Documentation/Calc Functions/CHISQINV

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    Function name:

    CHISQINV

    Category:

    Statistical Analysis

    Summary:

    Calculates the inverse of a probability value from the cumulative distribution function for the chi-square ([math]\displaystyle{ \chi }[/math]2) distribution with a given number of degrees of freedom. The value returned is the chi-square statistic that corresponds to the specified probability value.

    Chi-square distributions are a family of continuous probability distributions on the interval [0, +∞), with the shape of each distribution dependent on the number of degrees of freedom. Although few real-world observations follow a chi-square distribution, they are widely used in statistical hypothesis testing.

    CHISQINV is the inverse of CHISQDIST, so that for valid arguments [math]\displaystyle{ \text{CHISQINV}(\text{CHISQDIST}(x;\:df);\:df)~=~x }[/math].

    Syntax:

    CHISQINV(Probability; Degrees of Freedom)

    Returns:

    Returns a non-negative real number, which is the inverse of the given probability value from the cumulative distribution function for the given chi-square distribution.

    Arguments:

    Probability is a real number (expressed as a percentage, such as 2.5%, or a decimal fraction, such as 0.025), or a reference to a cell containing that number, which is the probability for which the inverse is required. Probability lies in the range [0, 1) (0 ≤ Probability < 1).

    Degrees of Freedom is a positive integer, or a reference to a cell containing that number, which is the number of degrees of freedom of the chi-square distribution.

    • If either Probability or Degrees of Freedom is non-numeric, then CHISQINV reports a #VALUE! error.
    • If Degrees of Freedom is less than 1.0, then CHISQINV reports an invalid argument error (Err:502).
    • If Degrees of Freedom is a non-integer value, then CHISQINV truncates it to an integer value.
    • If Probability is less than 0.0, or greater than or equal to 1.0, then CHISQINV reports an invalid argument error (Err:502).

    Additional details:

    • CHISQINV utilizes an iterative algorithm to determine the inverse of the specified cumulative distribution function probability.
    • The following figure shows inverse cumulative distribution function probability plots for five sample chi-square distributions.
    Chi square inverse CDF probability plots.png

    Examples:

    Formula Description Returns
    =CHISQINV(A1; A2) where cells A1:A2 contain the values 0.77686983985157 and 2 respectively. Calculates the value of the cumulative distribution function for the chi-square distribution with two degrees of freedom, evaluated at a probability of 0.77686983985157. 3
    =CHISQINV(7.4247191214056E-05; 15.95) Calculates the value of the cumulative distribution function for the chi-square distribution with 15 degrees of freedom, evaluated at a probability of 7.4247191214056E-05. Note that the non-integer value for the Degrees of Freedom argument is truncated to 15 and that the formula =CHISQINV(7.4247191214056E-05; 15) returns the same result. 2.3
    =CHISQINV(50%; 9) Calculates the value of the cumulative distribution function for the chi-square distribution with 9 degrees of freedom, evaluated at a probability of 50%. 8.34283269225296

    Related LibreOffice functions:

    CHIDIST

    CHIINV

    CHISQ.DIST

    CHISQ.DIST.RT

    CHISQ.INV

    CHISQ.INV.RT

    CHISQ.TEST

    CHISQDIST

    CHITEST

    ODF standard:

    Section 6.18.14, part 2

    Related (or similar) Excel functions:

    None