| Title: | A Modified Sequential Probability Ratio Test (MSPRT) |
|---|---|
| Description: | Given the maximum available sample size (N) for an experiment, and the target levels of Type I and II error probabilities, this package designs a modified SPRT (MSPRT). For any designed MSPRT the package can also obtain its operating characteristics and implement the test for a given sequentially observed data. The MSPRT is defined in a manner very similar to Wald's initial proposal. The proposed test has shown evidence of reducing the average sample size required to perform statistical hypothesis tests at specified levels of significance and power. Currently, the package implements one-sample proportion tests, one and two-sample z tests, and one and two-sample t tests. A brief user guidance for this package is provided below. One can also refer to the supplemental information for the same. |
| Authors: | Sandipan Pramanik [aut, cre], Valen E. Johnson [aut], Anirban Bhattacharya [aut] |
| Maintainer: | Sandipan Pramanik <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 3.0 |
| Built: | 2025-02-19 03:59:38 UTC |
| Source: | https://github.com/cran/MSPRT |
Given the maximum available sample size (N) for an experiment, and the target levels of Type I and II error probabilities, this package designs a modified SPRT (MSPRT). For any designed MSPRT the package can also obtain its operating characteristics and implement the test for a given sequentially observed data. The MSPRT is defined in a manner very similar to Wald's initial proposal. The proposed test has shown evidence of reducing the average sample size required to perform statistical hypothesis tests at specified levels of significance and power. Currently, the package implements one-sample proportion tests, one and two-sample z tests, and one and two-sample t tests. A brief user guidance for this package is provided below. One can also refer to the supplemental information for the same.
| Package: | MSPRT |
| Type: | Package |
| Version: | 3.0 |
| Date: | 11-11-2020 |
| License: | GPL>=2 |
Sandipan Pramanik [aut, cre], Valen E. Johnson [aut], Anirban Bhattacharya [aut]
Maintainer: Sandipan Pramanik <[email protected]>
Given the maximum available sample size and prespecified Type I & II error probabilities, this function designs/obtains the corresponding MSPRT.
design.MSPRT(test.type, side = "right", theta0, theta1 = T, Type1.target = 0.005, Type2.target = 0.2, N.max, N1.max, N2.max, sigma = 1, sigma1 = 1, sigma2 = 1, batch.size, batch1.size, batch2.size, nReplicate = 1e+06, verbose = T, seed = 1)design.MSPRT(test.type, side = "right", theta0, theta1 = T, Type1.target = 0.005, Type2.target = 0.2, N.max, N1.max, N2.max, sigma = 1, sigma1 = 1, sigma2 = 1, batch.size, batch1.size, batch2.size, nReplicate = 1e+06, verbose = T, seed = 1)
test.type |
Character. Type of test. Currently, the package only allows
|
side |
Character. Direction of the composite alternative hypothesis. |
theta0 |
Numeric. Hypothesized value of effect size ( Default: 0.5 in one-sample proportion tests, and 0 for others. |
theta1 |
Logical, numeric or list (two components with names
Note: In case of two-sided tests at a given level of significance, there are two effect sizes under |
Type1.target |
Numeric within [0,1]. Prespecified level of Type I error probability. Default: 0.005. The MSPRT exactly maintains its Type I error probability at this value. |
Type2.target |
Numeric within [0,1]. Prespecified level of Type 2 error probability. Default: 0.2. The MSPRT approximately maintains its Type II error probability at this value at the corresponding fixed-design alternative ( |
N.max |
Positive integer. Maximum available sample size in one-sample tests. |
N1.max |
Positive integer. Maximum available sample size from Group-1 in two-sample tests. |
N2.max |
Positive integer. Maximum available sample size from Group-2 in two-sample tests. |
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. |
batch.size |
Integer vector. A vector denoting the number of observations that are planned to be observed at each sequential step in one-sample tests. Default:
Default values mean the sequential analysis is performed after observing each observation. This corresponds to a sequential MSPRT. If any batch size is more than 1 (or more than 2 in the 1st step for t test) it corresponds to a group sequential MSPRT. Note: First batch size for t tests needs to be at least 2. The length of batch.size equals to the maximum number of planned sequential analyses. |
batch1.size |
Integer vector. A vector denoting the number of observations that are planned to be observed from Group-1 at each sequential step in two-sample tests. Default:
Default values mean the sequential analysis is performed after observing each observation from Group-1. |
batch2.size |
Integer vector. A vector denoting the number of observations that are planned to be observed from Group-2 at each sequential step in two-sample tests. Default:
Default values mean the sequential analysis is performed after observing each observation from Group-2. |
nReplicate |
Positive integer. Total number of replications to be used in Monte Carlo simulation for calculating the termination threshold and the operating characteristics of the MSPRT. Default: 1,000,000. |
verbose |
Logical. If |
seed |
Integer. Random number generating seed. Default: 1. |
List. The list has the following named components in case of one-sided one-sample tests:
TypeI.attained |
Numeric in [0,1]. Type I error probability attained by the designed MSPRT. |
Type2.attained |
Numeric in [0,1]. Type II error probability attained by the designed MSPRT at the specified alternative effect size |
N |
List.
|
EN |
Numeric vector.
|
UMPBT or theta.UMPBT |
The UMPBT alternative. Note: Not returned in t tests as it depends on the data. |
theta1 |
Returned only if |
Type2.fixed.design |
Numeric in [0,1]. Type II error probability attained by the fixed design test with sample size |
RejectH0.threshold |
Positive numeric. Threshold for rejecting |
RejectH1.threshold |
Positive numeric. Threshold for accepting |
termination.threshold |
Positive numeric. Termination threshold of the MSPRT. |
In case of one-sided two-sample tests the above components are returned with following modifications:
N: |
List.
|
EN |
List.
