Documentation/Calc Functions/T.INV

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    Function name:

    T.INV

    Category:

    Statistical Analysis

    Summary:

    Calculates the inverse of the cumulative distribution function for a t-distribution. The t-distribution is often known as the Student's t-distribution.

    T-distributions are a family of continuous probability distributions and each has a curve with the same general bell shape that is symmetric about 0. Each t-distribution is characterized by a parameter known as the number of degrees of freedom, often denoted by the lowercase Greek letter nu ([math]\displaystyle{ \nu }[/math]). The t-distribution approaches the normal distribution as the number of degrees of freedom increases. T-distributions are often used to model small sample sizes.

    Using the nomenclature of the previous paragraph, T.INV calculates the real number x such that [math]\displaystyle{ \text{T.DIST}(x;\:\nu;\:1)~=~p }[/math], where the given probability p lies in the range (0, 1).

    Syntax:

    T.INV(Number; Degrees freedom)

    Returns:

    Returns a real number, which is the value of the random variable that would give the specified probability in the cumulative distribution function for the specified t-distribution.

    Arguments:

    Number is a real number in the range (0, 1), or a reference to a cell containing that number, which is a probability in the cumulative distribution function of the t-distribution.

    Degrees freedom is a positive integer, or a reference to a cell containing that number, which is the number of degrees of freedom of the t-distribution. This is typically assumed to be the number of samples minus 1.

    • If either of Number or Degrees freedom is non-numeric, then T.INV reports a #VALUE! error.
    • If Number is less than or equal to 0, or greater than or equal to 1, then T.INV reports an invalid argument error (Err:502).
    • If Degrees freedom is less than 1, then T.INV reports an invalid argument error (Err:502).
    • If Degrees freedom is a non-integer value, then T.INV truncates it to an integer value.

    Additional details:

    • T.INV is provided for interoperability with Microsoft Excel.
    • The name space for T.INV is COM.MICROSOFT.T.INV.
    • For more information on the t-distribution, visit Wikipedia's Student's t-distribution page.

    Examples:

    Formula Description Returns
    =T.INV(A1; A2) where cells A1 and A2 contain the values 0.666666666666667 and 2 respectively. Here the function calculates the inverse of the given value from the cumulative distribution function for the specified t-distribution. Note that the formula =T.DIST(0.5; 2; 1) returns 0.666666666666667. 0.5
    =T.INV(0.001; 8) Here the function calculates the inverse of a small probability value from the cumulative distribution function for the specified t-distribution. -4.5007909337237
    =T.INV(0.999; 8) Here the function calculates the inverse of a large probability value from the cumulative distribution function for the specified t-distribution. 4.5007909337237

    Related LibreOffice functions:

    T.DIST

    T.DIST.2T

    T.DIST.RT

    T.INV.2T

    TDIST

    TINV

    ODF standard:

    None

    Related (or similar) Excel functions:

    T.INV since v.2010.