| 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
-
- The data sample may include missing values (NaN).
- 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: \[ \hat \sigma^2 \sim \chi_{\nu=T-1}^2 \] 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.
- 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 (\(\alpha/2\)).
- Requirements
-
Header SFSDK.H Library SFSDK.LIB DLL 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
-
- The data sample may include missing values (NaN).
- 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: \[ \hat \sigma^2 \sim \chi_{\nu=T-1}^2 \] 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.
- 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 (\(\alpha/2\)).
- Exceptions
-
Exception Type Condition None N/A
- Requirements
-
Namespace NumXLAPI Class SFSDK Scope Public Lifetime Static Package 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
