Exact calculations for sequential t, X2 and F tests

SUMMARY Sequential and group sequential procedures are proposed for monitoring repeated t, X2or F statistics. These can be used to construct sequential hypothesis tests or repeated confidence intervals when the parameter of interest is a normal mean with unknown variance or a multivariate normal mean with variance matrix known or known up to a scale factor. Exact methods for calculating error probabilities and sample size distributions are described and tables of critical values needed to implement the procedures are provided.

[1]  S. Rushton.  ON A TWO-SIDED SEQUENTIAL t-TEST , 1952 .

[2]  J. Hajnal.  A two-sample sequential t-test , 1961 .

[3]  J. Whitehead,et al.  A FORTRAN program for the design and analysis of sequential clinical trials. , 1983, Computers and biomedical research, an international journal.

[4]  C. Stein.  A Two-Sample Test for a Linear Hypothesis Whose Power is Independent of the Variance , 1945 .

[5]  G. A. Barnard,et al.  THE FREQUENCY JUSTIFICATION OF CERTAIN SEQUENTIAL TESTS , 1952 .

[6]  Christopher Jennison,et al.  Interim analyses: the repeated confidence interval approach , 1989 .

[7]  D. Siegmund.  Sequential Analysis: Tests and Confidence Intervals , 1985 .

[8]  P. O'Brien,et al.  A multiple testing procedure for clinical trials. , 1979, Biometrics.

[9]  G. Dantzig.  On the Non-Existence of Tests of "Student's" Hypothesis Having Power Functions Independent of $\sigma$ , 1940 .

[10]  P. Armitage,et al.  Closed sequential t-tests , 1962 .

[11]  P. Armitage,et al.  Repeated Significance Tests on Accumulating Data , 1969 .

[12]  B. Turnbull,et al.  Repeated confidence intervals for group sequential clinical trials. , 1984, Controlled clinical trials.

[13]  J. Edward Jackson,et al.  Sequential x 2 - and T2-Tests and Their Application to an Acceptance Sampling Problem , 1961 .

[14]  Sequential χ 2 and F tests and the related confidence intervals , 1980 .

[15]  S. Pocock.  Group sequential methods in the design and analysis of clinical trials , 1977 .

[16]  A. Lawrence Gould,et al.  Group sequential methods for clinical trials allowing early acceptance of Ho and incorporating costs , 1982 .

[17]  B. Iglewicz,et al.  A Truncated Sequential t-Test , 1970 .

[18]  P. Armitage,et al.  Boundaries for closed (wedge) sequential t test plans , 1966 .

[19]  S J Pocock,et al.  Interim analyses for randomized clinical trials: the group sequential approach. , 1982, Biometrics.

[20]  S. Rushton,et al.  On a sequential t-test. , 1950, Biometrika.

[21]  R. Suich,et al.  A Truncated Sequential t-Test for General α and β , 1973 .

[22]  J. Whitehead.  Supplementary analysis at the conclusion of a sequential clinical trial. , 1986, Biometrics.