- [id] => 290
- [recorddate] => 2016:08:26:11:41:12
- [lastupdate] => 2016:08:26:11:41:12
- [type] => conference
- [place] => Stockholm, Sweden
- [subject] => informatics - models implementation; informatics - simulation; mathematics - modeling; mathematics - probability theory; mathematics - statistics
- [relatedworks] =>
- 2 (average):
- 4 (some):

- [file] => ?f=290
- [mime] => application/pdf
- [size] => 267029
- [pubname] => 30
^{th}Anniversary Conference organized by Journal of Official Statistics - [pubinfo] => Statistiska CentralByrån
- [workinfo] => Poster H3
- [year] => 2015
- [title] => Agreement between Observation and Theoretical Model: Anderson Darling Statistic
- [authors] => Lorentz JÄNTSCHI, Sorana D. BOLBOACĂ
- [abstract] =>

Application of any statistical test is done under certain assumptions and violation of these assumptions led to misleading interpretations and unreliable results.

Anderson-Darling test is one statistical test used to assess the distribution of data (H0: Data follow the specified distribution vs. HA: Data do not follow the specified distribution).

The interpretation of the Anderson-Darling test is done by comparison of statistic with the critical value for a certain significance level (e.g. 20%, 10%, 5% and 1%).

Our study aimed to identify, assess and implement an explicit function for p-value associated to Anderson-Darling statistic able to take into consideration the value of the statistics and the sample size.

A Monte Carlo simulation study was conducted to determine the function able to estimate the probability associated to Anderson-Darling statistics (AD).

The following algorithm was used:

Step 1. Generate data sets of samples sizes from 2 to 46 using uniform continuous distribution [0,1];

Step 2. Repeat Step 1 for k×u times (where k=number of thresholds, e.g. 1,000; u=number of repetitions);

Step 3. Compute AD statistics for each replication in Step 2 and for each sample size;

Step 4. Order the AD value obtained in Step 3, and select a list of k values corresponding to success rates;

Step 5. Identify that function which best fit according to both sample size and the AD value.

Two equations has been obtained, one to be applied for the value of AD lower than a threshold line and the other one to be applied if the AD is higher than or equal with the value from the threshold line.

The calculation was implemented online and is available at http://l.academicdirect.org/Statistics/tests/AD/.

The input data are the sample size (2 = n = 1000) and the value of Anderson-Darling statistics (0.1 <= AD <= 10) while the output is represented by the probability to be observed a better agreement between the observed sample and the hypothetical distribution being tested (producing reliable output when 1.0×10^-11 <= min(p,1-p)). - [keywords] => Anderson-Darling statistic; measuring the agreement