UMPBT.alt: UMPBT alternative

In MSPRT: A Modified Sequential Probability Ratio Test (MSPRT)

Description

Given a sample size and prespecified Type I & II error probabilities, this function obtains the objective alternative in the Uniformly Most Powerful Bayesian Test (UMPBT).

Usage

UMPBT.alt(test.type, side = "right", theta0, 
          N, N1, N2, Type1 = 0.005, 
          sigma = 1, sigma1 = 1, sigma2 = 1, 
          obs, sd.obs, obs1, obs2, pooled.sd)

Arguments

test.type	Character. Type of test. Currently, the package only allows oneProp for one-sample proportion tests oneZ for one-sample z tests oneT for one-sample t tests twoZ for two-sample z tests twoT for two-sample t tests.
side	Character. Direction of the composite alternative hypothesis. right for H_1 : θ > θ_0 (default), and left for H_1 : θ < θ_0.
theta0	Numeric. Hypothesized value of effect size (θ_0) under H_0. Default: 0.5 in one-sample proportion tests, and 0 for others.
N	Positive integer. Sample size in one-sample tests.
N1	Positive integer. Sample size from Group-1 in two-sample tests.
N2	Positive integer. Sample size from Group-2 in two-sample tests.
Type1	Numeric in [0,1]. Prespecified Type I error probability. Default: 0.005.
sigma	Positive numeric. Known standard deviation in one-sample z tests. Default: 1.
sigma1	Positive numeric. Known standard deviation for Group-1 in two-sample z tests. Default: 1.
sigma2	Positive numeric. Known standard deviation for Group-2 in two-sample z tests. Default: 1.
obs	Numeric vector. The vector of observations based on which the UMPBT alternative in one-sample t test is determined. Either obs or sd.obs is required.
sd.obs	Positive numeric. The standard deviation (with divisor n-1) of observations based on which the UMPBT alternative in one-sample t test is determined. Either obs or sd.obs is required.
obs1	Numeric vector. The vector of observations from Group-1 based on which the UMPBT alternative in two-sample t test is determined. Either both obs1 and obs2, or pooled.sd is required.
obs2	Numeric vector. The vector of observations from Group-2 based on which the UMPBT alternative in two-sample t test is determined. Either both obs1 and obs2, or pooled.sd is required.
pooled.sd	Positive numeric. The pooled standard deviation of observations from Group-1 and 2 based on which the UMPBT alternative in two-sample t test is determined. Either both obs1 and obs2, or pooled.sd is required.

Value

List with two named components theta and mix.prob in one-sample proportion test. In this case, the UMPBT alternative is a mixture distribution of two points. theta contains the two points (effect sizes) and mix.prob contains their respective mixing probabilities.

Numeric in case of all the other tests. It is the UMPBT alternative effect size.

Author(s)

Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya

References

Johnson, V. E. (2013a). Revised standards for statistical evidence.Proceed-ings of the National Academy of Sciences, 110(48):19313-19317. [Article]

Johnson, V. E. (2013b). Uniformly most powerful Bayesian tests.TheAnnals of Statistics, 41(4):1716-1741. [Article]

Pramanik S., Johnson V. E. and Bhattacharya A. (2020+). A Modified Sequential Probability Ratio Test. [Arxiv]

Examples

##### one-sample proportion test #####

## right-sided
UMPBT.alt(test.type = "oneProp", N = 30)

## left-sided
UMPBT.alt(side = "left", test.type = "oneProp", N = 30)


##### one-sample z test #####

## right-sided
UMPBT.alt(test.type = "oneZ", N = 30)

## left-sided
UMPBT.alt(side = "left", test.type = "oneZ", N = 30)


##### one-sample t test #####

## observed data

set.seed(1)
x = rnorm(n = 30, mean = 0, sd = 1.5)
	
## right-sided
UMPBT.alt(test.type = "oneT", N = 30, obs = x)

## left-sided
UMPBT.alt(side = "left", test.type = "oneT", N = 30, obs = x)


##### two-sample z test #####

## right-sided
UMPBT.alt(test.type = "twoZ", N1 = 30, N2 = 30)

## left-sided
UMPBT.alt(side = "left", test.type = "twoZ", N1 = 30, N2 = 30)


##### two-sample t test #####

## observed data

set.seed(1)
x1 = rnorm(n = 30, mean = 0, sd = 1.5)
x2 = rnorm(n = 30, mean = 0, sd = 1.5)

## right-sided
UMPBT.alt(test.type = "twoT", N1 = 30, N2 = 30, 
          obs1 = x1, obs2 = x2)

## left-sided
UMPBT.alt(side = "left", test.type = "twoT", N1 = 30, N2 = 30, 
          obs1 = x1, obs2 = x2)

MSPRT documentation built on Nov. 13, 2020, 5:07 p.m.