Each of the named components |
In case of two-sided tests the above components are returned with following modifications:
Type2.attained |
Numeric vector of length 2 with both elements in [0,1]. The first and second component is the Type II error probability of the MSPRT at the specified alternative effect sizes |
N |
This is the same as in one-sided tests if |
EN |
Numeric vector. The same as in one-sided tests if |
Additionally, the output list also contains the provided arguments of design.MSPRT, and
nAnalyses |
Positive integer. This is the maximum number of sequential analyses that is planned. This equals to the |
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
Pramanik S., Johnson V. E. and Bhattacharya A. (2020+). A Modified Sequential Probability Ratio Test. [Arxiv]
##### one-sample proportion test ##### ## right-sided #design.MSPRT(test.type = 'oneProp', side = 'right', # N.max = 20) ## left-sided #design.MSPRT(test.type = 'oneProp', side = 'right', # N.max = 20) ## two-sided #design.MSPRT(test.type = 'oneProp', side = 'both', # N.max = 20) ##### one-sample z test ##### ## right-sided #design.MSPRT(test.type = 'oneZ', side = 'right', # N.max = 20) ## left-sided #design.MSPRT(test.type = 'oneZ', side = 'right', # N.max = 20) ## two-sided #design.MSPRT(test.type = 'oneZ', side = 'both', # N.max = 20) ##### one-sample t test ##### ## right-sided #design.MSPRT(test.type = 'oneT', side = 'right', # N.max = 20) ## left-sided #design.MSPRT(test.type = 'oneT', side = 'right', # N.max = 20) ## two-sided #design.MSPRT(test.type = 'oneT', side = 'both', # N.max = 20) ##### two-sample z test ##### ## right-sided #design.MSPRT(test.type = 'twoZ', side = 'right', # N1.max = 20, N2.max = 20) ## left-sided #design.MSPRT(test.type = 'twoZ', side = 'left', # N1.max = 20, N2.max = 20) ## two-sided #design.MSPRT(test.type = 'twoZ', side = 'both', # N1.max = 20, N2.max = 20) ##### two-sample t test ##### ## right-sided #design.MSPRT(test.type = 'twoT', side = 'right', # N1.max = 20, N2.max = 20) ## left-sided #design.MSPRT(test.type = 'twoT', side = 'left', # N1.max = 20, N2.max = 20) ## two-sided #design.MSPRT(test.type = 'twoT', side = 'both', # N1.max = 20, N2.max = 20)##### one-sample proportion test ##### ## right-sided #design.MSPRT(test.type = 'oneProp', side = 'right', # N.max = 20) ## left-sided #design.MSPRT(test.type = 'oneProp', side = 'right', # N.max = 20) ## two-sided #design.MSPRT(test.type = 'oneProp', side = 'both', # N.max = 20) ##### one-sample z test ##### ## right-sided #design.MSPRT(test.type = 'oneZ', side = 'right', # N.max = 20) ## left-sided #design.MSPRT(test.type = 'oneZ', side = 'right', # N.max = 20) ## two-sided #design.MSPRT(test.type = 'oneZ', side = 'both', # N.max = 20) ##### one-sample t test ##### ## right-sided #design.MSPRT(test.type = 'oneT', side = 'right', # N.max = 20) ## left-sided #design.MSPRT(test.type = 'oneT', side = 'right', # N.max = 20) ## two-sided #design.MSPRT(test.type = 'oneT', side = 'both', # N.max = 20) ##### two-sample z test ##### ## right-sided #design.MSPRT(test.type = 'twoZ', side = 'right', # N1.max = 20, N2.max = 20) ## left-sided #design.MSPRT(test.type = 'twoZ', side = 'left', # N1.max = 20, N2.max = 20) ## two-sided #design.MSPRT(test.type = 'twoZ', side = 'both', # N1.max = 20, N2.max = 20) ##### two-sample t test ##### ## right-sided #design.MSPRT(test.type = 'twoT', side = 'right', # N1.max = 20, N2.max = 20) ## left-sided #design.MSPRT(test.type = 'twoT', side = 'left', # N1.max = 20, N2.max = 20) ## two-sided #design.MSPRT(test.type = 'twoT', side = 'both', # N1.max = 20, N2.max = 20)
design.MSPRT calls this function for designing the MSPRT in one-sample proportion tests. Users please refer to design.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
design.MSPRT calls this function for designing the MSPRT in one-sample t tests. Users please refer to design.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
design.MSPRT calls this function for designing the MSPRT in one-sample z tests. Users please refer to design.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
design.MSPRT calls this function for designing the MSPRT in two-sample t tests. Users please refer to design.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
design.MSPRT calls this function for designing the MSPRT in two-sample z tests. Users please refer to design.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
Given a maximum sample size that is planned to use, this function obtains the maximum sample size () that is suggested to use in designing the MSPRT for one-sample proportion tests.
effectiveN.oneProp(N, side = "right", Type1 = 0.005, theta0 = 0.5, plot.it = T)effectiveN.oneProp(N, side = "right", Type1 = 0.005, theta0 = 0.5, plot.it = T)
N |
Positive integer. Maximum sample that is intended to use. |
side |
Character. Direction of the composite alternative hypothesis. |
Type1 |
Numeric in [0,1]. Prespecified Type I error probability. Default: 0.005. |
theta0 |
Numeric. Hypothesized value of effect size ( |
plot.it |
Logical. If |
Positive integer. This is suggested to use in OCandASN.MSPRT as the maximum availeble sample size () to design the MSPRT for one-sample proportion tests.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
Pramanik S., Johnson V. E. and Bhattacharya A. (2020+). A Modified Sequential Probability Ratio Test. [Arxiv]
effectiveN.oneProp(N = 30)effectiveN.oneProp(N = 30)
Given a sample size and prespecified Type I & II error probabilities, this function obtains the fixed-design alternative () for testing the point null hypothesis .
