Calculates the pvalue of the statistical test for the population standard deviation.
Syntax
TEST_STDEV(X, sigma, Return_type, Alpha)
X is the input data sample (one/two dimensional array of cells (e.g. rows or columns)).
sigma is the assumed population standard devation. If missing, the default value of one is assumed.
Return_type is a switch to select the return output (1 = PValue (default), 2 = Test Stats, 3 = Critical Value.
Method  Description 

1  PValue 
2  Test Statistics (e.g. Zscore) 
3  Critical Value 
Alpha is the statistical significance of the test (i.e. alpha). If missing or omitted, an alpha value of 5% is assumed.
Remarks
 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 hypothesis.
 $H_{1}$ 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 Chisquare sampling distribution:
$$ \hat \sigma \sim \chi_{\nu=T1}^2 $$
Where:
 $\hat \sigma $ is the sample standard deviation.
 $\chi_{\nu}^2()$ is the Chisquare probability distribution function.
 $\nu$ is the degrees of freedom for the Chisquare distribution.
 $T$ is the number of nonmissing values in the sample data.
 Using a given data sample, the sample data standard deviation is computed as:
$$ \hat \sigma(x) = \sqrt{\frac{\sum_{t=1}^T(x_t\bar x)^2}{T1}}$$
Where:
 $\hat \sigma(x)$ is the sample standard deviation.
 $\bar x$ is the sample average.
 $T$ is the number of nonmissing values in the data sample.
 The underlying population distribution is assumed normal (gaussian).
 This is a twosides (i.e. twotails) test, so the computed pvalue should be compared with half of the significance level ($\alpha/2$).
Examples
Example 1:


Formula  Description (Result)  

=STDEV($B$2:$B$17)  Sample standard deviation (1.3725)  
=TEST_STDEV($B$2:$B$17,1)  pvalue of the test when standard deviation = 1 (0.0232) 
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