Revisiting Clopper-Pearson
نویسندگان
چکیده
This paper adds one more contribution to the large literature on binomial confidence intervals for small samples (e.g., Clopper and Pearson 1934; Pearson and Hartley 1954; Sterne 1954; Crow 1956; Blyth and Still 1983; Blyth 1986; Santner and Duffy 1989; Agresti and Coull 1998; Henderson and Meyer 2001). Clopper and Peason (1934) gave the first two-sided binomial confidence intervals, in graphical form, with .95 and .99 coefficients. Their intervals satisfy the condition of equi-sized tails, so that each of the two corresponding one-sided tests has significance level ≤ α/2. Several authors (e.g., Sterne 1954; Crow 1956; Blyth and Still 1983) attempted to weaken the Clopper-Pearson restriction by aiming just at interval-valued confidence regions of confidence level ≥ 1−α. In particular, Sterne (1954) attempted to construct intervals by sequentially selecting most-probable variates for the coresponding two-sided acceptance regions, until their total probability is ≥ 1 − α. Crow (1956) pointed out
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