fixed_design.alt(test.type, side = "right", theta0, N, N1, N2, Type1 = 0.005, Type2 = 0.2, sigma = 1, sigma1 = 1, sigma2 = 1)fixed_design.alt(test.type, side = "right", theta0, N, N1, N2, Type1 = 0.005, Type2 = 0.2, sigma = 1, sigma1 = 1, sigma2 = 1)
test.type |
Character. Type of test. Currently, the package only allows
|
side |
Character. Direction of the composite alternative hypothesis. |
theta0 |
Numeric. Hypothesized value of effect size ( |
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. |
Type2 |
Numeric in [0,1]. Prespecified Type II error probability. Default: 0.2. |
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. |
Numeric. The fixed-design alternative effect size ().
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
Pramanik S., Johnson V. E. and Bhattacharya A. (2020+). A Modified Sequential Probability Ratio Test. [Arxiv]
##### one-sample proportion test ##### ## right-sided fixed_design.alt(test.type = "oneProp", N = 30) ## left-sided fixed_design.alt(side = "left", test.type = "oneProp", N = 30) ##### one-sample z test ##### ## right-sided fixed_design.alt(test.type = "oneZ", N = 30) ## left-sided fixed_design.alt(side = "left", test.type = "oneZ", N = 30) ##### one-sample t test ##### ## right-sided fixed_design.alt(test.type = "oneT", N = 30) ## left-sided fixed_design.alt(side = "left", test.type = "oneT", N = 30) ##### two-sample z test ##### ## right-sided fixed_design.alt(test.type = "twoZ", N1 = 30, N2 = 30) ## left-sided fixed_design.alt(side = "left", test.type = "twoZ", N1 = 30, N2 = 30) ##### two-sample t test ##### ## right-sided fixed_design.alt(test.type = "twoT", N1 = 30, N2 = 30) ## left-sided fixed_design.alt(side = "left", test.type = "twoT", N1 = 30, N2 = 30)##### one-sample proportion test ##### ## right-sided fixed_design.alt(test.type = "oneProp", N = 30) ## left-sided fixed_design.alt(side = "left", test.type = "oneProp", N = 30) ##### one-sample z test ##### ## right-sided fixed_design.alt(test.type = "oneZ", N = 30) ## left-sided fixed_design.alt(side = "left", test.type = "oneZ", N = 30) ##### one-sample t test ##### ## right-sided fixed_design.alt(test.type = "oneT", N = 30) ## left-sided fixed_design.alt(side = "left", test.type = "oneT", N = 30) ##### two-sample z test ##### ## right-sided fixed_design.alt(test.type = "twoZ", N1 = 30, N2 = 30) ## left-sided fixed_design.alt(side = "left", test.type = "twoZ", N1 = 30, N2 = 30) ##### two-sample t test ##### ## right-sided fixed_design.alt(test.type = "twoT", N1 = 30, N2 = 30) ## left-sided fixed_design.alt(side = "left", test.type = "twoT", N1 = 30, N2 = 30)
This function implements the MSPRT for a sequentially observed data.
implement.MSPRT(obs, obs1, obs2, design.MSPRT.object, termination.threshold, test.type, side = "right", theta0, Type1.target = 0.005, Type2.target = 0.2, N.max, N1.max, N2.max, sigma = 1, sigma1 = 1, sigma2 = 1, batch.size, batch1.size, batch2.size, verbose = T, plot.it = 2)implement.MSPRT(obs, obs1, obs2, design.MSPRT.object, termination.threshold, test.type, side = "right", theta0, Type1.target = 0.005, Type2.target = 0.2, N.max, N1.max, N2.max, sigma = 1, sigma1 = 1, sigma2 = 1, batch.size, batch1.size, batch2.size, verbose = T, plot.it = 2)
obs |
Numeric vector. The vector of data in the order they are sequentially observed for one-sample tests.
Note: Its length can't exceed the length of |
obs1 |
Numeric vector. The vector of data in the order they are sequentially observed from Group-1 for two-sample tests.
Note: Its length can't exceed the length of |
obs2 |
Numeric vector. The vector of data in the order they are sequentially observed from Group-2 for two-sample tests.
Note: Its length can't exceed the length of |
design.MSPRT.object |
List. The output returned from |
termination.threshold |
Positive numeric. Termination threshold of the designed MSPRT. |
test.type |
Same as in |
side |
Same as in |
theta0 |
Same as in |
Type1.target |
Same as in |
Type2.target |
Same as in |
N.max |
Same as in |
N1.max |
Same as in |
N2.max |
Same as in |
sigma |
Same as in |
sigma1 |
Same as in |
sigma2 |
Same as in |
batch.size |
Same as in |
batch1.size |
Same as in |
batch2.size |
Same as in |
verbose |
Logical. If TRUE (default), returns messages of the current proceedings. Otherwise it doesn't. |
plot.it |
0, 1 or 2 (default).
|
If design.MSPRT.object is provided, one can only additionally provide nReplicate, nCore, verbose and seed (Easier option). Otherwise, just like in design.MSPRT, all the other arguments together with termination.threshold (obtained from design.MSPRT) needs to be provided adequately.
List. The list has the following named components in case of one-sided one-sample tests:
n |
Positive integer. Number of samples required to reach the decision. |
decision |
Character. The decision reached. The possibilities are |
RejectH0.threshold |
Positive numeric. Threshold for rejecting |
RejectH1.threshold |
Positive numeric. Threshold for accepting |
LR |
Numeric vector. Vector of weighted likelihood ratios (proportion tests) or likelihood ratios (z tests) or Bayes factor (t tests) that are computed at each step of sequential analysis until either a decision is reached or the maximum available number of samples ( |
UMPBT alternative |
This stores the UMPBT alternative(s) as
|
In case of two-sample tests, the n output above is replaced by n1 and n2. They are positive integers and refer to the number of samples from Group-1 and 2 required to reach the decision.
