Formula Used
Welch Unpaired T Test
t = ((mean1 - mean2) - hypothesized difference) / sqrt((s1² / n1) + (s2² / n2))
df = ((s1² / n1) + (s2² / n2))² / (((s1² / n1)² / (n1 - 1)) + ((s2² / n2)² / (n2 - 1)))
Pooled Unpaired T Test
sp² = (((n1 - 1)s1²) + ((n2 - 1)s2²)) / (n1 + n2 - 2)
t = ((mean1 - mean2) - hypothesized difference) / sqrt(sp²(1 / n1 + 1 / n2))
df = n1 + n2 - 2
Effect Size
Cohen's d = (mean1 - mean2) / pooled standard deviation
Hedges' g = Cohen's d × correction factor
How to Use This Calculator
Select raw data if you have each observation. Paste group values into the two boxes. Use commas, spaces, or new lines.
Select summary statistics if you already know sample size, mean, and standard deviation for both groups.
Choose Welch for unequal variances. Choose pooled only when equal variance is a sound assumption.
Set alpha, confidence level, tail direction, and hypothesized mean difference. Then press Calculate.
Use CSV or PDF after entering data to save the current calculation.
Unpaired T Test Calculator Guide
An unpaired t test compares the means of two independent groups. It is useful when the same subjects are not measured twice. Typical examples include treatment versus control, male versus female, and two different production lines.
What the Result Means
The calculator reports the observed mean difference, standard error, t statistic, degrees of freedom, p value, and confidence interval. These values help you decide whether the group difference is larger than random sampling noise. The decision uses your selected alpha level.
Welch and Pooled Options
Welch t test is the safer default. It does not require equal group variances. The pooled test assumes both populations share one common variance. Use the pooled option only when that assumption is reasonable. Large variance differences can make the pooled result misleading.
Data and Summary Inputs
You may paste raw values for each group. Separate numbers with commas, spaces, or new lines. The tool then calculates sample size, mean, and sample standard deviation. You can also enter summary statistics. This is helpful when a paper or lab sheet already gives n, mean, and standard deviation.
Reading the P Value
A small p value suggests that the observed difference would be unusual if the null difference were true. It does not measure practical importance. Always review the confidence interval and effect size. A statistically significant result can still be small in real terms.
Confidence Interval
The confidence interval estimates a likely range for the true difference between population means. If a two sided interval excludes the hypothesized difference, the two sided test is significant at the matching level. Wider intervals indicate less precision.
Effect Size
Cohen's d expresses the difference in pooled standard deviation units. Hedges' g applies a small sample correction. These measures make results easier to compare across studies. They should be reported with the t statistic and p value.
Best Practice
Check assumptions before reporting. Groups should be independent. Values should be measured on a numeric scale. Severe outliers can distort the mean and standard deviation. For small samples, inspect distributions first. For skewed data, consider a nonparametric alternative. Keep records of cleaning rules, excluded values, and chosen test direction for transparent reporting later in any study.
FAQs
What is an unpaired t test?
It compares the means of two independent groups. The groups must contain different subjects or observations. It tests whether the observed mean difference is unlikely under a chosen null hypothesis.
When should I use Welch's test?
Use Welch's test when group variances may differ. It is often the best default. It adjusts the degrees of freedom and avoids the strict equal variance assumption.
When is the pooled test suitable?
The pooled test is suitable when both populations can reasonably share one variance. Use it carefully. Strongly different standard deviations can make pooled results unreliable.
What does the p value show?
The p value shows how unusual the result is under the null hypothesis. A smaller value gives stronger evidence against that null. It does not show effect importance.
What is the confidence interval?
The confidence interval gives a range for the true mean difference. A narrow interval means better precision. A wide interval means more uncertainty in the estimate.
Can I use summary data?
Yes. Select summary statistics. Enter sample size, mean, and standard deviation for each group. This is useful when raw observations are unavailable.
What is Cohen's d?
Cohen's d is an effect size. It reports the mean difference in pooled standard deviation units. It helps compare practical strength across different studies.
Do I need normally distributed data?
The test works best when each group is roughly normal. Larger samples reduce this concern. Severe skew, outliers, or ordinal data may require another method.