What are Mandel s k / h test statistics?

Transcription

1 What are Mandel k / h tet tatitic?

2 Obective of Mandel k/h conitency tet tatitic k and h tet tatitic are meaure for data conitency, articularly ueful for inter-laboratory tudie By tudying the collated data deviation and accuracy, the erformance of a laboratory in term of it reliability and error can be etablihed The laboratory with oor erformance can then do it own in-houe invetigation and make corrective action for uch deficiencie

3 Mandel k and h conitency tet tatitic are dicued in ASTM E691 tandard for interlaboratory analyi : Standard ractice for conducting an interlaboratory tudy to determine the reciion of a tet method

4 Inter-laboratory cro-check and roficiency teting rogram Inter-laboratory comarion of tet reult i an efficiency way to validate the reciion of a tet method and alo to comare the technical cometence of the laboratory eronnel in term of reciion and accuracy Many articiating laboratorie will carry out erie of analye on one or more given imilar amle at about the ame eriod. The data collated are tatitically analyzed

5 Evaluating k tet tatitic k value i a meaure of within-laboratory conitency in reeatability If there are number of articiating laboratorie (),and n i the number of reeat in a laboratory ( 1, 2, 3, i..., n-1, n ) The kvalue of lab ( ) i : r k 1 ) ( 1 2, n n i i r 1 2

6 Interretation of k value The k value comare the reeatability tandard deviation of a laboratory data et with the average of the reeatability tandard deviation of all other laboratorie From the k value, we can evaluate the read of the data et and it reciion Thi tet tatitic reflect the ingle lab reeatability againt the average reeatability of all articiating laboratorie The larger the k value, the bigger i the data deviation, indicating the oorer the reciion

7 k critical value for conitency (k-crit) k-crit value i the critical value of erioune for data deviation at a given robability k-crit define a: k crit 1+ ( 1) / F where: F value i from the F F ditribution, i the number of articiating laboratorie When the k value i higher than the k-crit, it can be concluded that the tet reult deviation i eriou with oor reciion and unaccetable.

8 How to obtain the F tet tatitic value? F (v1, v2) i the F F ditribution value Degree of freedom v1 (n-1), n i the number of reeat in a ingle laboratory Degree of freedom v2 (-1)(n-1) Uon knowing the degree of freedom, we can obtain the F value from the F-F table Or ue the Ecel function FINV(0.05,v1,v2)

9 Evaluating the h tet tatitic The h tet tatitic i ued to eamine the conitency of interlaboratory data, confirming if any laboratory data i an outlier In other word, it i to indicate the accuracy of a lab reult againt the other reorted Let be the number of articiating lab with the lab mean reult a follow: ( 1, 2,...,,... The overall mean reult of thi interlaboratory tudy i : ) 1

10 Evaluating the h tet tatitic The deviation of mean reult of a lab ( ) from the overall mean i: The tandard deviation of thee comarion i : The h value of lab ( ) i : d h d 1 d 2 1

11 Interretation of h tet value h tet tatitic value reflect the deviation of a ingle laboratory mean tet reult from the overall mean reult obtained from all articiating laboratorie The larger the h value, the bigger the deviation, the oorer i the accuracy of that ingle laboratory

12 h critical value for conitency (h-crit) h-crit i a meaure of erioune in a lab inaccuracy h-crit define a: h crit ± t( 1) ( t 2 + 2) where:ti the Student ditribution with degree of freedom v-2, and α 0.05 ; i the number of articiating laboratorie Whenthe hvalue i larger than the h-crit,it i concluded that the mean reult given by the laboratory concerned i not accurate and reliable

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