NDK_MEANTEST

int __stdcall NDK_MEANTEST ( 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 mean.

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 mean value. If missing, a default of zero is assumed.
[in] alpha  is the statistical significance level. If missing, the 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 sample data may include missing values (NaN).
  2. The test hypothesis for the population mean: \[H_{o}: \mu=\mu_o\] \[H_{1}: \mu\neq \mu_o\] Where:
    • \(H_{o}\) is the null hypothesis.
    • \(H_{1}\) is the alternate hypothesis.
    • \(\mu_o\) is the assumed population mean.
    • \(\mu\) is the actual population mean.
  3. For the case in which the underlying population distribution is normal, the sample mean/average has a Student's t with T-1 degrees of freedom sampling distribution: \[\bar x \sim t_{\nu=T-1}(\mu,\frac{S^2}{T}) \] Where:
    • \(\bar x\) is the sample average.
    • \(\mu\) is the population mean/average.
    • \(S\) is the sample standard deviation. \[ S^2 = \frac{\sum_{i=1}^T(x_i-\bar x)^2}{T-1}\]
    • \(T\) is the number of non-missing values in the data sample.
    • \(t_{\nu}()\) is the Student's t-Distribution.
    • \(\nu\) is the degrees of freedom of the Student's t-Distribution.
  4. The Student's t-Test for the population mean can be used for small and for large data samples.
  5. This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level (\(\frac{\alpha}{2}\)).
  6. The underlying population distribution is assumed normal (Gaussian).
Requirements
Header SFSDK.H
Library SFSDK.LIB
DLL SFSDK.DLL
Examples


   
Namespace:  NumXLAPI
Class:  SFSDK
Scope:  Public
Lifetime:  Static
int NDK_MEANTEST ( 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 mean.

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 mean value. If missing, a default of zero is assumed.
[in] alpha  is the statistical significance level. If missing, the 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 sample data may include missing values (NaN).
  2. The test hypothesis for the population mean: \[H_{o}: \mu=\mu_o\] \[H_{1}: \mu\neq \mu_o\] Where:
    • \(H_{o}\) is the null hypothesis.
    • \(H_{1}\) is the alternate hypothesis.
    • \(\mu_o\) is the assumed population mean.
    • \(\mu\) is the actual population mean.
  3. For the case in which the underlying population distribution is normal, the sample mean/average has a Student's t with T-1 degrees of freedom sampling distribution: \[\bar x \sim t_{\nu=T-1}(\mu,\frac{S^2}{T}) \] Where:
    • \(\bar x\) is the sample average.
    • \(\mu\) is the population mean/average.
    • \(S\) is the sample standard deviation. \[ S^2 = \frac{\sum_{i=1}^T(x_i-\bar x)^2}{T-1}\]
    • \(T\) is the number of non-missing values in the data sample.
    • \(t_{\nu}()\) is the Student's t-Distribution.
    • \(\nu\) is the degrees of freedom of the Student's t-Distribution.
  4. The Student's t-Test for the population mean can be used for small and for large data samples.
  5. This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level (\(\frac{\alpha}{2}\)).
  6. The underlying population distribution is assumed normal (Gaussian).
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