Paired T Test Calculator
Tests whether the population mean of paired differences is zero. The form displays t=d̄/(sd/√n) beside paired t test, using a worked condition that can be recalculated with the labeled inputs.
Describe the observed sample before reporting
Paired t test
Scope of the paired t test method
The paired t test page tests whether the population mean of paired differences is zero.
Paired t test is limited to the statistical quantity named by the result panel. The paired t test calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
Reading the paired t test fields
- Mean paired difference: For paired t test, the worked value for mean paired difference is 2.8. Treat the mean paired difference entry (2.8) explicitly as a count, proportion, rate, estimate, or model parameter before comparing paired t test conditions.
- SD of differences: For paired t test, the worked value for sd of differences is 5.5 units. Treat the sd of differences entry (5.5 units) explicitly as a count, proportion, rate, estimate, or model parameter before comparing paired t test conditions. The form enforces minimum 1e-06.
- Number of pairs: For paired t test, the worked value for number of pairs is 24 pairs. Treat the number of pairs entry (24 pairs) explicitly as a count, proportion, rate, estimate, or model parameter before comparing paired t test conditions. The form enforces minimum 2.
The entries used for paired t test must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid paired t test arithmetic for a nonexistent study.
How paired t test is calculated
For paired t test, match every symbol in the relationship to a labeled field before substituting numbers. Paired t test is reported in the scale implied by the inputs and formula.
While checking paired t test, inspect every denominator in t=d̄/(sd/√n). For paired t test, a zero or near-zero denominator can make paired t test undefined or unstable.
A reproducible paired t test case
The default paired t test condition is Mean paired difference = 2.8, SD of differences = 5.5 units, Number of pairs = 24 pairs.
The example produces t≈2.49 with 23 degrees of freedom and p≈0.020.
The live calculator reports t statistic 2.4940259 · Degrees of freedom 23 · Two-sided p-value 0.0202592. Repeating one intermediate step from t=d̄/(sd/√n) provides a fixed paired t test reference check for later code changes.
The surrounding workflow may also require one sample t test and welch two sample t test.
Conditions attached to paired t test
The analysis unit is the pair; substituting separate-group standard deviations changes the test.
For paired t test, a p-value measures compatibility with a stated null model; it is not the probability that the null hypothesis is true and it does not measure practical importance.
When paired t test can mislead
When interpreting paired t test, pair the test result with the effect direction, effect size, uncertainty, sampling design, and the rule used for one-sided or two-sided inference.
As a second check for paired t test, reversing the numerator and denominator answers a different question, so retain the direction printed in t=d̄/(sd/√n).
A controlled sensitivity check for paired t test
Change mean paired difference while holding the remaining entries fixed, then state why the direction and size of the paired t test change are plausible from t=d̄/(sd/√n).
Repeat the paired t test exercise with number of pairs. If a modest defensible change materially alters the interpretation, report both conditions rather than presenting that paired t test scenario as exact.
Where a plausible paired t test can go wrong
Before accepting paired t test, compare every entered value with its label, unit, and allowed domain after reading the printed relationship from left to right.
For paired t test, do not move a number between fields merely because the units look compatible; each label gives the number a different statistical role.
Another paired t test failure occurs when a rounded output is reused as though it were the original measurement. Carry guard digits through calculations that depend on paired t test, then round only the reported value.
Reporting paired t test reproducibly
Report paired t test using t=d̄/(sd/√n), followed by the entered values, units, exclusions, and analysis date. Name the paired t test population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including t statistic 2.4940259 · Degrees of freedom 23 · Two-sided p-value 0.0202592. A later paired t test review can then distinguish a changed input from a different convention or software implementation.
Questions about paired t test
How should paired t test be rounded?
Keep the unrounded paired t test for subsequent arithmetic, then report only the precision supported by the source measurements and the decision context. Extra digits in paired t test do not correct sampling or model error.
Which input deserves the closest boundary check?
For paired t test, start with number of pairs and then mean paired difference. Confirm the paired t test units and allowed domain because a valid-looking entry can still describe the wrong statistical setup.