In case of two-sided tests at level of significance , the MSPRT carries out a right and a left sided test simultaneously at level of significance . In this case the outputs are same as above with following changes in components in the returned list:
LR |
List. It has two components named |
UMPBT or theta.UMPBT |
List with two components named |
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
Pramanik S., Johnson V. E. and Bhattacharya A. (2020+). A Modified Sequential Probability Ratio Test. [Arxiv]
#################### one-sample proportion test #################### #### right sided #### ### design #design.oneprop.right = design.MSPRT(test.type = 'oneProp', side = 'right', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0.5 # change effect size to experiment #y = rbinom(20, 1, theta.gen) #implement.oneprop.right = implement.MSPRT(obs = y, # design.MSPRT.object = design.oneprop.right) #### left sided #### ### design #design.oneprop.left = design.MSPRT(test.type = 'oneProp', side = 'left', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0.5 # change effect size to experiment #y = rbinom(20, 1, theta.gen) #implement.oneprop.left = implement.MSPRT(obs = y, # design.MSPRT.object = design.oneprop.left) #### both sided #### ### design #design.oneprop.both = design.MSPRT(test.type = 'oneProp', side = 'both', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0.5 # change effect size to experiment #y = rbinom(20, 1, theta.gen) #implement.oneprop.both = implement.MSPRT(obs = y, # design.MSPRT.object = design.oneprop.both) #################### one-sample z test #################### #### right sided #### ### design #design.onez.right = design.MSPRT(test.type = 'oneZ', side = 'right', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y = rnorm(20, theta.gen, design.onez.right$sigma) #implement.onez.right = implement.MSPRT(obs = y, # design.MSPRT.object = design.onez.right) #### left sided #### ### design #design.onez.left = design.MSPRT(test.type = 'oneZ', side = 'left', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y = rnorm(20, theta.gen, design.onez.left$sigma) #implement.onez.left = implement.MSPRT(obs = y, # design.MSPRT.object = design.onez.left) #### both sided #### ### design #design.onez.both = design.MSPRT(test.type = 'oneZ', side = 'both', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y = rnorm(20, theta.gen, design.onez.both$sigma) #implement.onez.both = implement.MSPRT(obs = y, # design.MSPRT.object = design.onez.both) #################### one-sample t test #################### #### right sided #### ### design #design.onet.right = design.MSPRT(test.type = 'oneT', side = 'right', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y = rnorm(20, theta.gen, 1) #implement.onet.right = implement.MSPRT(obs = y, # design.MSPRT.object = design.onet.right) #### left sided #### ### design #design.onet.left = design.MSPRT(test.type = 'oneT', side = 'left', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y = rnorm(20, theta.gen, 1) #implement.onet.left = implement.MSPRT(obs = y, # design.MSPRT.object = design.onet.left) #### both sided #### ### design #design.onet.both = design.MSPRT(test.type = 'oneT', side = 'both', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y = rnorm(20, theta.gen, 1) #implement.onet.both = implement.MSPRT(obs = y, # design.MSPRT.object = design.onet.both) #################### two-sample z test #################### #### right sided #### ### design #design.twoz.right = design.MSPRT(test.type = 'twoZ', side = 'right', # N1.max = 20, N2.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y1 = rnorm(20, theta.gen/2, design.twoz.right$sigma1) #y2 = rnorm(20, -theta.gen/2, design.twoz.right$sigma2) #implement.twoz.right = implement.MSPRT(obs1 = y1, obs2 = y2, # design.MSPRT.object = design.twoz.right) #### left sided #### ### design #design.twoz.left = design.MSPRT(test.type = 'twoZ', side = 'left', # N1.max = 20, N2.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y1 = rnorm(20, theta.gen/2, design.twoz.left$sigma1) #y2 = rnorm(20, -theta.gen/2, design.twoz.left$sigma2) #implement.twoz.left = implement.MSPRT(obs1 = y1, obs2 = y2, # design.MSPRT.object = design.twoz.left) #### both sided #### ### design #design.twoz.both = design.MSPRT(test.type = 'twoZ', side = 'both', # N1.max = 20, N2.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y1 = rnorm(20, theta.gen/2, design.twoz.both$sigma1) #y2 = rnorm(20, -theta.gen/2, design.twoz.both$sigma2) #implement.twoz.both = implement.MSPRT(obs1 = y1, obs2 = y2, # design.MSPRT.object = design.twoz.both) #################### two-sample t test #################### #### right sided #### ### design #design.twot.right = design.MSPRT(test.type = 'twoT', side = 'right', # N1.max = 20, N2.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y1 = rnorm(20, theta.gen/2, 1) #y2 = rnorm(20, -theta.gen/2, 1) #implement.twot.right = implement.MSPRT(obs1 = y1, obs2 = y2, # design.MSPRT.object = design.twot.right) #### left sided #### ### design #design.twot.left = design.MSPRT(test.type = 'twoT', side = 'left', # N1.max = 20, N2.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y1 = rnorm(20, theta.gen/2, 1) #y2 = rnorm(20, -theta.gen/2, 1) #implement.twot.left = implement.MSPRT(obs1 = y1, obs2 = y2, # design.MSPRT.object = design.twot.left) #### both sided #### ### design #design.twot.both = design.MSPRT(test.type = 'twoT', side = 'both', # N1.max = 20, N2.