Quick Navigation

T.INV.2T Function

Q: What makes T.INV.2T different from T.INV?

T.INV.2T returns two-tailed critical values (P(|X|>t)=probability), while T.INV is one-tailed (P(X<t)=probability).

Q: Can I use T.INV.2T for one-tailed tests?

Yes, use 2*probability. For example, T.INV.2T(2*0.05,10) gives the one-tailed value of 1.812462.

Excel 2010+

Summary

The T.INV.2T function calculates the two-tailed inverse of the Student's t-distribution, returning the critical t-value for a given probability and degrees of freedom. Essential for hypothesis testing and confidence intervals in statistical analysis.

Syntax

T.INV.2T(probability, deg_freedom)

Parameters

Parameter	Type	Required	Description
probability	`Number`	Yes	The probability level (0 < probability ≤ 1) for the two-tailed test
deg_freedom	`Number`	Yes	Number of degrees of freedom (≥ 1)

Using the T.INV.2T Function

T.INV.2T is crucial for statistical analysis, particularly when constructing confidence intervals or performing two-tailed hypothesis tests. It finds the t-value where the probability of observing a more extreme value in both tails equals the specified probability.

Common T.INV.2T Examples

Basic Two-Tailed T-Value

=T.INV.2T(0.05, 10)

Returns 2.28139 - the critical t-value for α=0.05 with 10 degrees of freedom (two-tailed)

Confidence Interval Calculation

=T.INV.2T(0.1, 60)

Returns 0.606533 - used for 90% confidence interval with 60 degrees of freedom

Hypothesis Test Decision

=IF(ABS(t_statistic)>T.INV.2T(0.05,df), "Reject H0", "Fail to Reject")

Compares test statistic against critical value for decision making

Frequently Asked Questions

T.INV.2T returns two-tailed critical values (P(|X|>t)=probability), while T.INV is one-tailed (P(X<t)=probability).

Yes, use 2*probability. For example, T.INV.2T(2*0.05,10) gives the one-tailed value of 1.812462.

T.INV.2T returns #NUM! error.

Common Errors and Solutions

#VALUE!

Cause: Non-numeric arguments provided

Solution: Ensure both probability and deg_freedom are numbers

#NUM! (probability)

Cause: Probability ≤ 0 or > 1

Solution: Use probability between 0 (exclusive) and 1

#NUM! (degrees)

Cause: Degrees of freedom < 1

Solution: Use integer ≥ 1 for degrees of freedom

Notes

If deg_freedom is not an integer, Excel truncates it toward zero
Precision depends on T.DIST.2T function accuracy
Ideal for small sample statistical analysis (<30 observations)
Use with CONFIDENCE.T for confidence intervals

Compatibility

Available in: Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2007 and earlier

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2010+