MSPRT (version 2.1)

find.alt: Finding the `fixed design alternative'

Description

This function obtains the point alternative in one-sample binomial proportion tests, one & two-sample Z-tests, and one & two-sample T-tests in a fixed design.

Usage

find.alt(test.type, side = "right", null, n, n1, n2,
         type1 = 0.005, type2 = 0.2, sigma0 = 1)

Arguments

test.type

a character; denotes the type of test;

``oneProp'' for a one-sample binomial proportion test.

``oneZ'' for a one-sample Z-test.

``oneT'' for a one-sample T-test.

``twoZ'' for a two-sample Z-test.

``twoT'' for a two-sample T-test.

side

a character; direction of the alternative hypothesis H1.

Has to be one of "right" or "left".

Default: "right".

null

a numeric; required only in one-sample proportion tests and one-sample Z-tests; hypothesized value of the parameter under the null hypothesis.

The hypothesized parameters are proportion in one-sample proportion tests, population mean in one-sample Z & T-tests, and difference between the population mean of Group-2 and Group-1 in two-sample Z & T-tests.

In one-sample T-tests and two-sample Z & T-tests, only null=0 is allowed. This is done automatically. This argument is ignored in these cases.

Default: 0.5 in one-sample proportion tests, and 0 in one-sample Z-tests.

n

a positive numeric (integer); required only in one-sample tests; number of samples on which the fixed design one-sample test is based on.

n1

a positive numeric (integer); required only in two-sample tests; number of samples from Group-1 on which the fixed design two-sample test is based on.

n2

a positive numeric (integer); required only in two-sample tests; number of samples from Group-2 on which the fixed design two-sample test is based on.

type1

a numeric in (0,1); Type 1 error probability of the test.

Default: 0.005.

type2

a numeric in (0,1); Type 2 error probability.

Corresponding to this, the point alternative is obtained.

Default: 0.2.

sigma0

a positive numeric; required only in one & two-sample Z-tests.

The known population standard deviation in one-sample Z-tests.

The known common population standard deviation in two-sample Z-tests.

Default: 1.

Value

Returns a numeric which is the obtained `fixed design alternative'.

Details

At the `fixed design alternative', the fixed design test of size type1 has Type 2 error type2.

In one-sample tests, the fixed design is based on n samples. In two-sample tests, the fixed design is based on n1 & n2 samples from Group 1 & 2, respectively.

Examples

# NOT RUN {
## finding the alternative in case of a one-sample proportion test
## which provides 80% power against a right and left sided
## alternative, respectively

# default null = 0.5
find.alt(test.type="oneProp", n= 60, type1= 0.005, type2= 0.2)
         
find.alt(test.type="oneProp", side= "left", n= 60,
         type1= 0.005, type2= 0.2)

# null = 0.2         
find.alt(test.type="oneProp", null= 0.2, n= 60, 
         type1= 0.005, type2= 0.2)
         
find.alt(test.type="oneProp", side= "left", null= 0.2,
         n= 60, type1= 0.005, type2= 0.2)


## finding the alternative in case of a one-sample Z-test
## which provides 80% power against a right and left sided
## alternative, respectively
# default sigma0 = 1

# default null = 0
find.alt(test.type="oneZ", n= 60, type1= 0.005, type2= 0.2)

find.alt(test.type="oneZ", side= "left", n= 60, type1= 0.005,
         type2= 0.2)
         
# null = 3
find.alt(test.type="oneZ", null= 3, n= 60, type1= 0.005, type2= 0.2)

find.alt(test.type="oneZ", side= "left", null= 3, n= 60,
         type1= 0.005, type2= 0.2)
         

## finding the alternative in case of a one-sample T-test
## which provides 80% power against a right and left sided
## alternative, respectively

# default null = 0
find.alt(test.type="oneT", n= 60, type1= 0.005, type2= 0.2)
         
find.alt(test.type="oneT", side= "left", n= 60,
         type1= 0.005, type2= 0.2)
         
# null = 3
find.alt(test.type="oneT", null= 3, n= 60, type1= 0.005,
         type2= 0.2)
         
find.alt(test.type="oneT", side= "left", null= 3,
         n= 60, type1= 0.005, type2= 0.2)


## finding the alternative in case of a two-sample Z-test
## which provides 80% power against a right and left sided
## alternative, respectively
# default sigma0 = 1

find.alt(test.type="twoZ", n1= 60, n2= 50, type1= 0.005, type2= 0.2)

find.alt(test.type="twoZ", side= "left", n1= 60, n2= 50, type1= 0.005,
         type2= 0.2)

         
## finding the alternative in case of a two-sample T-test
## which provides 80% power against a right and left sided
## alternative, respectively

find.alt(test.type="twoT", n1= 60, n2= 50, type1= 0.005, type2= 0.2)

find.alt(test.type="twoT", side= "left", n1= 60, n2= 50, type1= 0.005,
         type2= 0.2)


# }