Abstract: The Sequential Probability Ratio Test (SPRT) has been widely applied in quality control and clinical studies. There are two important quantities in SPRT:for calculating the p-value and
for estimating the sample size, where
is the i.i.d. summation of random variables and
refers to the first time that
becomes positive. For non-arithmetic i.i.d. random variables, Woodroofe (1979) provided computation formulas for these two quantities. To find the threshold for the IBD score statistics in testing genetic linkage, Tu and Siegmund (1999) provided a computation formula to calculate
for arithmetic i.i.d. random variables when
is not too small. This paper gives another computation formula to calculate
for arithmetic i.i.d. random variables, which can be applied for any positive
including
. We also provide a computation formula for
to estimate the overshoot for arithmetic i.i.d. random variables. Furthermore, we show that these two formula reproduce Woodroofe's non-arithmetic formula by letting the span
go to zero, and we derive a computation formula to calculate
, that can be applied to estimate the number of 'new-high' points in reaching a threshold.
Key words and phrases: Arithmetic, ladder height, overshoot, sample size, second moment, sequential analysis.