Nstar {MSPRT}

Sample size required to achieve higher significance

Description

Given the sample size that is available at a lower level of significance, this function calculates the sample size that is required for achieving a higher level of significance so that a desired level of Type II error probability is maintained at a desired effect size.

Usage

Nstar(test.type, N, N1, N2, 
      N.increment = 1, N1.increment = 1, N2.increment = 1, 
      lower.signif = 0.05, higher.signif = 0.005, theta0, 
      side = "right", Type2.target = 0.2, theta, 
      sigma = 1, sigma1 = 1, sigma2 = 1, plot.it = T)

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.

N

Positive integer. Sample size available at the lower level of significance in one-sample tests.

N1

Positive integer. Sample size available from Group-1 at the lower level of significance in two-sample tests.

N2

Positive integer. Sample size available from Group-2 at the lower level of significance in two-sample tests.

N.increment

Positive integer. Increment in sample size allowed while searching for the sample size that is required for achieving the higher level of significance.

N1.increment

Positive integer. Increment in sample size from Group-1 allowed while searching for the sample size that is required for achieving the higher level of significance.

N2.increment

Positive integer. Increment in sample size from Group-2 allowed while searching for the sample size that is required for achieving the higher level of significance.

lower.signif

Numeric within [0,1]. Lower level of significance. Default 0.05.

higher.signif

Numeric within [0,1]. Higher level of significance. Default: 0.005.

theta0

Numeric. Hypothesized value of effect size (\theta_0) under H_0. Default: 0.5 in one-sample proportion tests, and 0 for others.

side

Character. Direction of the composite alternative hypothesis. right for H_1 : \theta > \theta_0 (default), and left for H_1 : \theta < \theta_0.

Type2.target

Numeric within [0,1]. Prespecified level of Type 2 error probability.

Default: 0.2.

theta

Numeric. Effect size value where Type2.target Type II error probability is desired at both levels of significance. Default: Fixed-design alternative (\theta_a) at the lower level of significance; that is, the effect size where the fixed design test with N samples and level of significance lower.signif has the Type II error probability Type2.target.

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.

plot.it

Logical. If TRUE (default), returns a plot. Otherwise it doesn't.

Value

• One-sample tests: Numeric. The required sample size.

• Two-sample tests: Numeric vector of length 2. The first and second components store the sample sizes required respectively from Group 1 and 2 for achieving the higher level of significance.

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
Nstar(test.type = "oneProp", N = 30)

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


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

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

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


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

## right-sided
Nstar(test.type = "oneT", N = 30)

## left-sided
Nstar(test.type = "oneT", side = "left", N = 30)


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

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

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


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

## right-sided
Nstar(test.type = "twoT", N1 = 30, N2 = 30)

## left-sided
Nstar(test.type = "twoT", side = "left", N1 = 30, N2 = 30)