Student's t Distribution is a continuous probability distribution for a real-valued random variable defined by the probability density function f (t) = Γ(ν+12)
√
πν
Γ(ν2)(1 + t2ν)-(ν+1)/2 , where ν is the number of degrees of freedom, Γ is the gamma function, and the Cumulative Distribution Function: F (x) =
∫
x-∞
f (t) d t
Please note:
Even though we calculate all of the numbers with the precission of 15 significant digits, for clarity, we are displaying the results rounded to 9 decimal places.
Please specify the number of degrees of freedom ν =
Mean μ =
Standard Deviation σ =
x
=
(Sample, Data Point, Raw Data, Raw Score)
Density
f (x)
=
(Probability Density, Probability Distribution)
Probability
F (x) = P (X < x)
=
(Cumulative Distribution Function, CDF)
P (X > x)
=
One-tail Quantile
P (0 < X < | x |)
=
One-tail Alpha level
P (X > | x |)
=
(One-tail Significance level)
Two-tails Quantile
P ( - | x | < X < | x |)
=
Two-tails Alpha level
P (X < - | x | ∨ X > | x |)
=
(Two-tails Significance level)
Z-Score
Z
=
(Standard Score, Number of Standard Deviations, Pull)
