= 0.15 and = : 0.30. fully sequential plan, based sequen- probability ratio (SPRT) (Wetherill, 1966, Chaps. 2-4), requires analysis after each decide whether continue. addition, boun- "open," which means realizations procedure might require extremely large sample sizes, perhaps somewhat larger fixed-sample-size procedure. these reasons, testing Stagewise Plans Stagewise plans compromises between efficiency fully sequential plans logistical practicality fixed-sample-size

doi:10.1201/9781482277128-10

Chapter

ABSTRACT

Table 2 Operating Characteristics of Wald Sequential Probability Ratio Plans to Test HI :p ~ PI Versus H2:p ~ P2 with Type I Error a and Power 1 - (3 Based on Quantal Response Data

PI P2 Ct 1-{3 E(NlpI) E(Nlp2) maxpE(Nlp) Pmax 0.15 0.30 0.05 0.95 43.4 36.8 64.4 0.22

0.90 32.7 33.0 48.4 0.22 0.80 22.0 26.5 32.4 0.23

0.10 0.95 38.9 27.7 49.2 0.20 0.90 28.8 24.4 35.9 0.20 0.80 18.8 18.9 23.2 0.22

0.10 0.30 0.05 0.95 22.8 17.2 31.4 0.17 0.90 17.1 15.5 23.6 0.19 0.80 11.5 12.4 15.6 0.19

0.10 0.95 20.4 13.0 24.3 0.17 0.90 15.1 11.4 17.7 0.17 0.80 9.8 8.9 11.3 0.19

0.20 0.30 0.05 0.95 103.0 94.1 160.1 0.25 0.90 77.5 84.4 120.2 0.25 0.80 52.1 67.7 81.1 0.26

0.10 0.95 92.3 70.8 121.2 0.24 0.90 68.3 62.4 89.2 0.25 0.80 44.5 48.4 57.8 0.25

0.15 0.35 0.05 0.95 26.3 21.7 38.1 0.24 0.90 19.8 19.4 28.6 0.24 0.80 13.3 15.6 19.1 0.26

0.10 0.95 23.5 16.3 29.2 0.22 0.90 17.4 14.4 21.3 0.22 0.80 11.4 11.1 13.8 0.24

0.15 0.25 0.05 0.95 89.0 78.3 135.6 0.20 0.90 67.0 70.2 101.8 0.20 0.80 45.1 56.3 68.4 0.21

0.10 0.95 79.8 58.9 103.1 0.19 0.90 59.1 52.0 75.5 0.20 0.80 38.5 40.3 48.9 0.20

k (n1,n2 , . · · , nk) (aI,a2 , . . · , ak) (rl,r2,··· ,rk)

plans. The test schedule is divided into a number of stages, specified prior to the outset of the program. At each stage a specified number of animals are placed on test. At the conclusion of each stage, the cumulative number of responses is updated and compared with prespecified acceptance and rejection points. If the observed number of responses is less than or equal to the acceptance level for that stage, H1 :p > PI is accepted. If the observed number of responses is greater than or equal to the rejection level for that stage, H2 :p ~ P2 is accepted. If the observed number of responses lies between the acceptance and rejection levels, the test continues to the next stage.