# NDK_STDEVTEST

 int __stdcall NDK_STDEVTEST ( double * X, size_t N, double target, double alpha, WORD method, WORD retType, double * retVal )

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

Returns
status code of the operation
Return values
 NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
Parameters
[in] X is the sample data (a one dimensional array).
[in] N is the number of observations in X.
[in] target is the assumed standard deviation value. If missing, a default of one is assumed
[in] alpha is the statistical significance level. If missing, a default of 5% is assumed.
[in] method is the statistical test to perform (1=parametric).
[in] retType is a switch to select the return output:
Method Value Description
TEST_PVALUE 1 P-Value
TEST_SCORE 2 Test statistics (aka score)
TEST_CRITICALVALUE 3 Critical value.
[out] retVal is the calculated test statistics.
Remarks
1. The data sample may include missing values (NaN).
2. 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.
3. For the case in which the underlying population distribution is normal, the sample standard deviation has a Chi-square sampling distribution: $\hat \sigma^2 \sim \chi_{\nu=T-1}^2$ Where:
• $$\hat \sigma^2$$ is the sample variance.
• $$\chi_{\nu}^2()$$ 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.
4. 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.
5. The underlying population distribution is assumed normal (Gaussian).
6. This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level ($$\alpha/2$$).
Requirements
Header SFSDK.H SFSDK.LIB SFSDK.DLL
 Namespace: NumXLAPI Class: SFSDK Scope: Public Lifetime: Static
 int NDK_STDEVTEST ( double[] pData, UIntPtr nSize, double target, double alpha, UInt16 argMethod, UInt16 retType, out double retVal )

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

Returns
status code of the operation
Return values
 NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
Parameters
[in] pData is the sample data (a one dimensional array).
[in] nSize is the number of observations in pData.
[in] target is the assumed standard deviation value. If missing, a default of one is assumed
[in] alpha is the statistical significance level. If missing, a default of 5% is assumed.
[in] argMethod is the statistical test to perform (1=parametric).
[in] retType is a switch to select the return output:
Method Value Description
TEST_PVALUE 1 P-Value
TEST_SCORE 2 Test statistics (aka score)
TEST_CRITICALVALUE 3 Critical value.
[out] retVal is the calculated test statistics.
Remarks
1. The data sample may include missing values (NaN).
2. 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.
3. For the case in which the underlying population distribution is normal, the sample standard deviation has a Chi-square sampling distribution: $\hat \sigma^2 \sim \chi_{\nu=T-1}^2$ Where:
• $$\hat \sigma^2$$ is the sample variance.
• $$\chi_{\nu}^2()$$ 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.
4. 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.
5. The underlying population distribution is assumed normal (Gaussian).
6. This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level ($$\alpha/2$$).
Exceptions
Exception Type Condition
None N/A
Requirements
Namespace NumXLAPI SFSDK Public Static NumXLAPI.DLL
Examples

References
* Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
* Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740
* D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
* Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848