Tham khảo tài liệu 'product and process comparisons_8', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . How can we determine whether two processes produce the same proportion of defectives ENGINEERING STATISTICS HANDBOOK hW tools raids lỉEÂtCH BACK Nixf 7. Product and Process Comparisons . Comparisons based on data from two processes . How can we determine whether two processes produce the same proportion of defectives Case 1 Large Samples Normal Approximation to Binomial The hypothesis of equal proportions can be tested using a z statistic If the samples are reasonably large we can use the normal approximation to the binomial to develop a test similar to testing whether two normal means are equal. Let sample 1 have X1 defects out of n1 and sample 2 have x2 defects out of n2. Calculate the proportion of defects for each sample and the z statistic below Pl ỷp l - l m l n2 where H1P1 ĨỈQP2 _ Xl 3Ĩ2 Compare z to the normal z o 2 table value for a 2-sided test. For a one sided test assuming the alternative hypothesis is p1 p2 compare z to the normal ztt table value. If the alternative hypothesis is p1 p2 compare z to -z . Case 2 An Exact Test for Small Samples http div898 handbook prc section3 1 of 5 5 1 2006 10 38 51 AM . How can we determine whether two processes produce the same proportion of defectives The Fisher Exact Probability test is an excellent choice for small samples Example of a 2x2 contingency table Determine whether two groups differ in the proportion with which they fall into two classifications The Fisher Exact Probability Test is an excellent nonparametric technique for analyzing discrete data either nominal or ordinal when the two independent samples are small in size. It is used when the results from two independent random samples fall into one or the other of two mutually exclusive classes . defect versus good or successes vs failures . In other words every subject in each group has one of two possible scores. These scores are represented by frequencies in a 2x2 contingency table. The following .