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y1 = rnorm(20, theta.gen/2, 1) #y2 = rnorm(20, -theta.gen/2, 1) #implement.twot.both = implement.MSPRT(obs1 = y1, obs2 = y2, # design.MSPRT.object = design.twot.both)#################### one-sample proportion test #################### #### right sided #### ### design #design.oneprop.right = design.MSPRT(test.type = 'oneProp', side = 'right', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0.5 # change effect size to experiment #y = rbinom(20, 1, theta.gen) #implement.oneprop.right = implement.MSPRT(obs = y, # design.MSPRT.object = design.oneprop.right) #### left sided #### ### design #design.oneprop.left = design.MSPRT(test.type = 'oneProp', side = 'left', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0.5 # change effect size to experiment #y = rbinom(20, 1, theta.gen) #implement.oneprop.left = implement.MSPRT(obs = y, # design.MSPRT.object = design.oneprop.left) #### both sided #### ### design #design.oneprop.both = design.MSPRT(test.type = 'oneProp', side = 'both', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0.5 # change effect size to experiment #y = rbinom(20, 1, theta.gen) #implement.oneprop.both = implement.MSPRT(obs = y, # design.MSPRT.object = design.oneprop.both) #################### one-sample z test #################### #### right sided #### ### design #design.onez.right = design.MSPRT(test.type = 'oneZ', side = 'right', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y = rnorm(20, theta.gen, design.onez.right$sigma) #implement.onez.right = implement.MSPRT(obs = y, # design.MSPRT.object = design.onez.right) #### left sided #### ### design #design.onez.left = design.MSPRT(test.type = 'oneZ', side = 'left', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y = rnorm(20, theta.gen, design.onez.left$sigma) #implement.onez.left = implement.MSPRT(obs = y, # design.MSPRT.object = design.onez.left) #### both sided #### ### design #design.onez.both = design.MSPRT(test.type = 'oneZ', side = 'both', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y = rnorm(20, theta.gen, design.onez.both$sigma) #implement.onez.both = implement.MSPRT(obs = y, # design.MSPRT.object = design.onez.both) #################### one-sample t test #################### #### right sided #### ### design #design.onet.right = design.MSPRT(test.type = 'oneT', side = 'right', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y = rnorm(20, theta.gen, 1) #implement.onet.right = implement.MSPRT(obs = y, # design.MSPRT.object = design.onet.right) #### left sided #### ### design #design.onet.left = design.MSPRT(test.type = 'oneT', side = 'left', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y = rnorm(20, theta.gen, 1) #implement.onet.left = implement.MSPRT(obs = y, # design.MSPRT.object = design.onet.left) #### both sided #### ### design #design.onet.both = design.MSPRT(test.type = 'oneT', side = 'both', # N.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y = rnorm(20, theta.gen, 1) #implement.onet.both = implement.MSPRT(obs = y, # design.MSPRT.object = design.onet.both) #################### two-sample z test #################### #### right sided #### ### design #design.twoz.right = design.MSPRT(test.type = 'twoZ', side = 'right', # N1.max = 20, N2.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y1 = rnorm(20, theta.gen/2, design.twoz.right$sigma1) #y2 = rnorm(20, -theta.gen/2, design.twoz.right$sigma2) #implement.twoz.right = implement.MSPRT(obs1 = y1, obs2 = y2, # design.MSPRT.object = design.twoz.right) #### left sided #### ### design #design.twoz.left = design.MSPRT(test.type = 'twoZ', side = 'left', # N1.max = 20, N2.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y1 = rnorm(20, theta.gen/2, design.twoz.left$sigma1) #y2 = rnorm(20, -theta.gen/2, design.twoz.left$sigma2) #implement.twoz.left = implement.MSPRT(obs1 = y1, obs2 = y2, # design.MSPRT.object = design.twoz.left) #### both sided #### ### design #design.twoz.both = design.MSPRT(test.type = 'twoZ', side = 'both', # N1.max = 20, N2.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y1 = rnorm(20, theta.gen/2, design.twoz.both$sigma1) #y2 = rnorm(20, -theta.gen/2, design.twoz.both$sigma2) #implement.twoz.both = implement.MSPRT(obs1 = y1, obs2 = y2, # design.MSPRT.object = design.twoz.both) #################### two-sample t test #################### #### right sided #### ### design #design.twot.right = design.MSPRT(test.type = 'twoT', side = 'right', # N1.max = 20, N2.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y1 = rnorm(20, theta.gen/2, 1) #y2 = rnorm(20, -theta.gen/2, 1) #implement.twot.right = implement.MSPRT(obs1 = y1, obs2 = y2, # design.MSPRT.object = design.twot.right) #### left sided #### ### design #design.twot.left = design.MSPRT(test.type = 'twoT', side = 'left', # N1.max = 20, N2.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y1 = rnorm(20, theta.gen/2, 1) #y2 = rnorm(20, -theta.gen/2, 1) #implement.twot.left = implement.MSPRT(obs1 = y1, obs2 = y2, # design.MSPRT.object = design.twot.left) #### both sided #### ### design #design.twot.both = design.MSPRT(test.type = 'twoT', side = 'both', # N1.max = 20, N2.max = 20) ### implementation #set.seed(1) #theta.gen = 0 # change effect size to experiment #y1 = rnorm(20, theta.gen/2, 1) #y2 = rnorm(20, -theta.gen/2, 1) #implement.twot.both = implement.MSPRT(obs1 = y1, obs2 = y2, # design.MSPRT.object = design.twot.both)
implement.MSPRT calls this function for implementing the MSPRT in one-sample proportion tests. Users please refer to implement.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
implement.MSPRT calls this function for implementing the MSPRT in one-sample t tests. Users please refer to implement.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
implement.MSPRT calls this function for implementing the MSPRT in one-sample z tests. Users please refer to implement.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
implement.MSPRT calls this function for implementing the MSPRT in two-sample t tests. Users please refer to implement.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
implement.MSPRT calls this function for implementing the MSPRT in two-sample z tests. Users please refer to implement.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
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.
