculator
Counts observations above and below a hypothesized median and applies an exact two-sided binomial test. The example keeps the method and inputs visible so the result can be checked independently.
Describe the observed sample for the stated inputs
One-sample sign test
What moves when an input changes in the worked condition
Create a second scenario that changes one uncertain input rather than mixing optimistic values from unrelated cases. Compare both the center and the uncertainty or test statistic. A reverse calculation can expose an inconsistency here.
If the interpretation reverses under a small defensible change, report that sensitivity. It is more informative than presenting one apparently exact test result. This is where a group-order error is easiest to catch.
One reproducibility test is to rebuild one sample sign test from a saved input record without looking at the original answer. If the calculation cannot be recovered because a tail convention, critical value, degrees of freedom, pairing rule, or count definition is missing, the record is not yet complete.
The quantity being estimated before the result is reused
Counts observations above and below a hypothesized median and applies an exact two-sided binomial test. The displayed result follows exact binomial count above and below m0, with every symbol tied to a labeled input. The numerical precision does not override that requirement.
The example has four positive, two negative, and two tied observations; the exact p-value is 0.6875. This worked condition is a reproducible arithmetic check, not evidence that the model fits every dataset. This condition can be checked without relying on the final display.
Interpretation of one sample sign test should follow the design that produced the inputs. Random assignment, random sampling, repeated measurements, matched pairs, and convenience observations support different conclusions even when they happen to produce the same statistic on this page.
Conditions behind the reference model during independent review
Values exactly equal to the null median are omitted, so the effective sample size may be smaller than the entered list. This check belongs before rounding.
The unit of analysis, sampling frame, dependence structure, and treatment of missing values remain outside the final number. Record those choices before interpreting this test. That step separates arithmetic from interpretation.
Preparing the statistical inputs
Check that counts are whole observations, scales refer to the same measurement, and standard errors or deviations come from the population or sample named on the page. A percentage and a proportion differ by a factor of 100. That distinction remains visible in the worked case.
If a critical value is entered, it must match the intended tail convention and reference degrees of freedom. Changing confidence level without changing that value creates a mislabeled result. This definition should travel with the copied result.
For a different inferential question, compare kruskal wallis test and runs test for randomness.
Testing the expected direction under the stated design
Recalculate one intermediate quantity from exact binomial count above and below m0 and then work backward from the displayed endpoint or statistic. This catches swapped groups, reversed quantiles, and copied denominators. The answer should retain that convention.
Vary one credible input while holding the rest fixed. The direction and size of the change should agree with the formula before the result is carried into a report. The calculation alone cannot supply that missing context.
Statistical evidence and practical size in the worked condition
The p-value measures compatibility between the observed statistic and the null model. It is not the probability that the null hypothesis is true. A reviewer should not have to infer that choice.
Practical importance requires the effect size, measurement scale, uncertainty, and consequences of a decision. A threshold crossing by itself does not supply that context. The labeled fields make the assumption auditable.
Alternative models for different data before the result is reused
Sparse cells, strong skew, influential observations, clustering, pairing, estimated nuisance parameters, or unequal variances can change the reference distribution. Values exactly equal to the null median are omitted, so the effective sample size may be smaller than the entered list. The worked values provide a baseline for the comparison.
Do not choose among methods by selecting the answer that looks most favorable. Choose from the data-generating design, then preserve the method name and convention. The report should state this boundary plainly.
Before reporting the result for the stated inputs
When the sample changes, can a missing value be entered as zero?
Only when zero was observed. Missingness and a measured zero have different statistical meanings. For this page, the reported quantity is one-sample sign test.
For this result, does a narrow interval prove the estimate is unbiased?
No. Precision under a model does not repair selection, measurement, nonresponse, or specification bias. For this page, the reported quantity is one-sample sign test.
With the stated model, what belongs in a reproducible record?
Save the input summaries or data, unit of analysis, formula convention, exclusions, unrounded output, and software or table method used. For this page, the reported quantity is one-sample sign test.
In a reproducible analysis, what does the reported p-value mean?
It describes how unusual this statistic or a more extreme one would be under the stated null model; it is not the probability that the null is true. For this page, the reported quantity is one-sample sign test.