MSPRT (version 2.1)

umpbt.twoT: The UMPBT alternative in two-sample T-tests

Description

This function finds the approximate data dependent UMPBT alternative in two-sample T-tests. The value of hypothesized parameter, the difference between the population means of Group-2 and Group-1, under the simple null hypothesis is set at 0.

Usage

umpbt.twoT(side = "right", type1 = 0.005, n1, n2, obs1, obs2, s)

Arguments

side

a character; direction of the alternative hypothesis H1.

Has to be one of "right" or "left".

Default: "right".

type1

a numeric in (0,1); prespecified Type 1 error probability.

Default: 0.005.

n1

a positive numeric (integer); sample size from Group-1 to be used.

n2

a positive numeric (integer); sample size from Group-2 to be used.

obs1

a numeric vector; the vector of observations from Group-1 based on which the alternative is calculated.

obs2

a numeric vector; the vector of observations from Group-2 based on which the alternative is calculated.

s

a positive numeric; the pooled sample standard deviation (sd) based on obs1 and obs2.

Can be missing if obs1 and obs2 are provided.

Value

Returns a numeric which is the UMPBT alternative in the two-sample T-test.

Details

We need either obs1 & obs2, or s.

When we are implementing the MSPRT in a two-sample T-test and we need the alternative at Step-5, this function requires all the data from both groups observed until that step in the order they were observed.

References

MSPRT: main article and supplemental information

Johnson, Valen E., Uniformly most powerful Bayesian tests., Ann. of Stat., 41, (4), 2013, pp. 1716-1741

Johnson, Valen E., Revised standards for statistical evidence., Proceedings of the National Academy of Sciences, 16, 1945. (Specially it's supplemental file)

Examples

# NOT RUN {
# suppose we get data from both groups after each observation
# a simulated ordered data at Step-30
x1.seq = rnorm(30,2,1.5)
x2.seq = rnorm(30,2,1.5)

## UMPBT alternative at step-30
# providing the data x1.seq & x2.seq
umpbt.twoT(n1= 60, n2= 60, obs1= x1.seq, obs2= x2.seq)
# }