Pooled Two Sample T Test Calculator
Tests independent means with a common variance estimated by pooling both sample variances. The form displays t=(x̄1−x̄2)/(sp√(1/n1+1/n2)) beside pooled two-sample t test, using a worked condition that can be recalculated with the labeled inputs.
Supply the analysis inputs when the sample changes
Pooled two-sample t test
What pooled two-sample t test answers
The pooled two sample t test page tests independent means with a common variance estimated by pooling both sample variances.
Pooled two-sample t test is limited to the statistical quantity named by the result panel. The pooled two-sample t test calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
Measurements required for pooled two-sample t test
- Group 1 mean: The displayed group 1 mean is 54; retain its unit, group, and statistical role when reproducing pooled two-sample t test.
- Group 1 SD: The displayed group 1 sd is 9 units; retain its unit, group, and statistical role when reproducing pooled two-sample t test.
- Group 1 size: The displayed group 1 size is 32 observations; retain its unit, group, and statistical role when reproducing pooled two-sample t test.
- Group 2 mean: The displayed group 2 mean is 48; retain its unit, group, and statistical role when reproducing pooled two-sample t test.
- Group 2 SD: The displayed group 2 sd is 10 units; retain its unit, group, and statistical role when reproducing pooled two-sample t test.
- Group 2 size: The displayed group 2 size is 28 observations; retain its unit, group, and statistical role when reproducing pooled two-sample t test.
The entries used for pooled two-sample t test must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid pooled two-sample t test arithmetic for a nonexistent study.
Working through the pooled two sample t test formula
For pooled two-sample t test, match every symbol in the relationship to a labeled field before substituting numbers. Pooled two-sample t test is reported in the scale implied by the inputs and formula.
While checking pooled two-sample t test, inspect every denominator in t=(x̄1−x̄2)/(sp√(1/n1+1/n2)). For pooled two-sample t test, a zero or near-zero denominator can make pooled two-sample t test undefined or unstable.
Checking the displayed example
The default pooled two-sample t test condition is Group 1 mean = 54, Group 1 SD = 9 units, Group 1 size = 32 observations, Group 2 mean = 48, Group 2 SD = 10 units, Group 2 size = 28 observations.
The example gives t≈2.45 with 58 degrees of freedom and p≈0.017.
The live calculator reports t statistic 2.44615 · Degrees of freedom 58 · Two-sided p-value 0.01749296 · Pooled standard deviation 9.4786511. Repeating one intermediate step from t=(x̄1−x̄2)/(sp√(1/n1+1/n2)) provides a fixed pooled two-sample t test reference check for later code changes.
What the pooled two sample t test arithmetic assumes
Equal variance is a model assumption; it should not be selected merely because a preliminary variance test was nonsignificant.
For pooled two sample 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.
A nearby method may answer the next question: welch two sample t test, one proportion z test, paired t test, and two proportion z test.
How to interpret the pooled two sample t test output
When interpreting pooled two sample 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 pooled two-sample t test, reversing the numerator and denominator answers a different question, so retain the direction printed in t=(x̄1−x̄2)/(sp√(1/n1+1/n2)).
Rebuilding this pooled two sample t test calculation later
Report pooled two-sample t test using t=(x̄1−x̄2)/(sp√(1/n1+1/n2)), followed by the entered values, units, exclusions, and analysis date. Name the pooled two-sample t test population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including t statistic 2.44615 · Degrees of freedom 58 · Two-sided p-value 0.01749296 · Pooled standard deviation 9.4786511. A later pooled two-sample t test review can then distinguish a changed input from a different convention or software implementation.
Questions about pooled two-sample t test
Which input deserves the closest boundary check?
For pooled two-sample t test, start with group 2 size and then group 1 mean. Confirm the pooled two-sample t test units and allowed domain because a valid-looking entry can still describe the wrong statistical setup.
Why could another program report a different pooled two-sample t test?
A different convention for rounding, tails, ties, interpolation, parameterization, or missing values can change pooled two-sample t test. Compare the printed pooled two-sample t test formula and its input definitions before treating either output as wrong.
What does pooled two-sample t test represent on this page?
It is the quantity produced by t=(x̄1−x̄2)/(sp√(1/n1+1/n2)) from the displayed group 1 mean, group 1 sd, group 1 size, group 2 mean, group 2 sd, group 2 size. This page tests independent means with a common variance estimated by pooling both sample variances.