Paired T Test Calculator
Tests whether the population mean of paired differences is zero. The example keeps the method and inputs visible so the result can be checked independently.
Describe the observed sample before reporting
Paired t test
A controlled change to one input under the stated design
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. This check belongs before rounding.
If the interpretation reverses under a small defensible change, report that sensitivity. It is more informative than presenting one apparently exact test result. That step separates arithmetic from interpretation.
The numerical behavior of paired t test can also be checked at a boundary case. Equal group estimates should remove a reported difference, larger standard errors should widen uncertainty or weaken a test statistic, and larger independent samples should ordinarily reduce standard error when other inputs remain fixed.
For a different inferential question, compare one sample t test and welch two sample t test.
What the procedure returns in the worked condition
Tests whether the population mean of paired differences is zero. The displayed result follows t=d̄/(sd/√n), with every symbol tied to a labeled input. That distinction remains visible in the worked case.
The example produces t≈2.49 with 23 degrees of freedom and p≈0.020. This worked condition is a reproducible arithmetic check, not evidence that the model fits every dataset. This definition should travel with the copied result.
One reproducibility test is to rebuild paired t 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.
Scope of the inferential claim before the result is reused
The analysis unit is the pair; substituting separate-group standard deviations changes the test. The answer should retain that convention.
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. The calculation alone cannot supply that missing context.
Labels before arithmetic during independent review
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. A reviewer should not have to infer that choice.
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. The labeled fields make the assumption auditable.
Checking an intermediate quantity
Recalculate one intermediate quantity from t=d̄/(sd/√n) and then work backward from the displayed endpoint or statistic. This catches swapped groups, reversed quantiles, and copied denominators. The worked values provide a baseline for the comparison.
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 report should state this boundary plainly.
The inferential claim in context under the stated design
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 changed sample requires the same check again.
Practical importance requires the effect size, measurement scale, uncertainty, and consequences of a decision. A threshold crossing by itself does not supply that context. This point matters before the result enters another model.
Where another calculation belongs in the worked condition
Sparse cells, strong skew, influential observations, clustering, pairing, estimated nuisance parameters, or unequal variances can change the reference distribution. The analysis unit is the pair; substituting separate-group standard deviations changes the test. This prevents a plausible number from carrying the wrong meaning.
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. That is a design choice, not a display setting.
Before reporting the result before reporting
During an independent check, 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 paired t test.
When inputs are revised, why can another program give a different answer?
Tail conventions, critical values, continuity corrections, treatment of ties, and numerical approximations can differ. Preserve the stated method with the result. For this page, the reported quantity is paired t test.
When should paired t test be repeated?
Repeat it when an input, exclusion, group definition, confidence level, tail choice, or model assumption changes. For this page, the reported quantity is paired t test.