Type2.fixed_design: Type II error probability of fixed design tests

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

Description

Obtains the Type II error probability of fixed-design tests for testing the point null hypothesis H_0 : θ = θ_0.

Usage

Type2.fixed_design(theta, test.type, side = "right", theta0, 
                   N, N1, N2, Type1 = 0.005, 
                   sigma = 1, sigma1 = 1, sigma2 = 1)

Arguments

theta	Numeric. Effect size where the Type II error probability is desired.
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.

Value

Numeric in [0,1]. The Type II error probability of the fixed-design test at the specified effect size value theta.

Author(s)

Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya

References

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

Examples

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

## right-sided
Type2.fixed_design(theta = seq(0, 1, length.out = 10), 
                   test.type = "oneProp", N = 30)

## left-sided
Type2.fixed_design(theta = seq(0, 1, length.out = 10), side = "left", 
                   test.type = "oneProp", N = 30)


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

## right-sided
Type2.fixed_design(theta = seq(0, 1, length.out = 10), 
                   test.type = "oneZ", N = 30)

## left-sided
Type2.fixed_design(theta = seq(-1, 0, length.out = 10), side = "left", 
                   test.type = "oneZ", N = 30)


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

## right-sided
Type2.fixed_design(theta = seq(0, 1, length.out = 10), 
                   test.type = "oneT", N = 30)

## left-sided
Type2.fixed_design(theta = seq(-1, 0, length.out = 10), side = "left", 
                   test.type = "oneT", N = 30)


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

## right-sided
Type2.fixed_design(theta = seq(0, 1, length.out = 10), 
                   test.type = "twoZ", N1 = 30, N2 = 30)

## left-sided
Type2.fixed_design(theta = seq(-1, 0, length.out = 10), side = "left",
                   test.type = "twoZ", N1 = 30, N2 = 30)


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

## right-sided
Type2.fixed_design(theta = seq(0, 1, length.out = 10), 
                   test.type = "twoT", N1 = 30, N2 = 30)

## left-sided
Type2.fixed_design(theta = seq(-1, 0, length.out = 10), side = "left", 
                   test.type = "twoT", N1 = 30, N2 = 30)

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