Calculates the p-value 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 deviation. If missing, the default value of one is assumed.
- Return_type
- is a switch to select the return output (1 = P-Value (default), 2 = Test Stats, 3 = Critical Value.
Method Description 1 P-Value. 2 Test Statistics (e.g., Z-score). 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 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 ($\alpha/2$).

## Files Examples

## Comments

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