Example Data Table
| t |
n |
DF method |
Tail |
Alpha |
Approx p value |
Decision |
| 2.228 |
10 |
n - 1 |
Two tailed |
0.05 |
0.0527 |
Not significant |
| 1.833 |
10 |
n - 1 |
Right tailed |
0.05 |
0.0500 |
Near cutoff |
| -2.306 |
9 |
n - 2 |
Left tailed |
0.05 |
0.0272 |
Significant |
Formula Used
The calculator uses the Student t distribution. Degrees of freedom can be
df = n - 1, df = n - 2, or a custom value.
First compute x = df / (df + t²). The cumulative probability is found
with the regularized incomplete beta function. For t greater than zero,
F(t) = 1 - 0.5 × I(x; df / 2, 1 / 2). For t less than zero,
F(t) = 0.5 × I(x; df / 2, 1 / 2).
Left tailed p = F(t). Right tailed p = 1 - F(t).
Two tailed p = 2 × min(F(t), 1 - F(t)).
How To Use This Calculator
- Enter the t statistic from your test.
- Enter the sample size n.
- Select the correct degrees of freedom method.
- Choose left tailed, right tailed, or two tailed.
- Enter the alpha level, such as 0.05.
- Press the calculate button.
- Review the p value, decision, and critical rule.
- Download the result as CSV or PDF if needed.
About This Calculator
A p value links a test statistic to probability. This calculator starts with a t score and sample size. It then estimates the chance of observing a result at least as extreme. You can choose a left tailed, right tailed, or two tailed test. You can also set the alpha level. The page reports degrees of freedom, cumulative probability, final p value, and a significance decision.
Why T And N Matter
The t score measures distance from a null value in standard error units. Larger absolute values usually create smaller p values. Sample size changes the degrees of freedom. More degrees of freedom make the t curve closer to the normal curve. Small samples have heavier tails. That means the same t score may give a larger p value.
Interpreting The Output
A low p value suggests the observed statistic is unlikely under the null model. It does not prove the alternative is true. It also does not measure effect size by itself. Use the reported tail choice carefully. A right tailed test checks unusually high t values. A left tailed test checks unusually low values. A two tailed test checks both directions.
Helpful Use Cases
Students can check homework without a long table. Researchers can confirm hand calculations. Teachers can prepare examples for class. Analysts can document quick inference checks. The export buttons help keep records in spreadsheets or reports.
Good Practice Notes
Choose the tail direction before viewing results. Do not switch tails only to make a result significant. Confirm whether your study uses n minus one, n minus two, or a custom degree value. One sample and paired tests often use n minus one. Correlation based t tests often use n minus two. Report the t score, degrees of freedom, p value, tail type, and alpha level together. Rounding may slightly change the last decimal place. For formal work, also review assumptions such as independence, random sampling, and approximate normality. Statistical software may use more precision internally. This calculator is designed for learning, review, and transparent reporting.
Result Quality
Check every input before export. Keep original data nearby. Recalculate when sample size changes. Small edits can shift the conclusion. Use clear labels in reports.
FAQs
What does this p value calculator do?
It converts a t statistic and sample size into a p value. It also shows degrees of freedom, tail probabilities, a significance decision, and a critical rule.
Which degrees of freedom should I choose?
Use n minus one for many one sample or paired tests. Use n minus two for correlation based t tests. Use custom df when your method gives a different value.
What is a two tailed p value?
A two tailed p value checks extreme results in both directions. It doubles the smaller tail probability, with a maximum value of one.
What is a left tailed p value?
A left tailed p value is the cumulative probability F(t). It is used when the alternative hypothesis expects a lower value than the null condition.
What is a right tailed p value?
A right tailed p value is 1 minus F(t). It is used when the alternative hypothesis expects a higher value than the null condition.
Does a low p value prove my hypothesis?
No. A low p value shows the result is unlikely under the null model. It does not prove the alternative, show practical importance, or remove study limitations.
Why does sample size change the result?
Sample size affects degrees of freedom. Smaller degrees of freedom create heavier t distribution tails. That can make p values larger for the same t statistic.
Can I export the result?
Yes. After calculation, use the CSV or PDF button. The export includes the t statistic, sample size, df, tail type, alpha, p value, and decision.