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)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)
test.type |
Character. Type of test. Currently, the package only allows
|
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 ( |
side |
Character. Direction of the composite alternative hypothesis. |
Type2.target |
Numeric within [0,1]. Prespecified level of Type 2 error probability. Default: 0.2. |
theta |
Numeric. Effect size value where |
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 |
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.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
Pramanik S., Johnson V. E. and Bhattacharya A. (2020+). A Modified Sequential Probability Ratio Test. [Arxiv]
##### 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)##### 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)
This function obtains the operating characteristics, that is the probability of accepting and the sample size required on average for reaching a decision, for a designed MSPRT at the specified effect size(s).
OCandASN.MSPRT(theta, design.MSPRT.object, termination.threshold, test.type, side = "right", theta0, Type1.target = 0.005, Type2.target = 0.2, N.max, N1.max, N2.max, sigma = 1, sigma1 = 1, sigma2 = 1, batch.size, batch1.size, batch2.size, nReplicate = 1e+06, nCore = max(1, detectCores() - 1), verbose = T, seed = 1)OCandASN.MSPRT(theta, design.MSPRT.object, termination.threshold, test.type, side = "right", theta0, Type1.target = 0.005, Type2.target = 0.2, N.max, N1.max, N2.max, sigma = 1, sigma1 = 1, sigma2 = 1, batch.size, batch1.size, batch2.size, nReplicate = 1e+06, nCore = max(1, detectCores() - 1), verbose = T, seed = 1)
theta |
Numeric vector. Vector of effect size(s) where the operating characteristics of the MSPRT is desired. |
design.MSPRT.object |
List. The output returned from |
termination.threshold |
Positive numeric. Termination threshold of the designed MSPRT. |
test.type |
Same as in |
side |
Same as in |
theta0 |
Same as in |
Type1.target |
Same as in |
Type2.target |
Same as in |
N.max |
Same as in |
N1.max |
Same as in |
N2.max |
Same as in |
sigma |
Same as in |
sigma1 |
Same as in |
sigma2 |
Same as in |
batch.size |
Same as in |
batch1.size |
Same as in |
batch2.size |
Same as in |
nReplicate |
Positive integer. Total number of replications to be used in Monte Carlo simulation for calculating the termination threshold and the operating characteristics of the MSPRT. Default: 1,000,000. |
verbose |
Logical. If |
nCore |
Positive integer. Total number of cores available for computation. Can be anything Default: |
seed |
Integer. Random number generating seed. Default: 1. |
If design.MSPRT.object is provided, one can only additionally provide nReplicate, nCore, verbose and seed (Easier option). Otherwise, just like in design.MSPRT, all the other arguments together with termination.threshold (obtained from design.MSPRT) needs to be provided adequately.
Data frame.
One-sample tests: The data frame has 3 columns named theta, acceptH0.prob and EN, and the number of rows equals to the number of effect sizes (length of theta) where the operating characteristics are evaluated. Each row corresponds to a particular value of theta (effect size). The columns respectively contain the value of a particular theta (effect size), and the probability of accepting the $H_0$ and the average sample size required by the MSPRT for reaching a decision thereat.
Two-sample tests: The data frame has 4 columns named theta, acceptH0.prob, EN1 and EN2, and the number of rows equals to the number of effect sizes (length of theta) where the operating characteristics are evaluated. Each row corresponds to a particular value of theta (effect size). The columns respectively contain the value of a particular theta (effect size), and the probability of accepting the at that effect size, and the average sample size from Group-1 & 2 that is required by the MSPRT for reaching a decision thereat.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
Pramanik S., Johnson V. E. and Bhattacharya A. (2020+). A Modified Sequential Probability Ratio Test. [Arxiv]
#################### one-sample proportion test #################### #### right sided #### ### design #design.oneprop.right <- design.MSPRT(test.type = 'oneProp', side = 'right', # N.max = 20) ### OC and ASN #OC.oneprop.right <- OCandASN.MSPRT(theta = seq(design.oneprop.right$theta0, 1, # length.out = 3), # design.MSPRT.object = design.oneprop.right) #### left sided #### ### design #design.oneprop.left = design.MSPRT(test.type = 'oneProp', side = 'left', # N.max = 20) ### OC and ASN #OC.oneprop.left = OCandASN.MSPRT(theta = seq(0, design.oneprop.right$theta0, # length.out = 3), # design.MSPRT.object = design.oneprop.left) #### both sided #### ### design #design.oneprop.both = design.MSPRT(test.type = 'oneProp', side = 'both', # N.max = 20) ### OC and ASN #OC.oneprop.both = OCandASN.MSPRT(theta = seq(0, 1, length.out = 3), # design.MSPRT.object = design.oneprop.both) #################### one-sample z test #################### #### right sided #### ### design #design.onez.right = design.MSPRT(test.type = 'oneZ', side = 'right', # N.max = 20) ### OC and ASN #OC.onez.right = OCandASN.MSPRT(theta = seq(design.onez.right$theta0, # design.onez.right$theta0 + 3*design.onez.right$sigma, # length.out = 3), # design.MSPRT.object = design.onez.right) #### left sided #### ### design #design.onez.left = design.MSPRT(test.type = 'oneZ', side = 'left', # N.max = 20) ### OC and ASN #OC.onez.left = OCandASN.MSPRT(theta = seq(design.onez.left$theta0 - 3*design.onez.left$sigma, # design.onez.left$theta0, # length.out = 3), # design.MSPRT.object = design.onez.left) #### both sided #### ### design #design.onez.both = design.MSPRT(test.type = 'oneZ', side = 'both', # N.max = 20) ### OC and ASN #OC.onez.both = OCandASN.MSPRT(theta = seq(design.onez.both$theta0 - 3*design.onez.both$sigma, # design.onez.both$theta0 + 3*design.onez.both$sigma, # length.out = 3), # design.MSPRT.object = design.onez.both) #################### one-sample t test #################### #### right sided #### ### design #design.onet.right = design.MSPRT(test.type = 'oneT', side = 'right', # N.max = 20) ### OC and ASN #OC.onet.right = OCandASN.MSPRT(theta = seq(design.onet.right$theta0, 1, # length.out = 3), # design.MSPRT.object = design.onet.right) #### left sided #### ### design #design.onet.left = design.MSPRT(test.type = 'oneT', side = 'left', # N.max = 20) ### OC and ASN #OC.onet.left = OCandASN.MSPRT(theta = seq(-1, design.onet.left$theta0, # length.out = 3), # design.MSPRT.object = design.onet.left) #### both sided #### ### design #design.onet.both = design.MSPRT(test.type = 'oneT', side = 'both', # N.max = 20) ### OC and ASN #OC.onet.both = OCandASN.MSPRT(theta = seq(-1, 1, length.out = 3), # design.MSPRT.object = design.onet.both) #################### two-sample z test #################### #### right sided #### ### design #design.twoz.right = design.MSPRT(test.type = 'twoZ', side = 'right', # N1.max = 20, N2.max = 20) ### OC and ASN #OC.twoz.right = OCandASN.MSPRT(theta = seq(design.twoz.right$theta0, # design.twoz.right$theta0 + 2, # length.out = 3), # design.MSPRT.object = design.twoz.right) #### left sided #### ### design #design.twoz.left = design.MSPRT(test.type = 'twoZ', side = 'left', # N1.max = 20, N2.max = 20) ### OC and ASN #OC.twoz.left = OCandASN.MSPRT(theta = seq(design.twoz.left$theta0 - 2, # design.twoz.left$theta0, # length.out = 3), # design.MSPRT.object = design.twoz.left) #### both sided #### ### design #design.twoz.both = design.MSPRT(test.type = 'twoZ', side = 'both', # N1.max = 20, N2.max = 20) ### OC and ASN #OC.twoz.both = OCandASN.MSPRT(theta = seq(design.twoz.both$theta0 - 2, # design.twoz.both$theta0 + 2, # length.out = 3), # design.MSPRT.object = design.twoz.both) #################### two-sample t test #################### #### right sided #### ### design #design.twot.right = design.MSPRT(test.type = 'twoT', side = 'right', # N1.max = 20, N2.max = 20) ### OC and ASN #OC.twot.right = OCandASN.MSPRT(theta = seq(design.twot.right$theta0, # design.twot.right$theta0 + 2, # length.out = 3), # design.MSPRT.object = design.twot.right) #### left sided #### ### design #design.twot.left = design.MSPRT(test.type = 'twoT', side = 'left', # N1.max = 20, N2.max = 20) ### OC and ASN #OC.twot.left = OCandASN.MSPRT(theta = seq(design.twot.left$theta0 - 2, # design.twot.left$theta0, # length.out = 3), # design.MSPRT.object = design.twot.left) #### both sided #### ### design #design.twot.both = design.MSPRT(test.type = 'twoT', side = 'both', # N1.max = 20, N2.max = 20) ### OC and ASN #OC.twot.both = OCandASN.MSPRT(theta = seq(design.twot.both$theta0 - 2, # design.twot.both$theta0 + 2, # length.out = 3), # design.MSPRT.object = design.twot.both)#################### one-sample proportion test #################### #### right sided #### ### design #design.oneprop.right <- design.MSPRT(test.type = 'oneProp', side = 'right', # N.max = 20) ### OC and ASN #OC.oneprop.right <- OCandASN.MSPRT(theta = seq(design.oneprop.right$theta0, 1, # length.out = 3), # design.MSPRT.object = design.oneprop.right) #### left sided #### ### design #design.oneprop.left = design.MSPRT(test.type = 'oneProp', side = 'left', # N.max = 20) ### OC and ASN #OC.oneprop.left = OCandASN.MSPRT(theta = seq(0, design.oneprop.right$theta0, # length.out = 3), # design.MSPRT.object = design.oneprop.left) #### both sided #### ### design #design.oneprop.both = design.MSPRT(test.type = 'oneProp', side = 'both', # N.max = 20) ### OC and ASN #OC.oneprop.both = OCandASN.MSPRT(theta = seq(0, 1, length.out = 3), # design.MSPRT.object = design.oneprop.both) #################### one-sample z test #################### #### right sided #### ### design #design.onez.right = design.MSPRT(test.type = 'oneZ', side = 'right', # N.max = 20) ### OC and ASN #OC.onez.right = OCandASN.MSPRT(theta = seq(design.onez.right$theta0, # design.onez.right$theta0 + 3*design.onez.right$sigma, # length.out = 3), # design.MSPRT.object = design.onez.right) #### left sided #### ### design #design.onez.left = design.MSPRT(test.type = 'oneZ', side = 'left', # N.max = 20) ### OC and ASN #OC.onez.left = OCandASN.MSPRT(theta = seq(design.onez.left$theta0 - 3*design.onez.left$sigma, # design.onez.left$theta0, # length.out = 3), # design.MSPRT.object = design.onez.left) #### both sided #### ### design #design.onez.both = design.MSPRT(test.type = 'oneZ', side = 'both', # N.max = 20) ### OC and ASN #OC.onez.both = OCandASN.MSPRT(theta = seq(design.onez.both$theta0 - 3*design.onez.both$sigma, # design.onez.both$theta0 + 3*design.onez.both$sigma, # length.out = 3), # design.MSPRT.object = design.onez.both) #################### one-sample t test #################### #### right sided #### ### design #design.onet.right = design.MSPRT(test.type = 'oneT', side = 'right', # N.max = 20) ### OC and ASN #OC.onet.right = OCandASN.MSPRT(theta = seq(design.onet.right$theta0, 1, # length.out = 3), # design.MSPRT.object = design.onet.right) #### left sided #### ### design #design.onet.left = design.MSPRT(test.type = 'oneT', side = 'left', # N.max = 20) ### OC and ASN #OC.onet.left = OCandASN.MSPRT(theta = seq(-1, design.onet.left$theta0, # length.out = 3), # design.MSPRT.object = design.onet.left) #### both sided #### ### design #design.onet.both = design.MSPRT(test.type = 'oneT', side = 'both', # N.max = 20) ### OC and ASN #OC.onet.both = OCandASN.MSPRT(theta = seq(-1, 1, length.out = 3), # design.MSPRT.object = design.onet.both) #################### two-sample z test #################### #### right sided #### ### design #design.twoz.right = design.MSPRT(test.type = 'twoZ', side = 'right', # N1.max = 20, N2.max = 20) ### OC and ASN #OC.twoz.right = OCandASN.MSPRT(theta = seq(design.twoz.right$theta0, # design.twoz.right$theta0 + 2, # length.out = 3), # design.MSPRT.object = design.twoz.right) #### left sided #### ### design #design.twoz.left = design.MSPRT(test.type = 'twoZ', side = 'left', # N1.max = 20, N2.max = 20) ### OC and ASN #OC.twoz.left = OCandASN.MSPRT(theta = seq(design.twoz.left$theta0 - 2, # design.twoz.left$theta0, # length.out = 3), # design.MSPRT.object = design.twoz.left) #### both sided #### ### design #design.twoz.both = design.MSPRT(test.type = 'twoZ', side = 'both', # N1.max = 20, N2.max = 20) ### OC and ASN #OC.twoz.both = OCandASN.MSPRT(theta = seq(design.twoz.both$theta0 - 2, # design.twoz.both$theta0 + 2, # length.out = 3), # design.MSPRT.object = design.twoz.both) #################### two-sample t test #################### #### right sided #### ### design #design.twot.right = design.MSPRT(test.type = 'twoT', side = 'right', # N1.max = 20, N2.max = 20) ### OC and ASN #OC.twot.right = OCandASN.MSPRT(theta = seq(design.twot.right$theta0, # design.twot.right$theta0 + 2, # length.out = 3), # design.MSPRT.object = design.twot.right) #### left sided #### ### design #design.twot.left = design.MSPRT(test.type = 'twoT', side = 'left', # N1.max = 20, N2.max = 20) ### OC and ASN #OC.twot.left = OCandASN.MSPRT(theta = seq(design.twot.left$theta0 - 2, # design.twot.left$theta0, # length.out = 3), # design.MSPRT.object = design.twot.left) #### both sided #### ### design #design.twot.both = design.MSPRT(test.type = 'twoT', side = 'both', # N1.max = 20, N2.max = 20) ### OC and ASN #OC.twot.both = OCandASN.MSPRT(theta = seq(design.twot.both$theta0 - 2, # design.twot.both$theta0 + 2, # length.out = 3), # design.MSPRT.object = design.twot.both)
OCandASN.MSPRT calls this function for obtaining the OC and ASN of a designed MSPRT for one-sample proportion tests. Users please refer to OCandASN.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
OCandASN.MSPRT calls this function for obtaining the OC and ASN of a designed MSPRT for one-sample t tests. Users please refer to OCandASN.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
OCandASN.MSPRT calls this function for obtaining the OC and ASN of a designed MSPRT for one-sample z tests. Users please refer to OCandASN.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
OCandASN.MSPRT calls this function for obtaining the OC and ASN of a designed MSPRT for two-sample t tests. Users please refer to OCandASN.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
OCandASN.MSPRT calls this function for obtaining the OC and ASN of a designed MSPRT for two-sample z tests. Users please refer to OCandASN.MSPRT.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
Obtains the Type II error probability of fixed-design tests for testing the point null hypothesis .
Type2.fixed_design(theta, test.type, side = "right", theta0, N, N1, N2, Type1 = 0.005, sigma = 1, sigma1 = 1, sigma2 = 1)Type2.fixed_design(theta, test.type, side = "right", theta0, N, N1, N2, Type1 = 0.005, sigma = 1, sigma1 = 1, sigma2 = 1)
theta |
Numeric. Effect size where the Type II error probability is desired. |
test.type |
Character. Type of test. Currently, the package only allows
|
side |
Character. Direction of the composite alternative hypothesis. |
theta0 |
Numeric. Hypothesized value of effect size ( |
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 |
sigma1 |
Positive numeric. Known standard deviation for Group-1 in two-sample |
sigma2 |
Positive numeric. Known standard deviation for Group-2 in two-sample |
Numeric in [0,1]. The Type II error probability of the fixed-design test at the specified effect size value theta.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
Pramanik S., Johnson V. E. and Bhattacharya A. (2020+). A Modified Sequential Probability Ratio Test. [Arxiv]
##### 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)##### 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)
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).
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)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)
test.type |
Character. Type of test. Currently, the package only allows
|
side |
Character. Direction of the composite alternative hypothesis. |
theta0 |
Numeric. Hypothesized value of effect size ( |
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 |
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 |
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 |
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 |
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 |
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.
Sandipan Pramanik, Valen E. Johnson and Anirban Bhattacharya
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]
##### 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)##### 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)