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Cumulative Distribution Function (CDF) Calculator for the t-Distribution
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Cumulative Distribution Function (CDF) Calculator for the t-Distribution
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This calculator will compute the cumulative distribution function (CDF) for Student's t-distribution (i.e., the area under the t-distribution from negative infinity to t), given a t-value and the degrees of freedom.
Please supply the necessary parameter values, and then click 'Calculate'.
Degrees of freedom:
The degrees of freedom for the distribution.
t-value:
A value from the t-distribution.
Formulas
The following formulas are involved in the calculation of cumulative distribution function (CDF) values for Student's t-distribution:
Beta function:
Lower incomplete beta function:
Regularized lower incomplete beta function:
where the numerator is the lower incomplete beta function, and the denominator is the beta function.
t-distribution cumulative distribution function (CDF):
where
v
is the degrees of freedom,
t
is the upper limit of integration, and
I
is the regularized lower incomplete beta function.
References
The following references can be used to cite this cumulative distribution function (cdf) calculator for the t-distribution:
Soper, D.S. (2013). Cumulative Distribution Function (CDF) Calculator for the t-Distribution [Software]. Available from http://www.danielsoper.com/statcalc
Abramowitz, M. and Stegun, I.A., eds. (1965). Handbook of Mathematical Functions. New York, NY: Dover.
Student [William Sealy Gosset] (1908). The probable error of a mean. Biometrika, 6 (1), pp. 1-25.
Related Calculators
The following statistics calculators are related to this cumulative distribution function (cdf) calculator for the t-distribution, and may be useful for your research:
Cumulative Distribution Function (CDF) Calculators
Cumulative Distribution Function (CDF) Calculator for the Beta Distribution
Cumulative Distribution Function (CDF) Calculator for the Binomial Distribution
Cumulative Distribution Function (CDF) Calculator for the Chi-Square Distribution
Cumulative Distribution Function (CDF) Calculator for the F-Distribution
Cumulative Distribution Function (CDF) Calculator for the Noncentral F-Distribution
Cumulative Distribution Function (CDF) Calculator for the Noncentral t-Distribution
Cumulative Distribution Function (CDF) Calculator for the Normal Distribution
Cumulative Distribution Function (CDF) Calculator for the Poisson Distribution
Cumulative Distribution Function (CDF) Calculator for the Standard Normal Distribution
Cumulative Distribution Function (CDF) Calculator for the Uniform Distribution
t-Distribution Calculators
A-priori Sample Size Calculator for Student t-Tests
Beta (Type II Error Rate) Calculator for a Student t-Test
Confidence Interval Calculator for the Population Mean
Cumulative Distribution Function (CDF) Calculator for the Noncentral t-Distribution
Effect Size (Cohen's d) Calculator for a Student t-Test
One-Sample t-Test Calculator
p-Value Calculator for a Student t-Test
Post-hoc Statistical Power Calculator for a Student t-Test
Probability Density Function (PDF) Calculator for the Noncentral t-Distribution
Probability Density Function (PDF) Calculator for the t-Distribution
Student t-Value Calculator
t-Statistic and Degrees of Freedom Calculator
t-Value Calculator for Correlation Coefficients
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