Documentation/Calc Functions/CONFIDENCE.T

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    Function name:

    CONFIDENCE.T

    Category:

    Statistical Analysis

    Summary:

    Calculates half the width of the confidence interval for a population mean, using the Student’s t-distribution. The confidence interval is a range of values that is expected to encompass the true population mean, with a specified degree of certainty.

    Half the width of the confidence interval is often known as the margin of error and then the confidence interval is equal to the sample mean ± the margin of error.

    Use CONFIDENCE.T when you do not know the population standard deviation in advance.

    Syntax:

    CONFIDENCE.T(Alpha; STDEV; Size)

    Returns:

    Returns a positive real number, which is half the width of the confidence interval for the population mean given the specified arguments.

    Arguments:

    Alpha is a real number in the range 0 < Alpha < 1, or a reference to a cell containing that number, which is the likelihood that the population mean lies outside the confidence interval. The confidence level is the likelihood that the population mean lies inside the confidence interval and is equal to 1-Alpha.

    STDEV is a positive real number, or a reference to a cell containing that number, which is the sample standard deviation.

    Size is a positive integer, or a reference to a cell containing that number, which is the sample size.

    • If any of Alpha, STDEV, or Size is non-numeric, then CONFIDENCE.T reports a #VALUE! error.
    • If Alpha is less than or equal to 0.0, or greater than or equal to 1.0, then CONFIDENCE.T reports an invalid argument error (Err:502).
    • If STDEV is less than or equal to 0.0, then CONFIDENCE.T reports an invalid argument error (Err:502).
    • If Size is not an integer value, then CONFIDENCE.T truncates it to an integer value.
    • If Size is less than 1, then CONFIDENCE.T reports an invalid argument error (Err:502).
    • If Size is equal to 1, then CONFIDENCE.T reports a #DIV/0! error.

    Additional details:

    • The equation for CONFIDENCE.T is:
    [math]\displaystyle{ \text{CONFIDENCE.T}(\alpha;\:\sigma;\:n)~=~t\:\times\:\frac{\sigma}{\sqrt{n}} }[/math]
    where the value of t (sometimes known as a t-score) is dependent on both the sample size and the confidence level.
    The confidence interval (CI) is then given by:
    [math]\displaystyle{ CI~=~\bar{x}~\pm \text{CONFIDENCE.T}(\alpha;\:\sigma;\:n) }[/math]
    where [math]\displaystyle{ \bar{x} }[/math] is the sample mean.
    • For in-range arguments, the formula =T.INV.2T(Alpha; Size - 1) * STDEV / SQRT (Size) is equivalent to =CONFIDENCE.T(Alpha; STDEV; Size).
    • For more more information about confidence intervals, visit Wikipedia's Confidence interval page.

    Examples:

    Formula Description Returns
    =CONFIDENCE.T(A1; A2; A3) where cells A1:A3 contain the values 0.05, 2.5, and 50 respectively. Here the function calculates the margin of error for the population mean, assuming a significance level of 0.05, a sample standard deviation of 2.5, and a sample size of 50. The significance level of 5% corresponds to a confidence level of 95% and a t-score of 2.010 for the given sample size. Note that the formula =T.DIST.2T(2.010; A3-1) is approximately equal to 0.05. 0.710492138739324
    =CONFIDENCE.T(1%; 3.78; 10) Here the function calculates the margin of error for the population mean, assuming a significance level of 0.01, a sample standard deviation of 3.78, and a sample size of 10. The significance level of 1% corresponds to a confidence level of 99% and a t-score of 3.250 for the given sample size. 3.88466152164644
    =CONFIDENCE.T(1%; 3.78; 100) Similar to the previous example, except for the sample size of 100. Note how the greater number of samples narrows the confidence interval. 0.992781262852154

    Related LibreOffice functions:

    CONFIDENCE

    CONFIDENCE.NORM

    ODF standard:

    None

    Related (or similar) Excel functions:

    CONFIDENCE.T since v.2010.