TEST_MEAN

Calculates the p-value of the statistical test for the population mean.

Syntax

TEST_MEAN(x, mean)

x
is the data sample (a one dimensional array of cells (e.g. rows or columns)).

mean
is the assumed population mean. If missing, the default value of zero is assumed.

The sample data may include missing values (e.g. #N/A).
The test hypothesis for the population mean:

$H_{o}: \mu=\mu_o$

$H_{1}: \mu\neq \mu_o$

Where:
- $H_{o}$ is the null hypothesisⁱ.
- $H_{1}$ is the alternate hypothesis.
- $\mu_o$ is the assumed population mean.
- $\mu$ is the actual population mean.
For the case in which the underlying population distribution is normal, the sample mean/average has a Student's t with T-1 degrees of freedom sampling distribution:

$\bar x \sim t_{\nu=T-1}(\mu,\frac{S^2}{T})$

Where:
- $\bar x$ is the sample average.
- $\mu$ is the population mean/average.
- $S$ is the sample standard deviation.
  
  $S^2 = \frac{\sum_{i=1}^T(x_i-\bar x)^2}{T-1}$
- $T$ is the number of non-missing values in the data sample.
- $t_{\nu}()$ is the Student's t-Distribution.
- $\nu$ is the degrees of freedom of the Student's t-Distribution.
The Student's t-Test for the population mean can be used for small and for large data samples.
This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level ( $\alpha/2$ ).
The underlying population distribution is assumed normal (Gaussian).

Example 1:

	Formula	Description (Result)
	=AVERAGE($B$2:$B$11)	Sample mean (-0.0256)
	=TEST_MEAN($B$2:$B$11,0)	p-value of the test (0.472)

K.L. Lange, R.J.A. Little and J.M.G. Taylor. "Robust Statistical Modeling Using the t Distribution." Journal of the American Statistical Association 84, 881-896, 1989