Documentation/Calc Functions/CRITBINOM

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    Function name:

    CRITBINOM

    Category:

    Statistical Analysis

    Summary:

    Given the total number of independent trials and the probability of a successful outcome on each trial, CRITBINOM determines the minimum number of trial successes for which the binomial cumulative density function gives a probability of greater than or equal to a supplied criterion probability.

    Syntax:

    CRITBINOM(Trials; SP; Alpha)

    Returns:

    Returns a non-negative integer, which is the minimum number of trial successes for the given arguments.

    Arguments:

    Trials is a non-negative integer, or a reference to a cell containing that integer, that is the total number of independent trials.

    SP 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, that is the probability of a successful outcome on each trial. As a probability, SP lies in the range [0, 1] (or equivalently 0% ≤ SP ≤ 100%).

    Alpha 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, that is the criterion probability to be reached or exceeded. As a probability, Alpha lies in the range [0, 1] (or equivalently 0% ≤ Alpha ≤ 100%).

    • If any of Trials, SP, and Alpha is non-numeric, then CRITBINOM reports a #VALUE! error.
    • If Trials is a non-integer value, then CRITBINOM truncates it to an integer value.
    • If Trials is a less than 0, then CRITBINOM reports an invalid argument error (Err:502).
    • If either SP or Alpha is less than 0.0 or greater than 1.0, then CRITBINOM reports an invalid argument error (Err:502).

    Additional details:

    • Calc's CRITBINOM and BINOM.INV functions perform the same calculations. The requirements for CRITBINOM are specified in ODF 1.2; BINOM.INV is provided for interoperability with Microsoft Excel.
    • The binomial distribution should be used in its intended circumstances and this is when there are a fixed number of independent trials, each having two possible outcomes (success or failure), with a constant probability of achieving a successful outcome for each trial.

    Examples:

    Formula Description Returns
    =CRITBINOM(A1; A2; A3) where cells A1:A3 contain the values 100, 0.5, and 0.1 respectively. Here there are 100 independent trials, with the probability of a successful outcome on each trial being 0.5 (50%), with a criterion probability to be reached or exceeded of 0.1 (10%). The function calculates the smallest number of trial successes for which the cumulative binomial distribution is greater than or equal to a criterion value. Here the function returns the minimum number of trial successes as 44. Note that the formula =BINOMDIST(43; 100, 0.5, TRUE()) returns the value 0.0966739522478212 (<10%), while the formula =BINOMDIST(44; 100, 0.5, TRUE()) returns the value 0.135626512036917 (>10%). 44
    =CRITBINOM(100; 50%; 50%) Here the function returns the minimum number of trial successes as 50. 50
    =CRITBINOM(100; 50%; 95%) Here the function returns the minimum number of trial successes as 58. 58

    Related LibreOffice functions:

    B

    BINOMDIST

    BINOM.DIST

    BINOM.INV

    ODF standard:

    Section 6.18.19, part 2

    Related (or similar) Excel functions:

    CRITBINOM