MSPRT (version 3.0)

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

Description

Obtains the Type II error probability of fixed-design tests for testing the point null hypothesis \(H_0 : \theta = \theta_0\).

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 \(H_1 : \theta > \theta_0\) (default), and left for \(H_1 : \theta < \theta_0\).

theta0

Numeric. Hypothesized value of effect size (\(\theta_0\)) 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.

References

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

Examples

# NOT RUN {
##### 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)
# }