X Y T Test Calculator

Calculator Form

X sample values

Use commas, spaces, or new lines.

Y sample values

Keep rows aligned for paired testing.

Test type

Alternative hypothesis

Hypothesized difference

Alpha level

Confidence level

Decimal places

Example Data Table

Pair	X	Y	X - Y
1	12	10	2
2	15	11	4
3	14	13	1
4	16	12	4
5	13	14	-1

Formula Used

Welch test: t = ((mean X - mean Y) - d0) / sqrt(sX² / nX + sY² / nY).

Welch degrees of freedom: df = (sX² / nX + sY² / nY)² / (((sX² / nX)² / (nX - 1)) + ((sY² / nY)² / (nY - 1))).

Equal variance test: sp² = ((nX - 1)sX² + (nY - 1)sY²) / (nX + nY - 2).

Paired test: t = (mean difference - d0) / (sd difference / sqrt(n)).

Confidence interval: observed difference ± critical t × standard error.

How To Use This Calculator

Paste numeric X values in the first sample box.
Paste numeric Y values in the second sample box.
Select Welch, equal variance, or paired testing.
Choose the alternative hypothesis and alpha level.
Set the confidence level and hypothesized difference.
Press Calculate to view the result below the header.
Use CSV or PDF buttons to save the current output.

Understanding the X Y T Test

An X Y t test compares two numeric groups. The groups may be independent. They may also be paired by row. This calculator supports both ideas. It reads raw values for X and Y. Then it builds the needed summary statistics.

Why This Tool Helps

Many users know their data, not the formula. This page keeps the process clear. You enter the samples. You choose the test type. You set the hypothesized mean difference. The result shows means, standard deviations, the standard error, degrees of freedom, the t statistic, and the p value. It also reports a confidence interval. That interval helps show practical size, not only statistical signal.

Independent And Paired Choices

Use Welch independent test when group spreads may differ. It is a safe default. Use equal variance only when that assumption is reasonable. Use paired test when each X value belongs with the Y value in the same row. Examples include before and after readings, matched subjects, or repeated measures.

Interpreting The Result

The p value measures how unusual the observed difference is under the null claim. A small p value suggests that the observed gap is unlikely under that claim. Compare it with alpha. If p is less than or equal to alpha, reject the null claim. Still review the interval and effect size. A significant result may be small in practice. A non significant result may still need more data.

Data Quality Matters

Clean data improves every answer. Remove labels, blanks, and text. Keep paired rows aligned. Use the same measurement unit in both samples. Watch for outliers. Outliers can strongly change the mean and the test statistic. If values are very skewed, consider a graph or a robust method.

Export And Reporting

The calculator can export the current result as CSV. It can also create a simple PDF report. These files help with worksheets, audits, notes, and classroom records. Always record the test type, alpha level, alternative hypothesis, and confidence level. Those details make the conclusion easier to check later during review. Use the example table to test the workflow first. Then replace it with your own values. Save exports after every important analysis and compare notes easily.

FAQs

What is an X Y t test?

It is a test for comparing two numeric samples. X and Y may be independent groups or paired measurements. The calculator reports the t statistic, degrees of freedom, p value, interval, and decision.

When should I choose Welch testing?

Choose Welch testing when the two samples are independent and may have different variances. It is often the safer default because it does not require equal spread between groups.

When should I use paired testing?

Use paired testing when every X value directly matches one Y value. Common examples include before and after measurements, matched subjects, repeated tests, or paired lab readings.

What does the p value mean?

The p value shows how unusual the observed result is if the null claim is true. A smaller value gives stronger evidence against that null claim.

What is alpha?

Alpha is the chosen significance cutoff. A common value is 0.05. If the p value is less than or equal to alpha, the calculator rejects the null hypothesis.

What does the confidence interval show?

The interval gives a likely range for the true mean difference. It adds practical context because it shows the size and direction of the estimated effect.

Can I paste values from a spreadsheet?

Yes. Paste numbers separated by commas, spaces, tabs, or new lines. The parser ignores nonnumeric tokens, but clean numeric input is always better.

Why do exports recalculate the result?

The export buttons submit the same form values again. This keeps the downloaded CSV or PDF matched to the latest inputs and selected test settings.