Anderson Darling Test

Sepasoft MES Module Suite

The event is created to calculate an Anderson-Darling test. This test will determine if a data set comes from a specified distribution, in our case, the normal distribution. The test makes use of the cumulative distribution function.

Brief discussion on the variables used for AD test

The Anderson-Darling statistic AD is given by the following formula:

Anderson-Darling Statistic

where n = sample size, F(X) = cumulative distribution function for the specified distribution and i = the ith sample when the data is sorted in ascending order.  

 

The summation portion of the equation is given below, the summation term S in the Anderson-Darling equation:

anderson-darling summation term

 

The value of AD needs to be adjusted for small sample sizes. The adjusted AD value is given by:

adjusted anderson-darling equation

The p-value is defined as the probability of obtaining a result equal to or "more extreme" than what was actually observed, when the null hypothesis is true. For typical analysis, using the standard α = 0.05 cutoff, the null hypothesis is rejected when p < .05 and not rejected when p > .05. The p-value does not in itself support reasoning about the probabilities of hypotheses but is only a tool for deciding whether to reject the null hypothesis: -wikipedia

Properties 

getAd()

Description

Returns the AD.

Syntax

getAd()


  • Parameters

None

  • Returns

Double ad - The AD.

  • Scope

All

getAdStar()

Description

Returns the AD*.

Syntax

getAdStar()


  • Parameters

None

  • Returns

Double adStar - The AD*.

  • Scope

All

getData()

Description

Returns the SPC data.

Syntax

getData()


  • Parameters

None

  • Returns

AnalysisDataset data - The SPC data.

  • Scope

All

getMean()

Description

Returns the mean.

Syntax

getMean()


  • Parameters

None

  • Returns

Double mean - The mean.

  • Scope

All

getMeasurementCount()

Description

Returns the measurement count.

Syntax

getMeasurementCount()


  • Parameters

None

  • Returns

int measurementCount - The measurement count.

  • Scope

All

getPValue()

Description

Get the p-value for the test statistics. If the p-value is less than a chosen alpha (usually 0.05 or 0.10), then reject the null hypothesis that the data come from that distribution. 

Syntax

getPValue()


  • Parameters

None

  • Returns

Double pValue - The p-value of the Anderson Darling Test.

  • Scope

All

getS()

Description

Returns the S value in the Anderson Darling Test.

Syntax

getS()


  • Parameters

None

  • Returns

Double s - The s of the Anderson Darling Test.

  • Scope

All

getStandardDeviation()

Description

Returns the actual standard deviation.

Syntax

getStandardDeviation()


  • Parameters

None

  • Returns

Double standardDeviation - The standard deviation.

  • Scope

All

setAd(ad)

Description

Sets the AD.

Syntax

setAd(ad)


  • Parameters

Double ad - The AD.

  • Returns

Nothing

  • Scope

All

setAdStar(adStar)

Description

Sets the AD*.

Syntax

setAdStar(adStar)


  • Parameters

Double data - The AD*.

  • Returns

Nothing

  • Scope

All

setMean(mean)

Description

Sets the mean.

Syntax

setMean(mean)


  • Parameters

Double mean - The mean to set for.

  • Returns

Nothing

  • Scope

All

setPValue(pValue)

Description

Sets the p-value.

Syntax

setPValue(pValue)


  • Parameters

Double pValue - The p-value to set for.

  • Returns

Nothing

  • Scope

All

setS(s)

Description

Sets the S.

Syntax

setS(s)


  • Parameters

Double s - The s.

  • Returns

Nothing

  • Scope

All

setStandardDeviation(standardDeviation)

Description

Sets the actual standard deviation.

Syntax

setStandardDeviation(standardDeviation)


  • Parameters

Double standardDeviation - The standard deviation.

  • Returns

Nothing

  • Scope

All

 

 

 

Sepasoft MES Module Suite