TEST_STDEV

Calculates the p-value of the statistical test for the population standard deviation.

Syntax

TEST_STDEVⁱ(X, sigma)

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

sigma
is the assumed population standard deviation. If missing, the default value of one is assumed.

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

$H_{o}: \sigma =\sigma_o$

$H_{1}: \sigma \neq \sigma_o$

Where:
- $H_{o}$ is the null hypothesisⁱ.
- $H_{1}$ is the alternate hypothesis.
- $\sigma_o$ is the assumed population standard deviation.
- $\sigma$ is the actual (real) population standard deviation.
For the case in which the underlying population distribution is normal, the sample standard deviation has a Chi-square sampling distribution:

$\hat \sigma \sim \chi_{\nu=T-1}^2$

Where:
- $\hat \sigma$ is the sample standard deviation.
- $\chi_{\nu}^2()$ is the Chi-square probability distribution function.
- $\nu$ is the degrees of freedom for the Chi-square distribution.
- $T$ is the number of non-missing values in the sample data.
Using a given data sample, the sample data standard deviation is computed as:

$\hat \sigma(x) = \sqrt{\frac{\sum_{t=1}^T(x_t-\bar x)^2}{T-1}}$

Where:
- $\hat \sigma(x)$ is the sample standard deviation.
- $\bar x$ is the sample average.
- $T$ is the number of non-missing values in the data sample.
The underlying population distribution is assumed normal (Gaussian).
This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level ( $\alpha/2$ ).

Example 1:

	Formula	Description (Result)
	=STDEV($B$2:$B$17)	Sample standard deviation (1.3725)
	=TEST_STDEV($B$2:$B$17,1)	p-value of the test when standard deviation = 1 (0.0232)