Print descriptive statistics

Description

This function prints descriptive statistics for the seqtest object

Usage

descript(x, digits = 2, output = TRUE)

Arguments

Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at

References

Rasch, D., Pilz, J., Verdooren, L. R., & Gebhardt, G. (2011). Optimal experimental design with R. Boca Raton: Chapman & Hall/CRC.

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. New York: John Wiley & Sons.

Schneider, B., Rasch, D., Kubinger, K. D., & Yanagida, T. (2015). A Sequential triangular test of a correlation coefficient's null-hypothesis: 0 < \rho \le \rho0. Statistical Papers, 56, 689-699.

See Also

seqtest.mean, seqtest.prop, seqtest.cor, plot.seqtest, descript

Examples

#--------------------------------------
# Sequential triangular test for the arithmetic mean in one sample

seq.obj <- seqtest.mean(56, mu = 50, theta = 0.5,
                        alpha = 0.05, beta = 0.2)

seq.obj <- update(seq.obj, x = c(54, 52, 46, 49))

descript(seq.obj)

#--------------------------------------
# Sequential triangular test for the proportion in one sample

seq.obj <- seqtest.prop(c(1, 1, 0, 1), pi = 0.5, delta = 0.2,
                        alpha = 0.05, beta = 0.2)

seq.obj <- update(seq.obj, x = c(1, 1, 1, 1, 1, 0, 1, 1, 1))

descript(seq.obj)

#--------------------------------------
# Sequential triangular test for Pearson's correlation coefficient

seq.obj <- seqtest.cor(0.46, k = 14, rho = 0.3, delta = 0.2,
                       alpha = 0.05, beta = 0.2, plot = TRUE)

seq.obj <- update(seq.obj, c(0.56, 0.76, 0.56, 0.52))

descript(seq.obj)

Plot seqtest

Description

This function plots the seqtest object

Usage

## S3 method for class 'seqtest'
plot(x, ...)

Arguments

Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at

References

Rasch, D., Pilz, J., Verdooren, L. R., & Gebhardt, G. (2011). Optimal experimental design with R. Boca Raton: Chapman & Hall/CRC.

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. New York: John Wiley & Sons.

Schneider, B., Rasch, D., Kubinger, K. D., & Yanagida, T. (2015). A Sequential triangular test of a correlation coefficient's null-hypothesis: 0 < \rho \le \rho0. Statistical Papers, 56, 689-699.

See Also

seqtest.mean, seqtest.prop, seqtest.cor, print.seqtest, descript

Examples

#--------------------------------------
# Sequential triangular test for the arithmetic mean in one sample

seq.obj <- seqtest.mean(56, mu = 50, theta = 0.5,
                        alpha = 0.05, beta = 0.2)
plot(seq.obj)

#--------------------------------------
# Sequential triangular test for the proportion in one sample

seq.obj <- seqtest.prop(c(1, 1, 0, 1), pi = 0.5, delta = 0.2,
                        alpha = 0.05, beta = 0.2)
plot(seq.obj)

#--------------------------------------
# Sequential triangular test for Pearson's correlation coefficient

seq.obj <- seqtest.cor(0.46, k = 14, rho = 0.3, delta = 0.2,
                       alpha = 0.05, beta = 0.2)

plot(seq.obj)

Plot sim.seqtest

Description

This function plots the sim.seqtest.cor object

Usage

## S3 method for class 'sim.seqtest.cor'
plot(x, plot.lines = TRUE, plot.nom = TRUE,
     ylim = NULL, type = "b", pch = 19, lty = 1, lwd = 1, ...)

Arguments

Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at

References

Schneider, B., Rasch, D., Kubinger, K. D., & Yanagida, T. (2015). A Sequential triangular test of a correlation coefficient's null-hypothesis: 0 < \rho \le \rho0. Statistical Papers, 56, 689-699.

See Also

sim.seqtest.cor, seqtest.cor

Examples

## Not run: 

#---------------------------------------------
# Determine optimal k and nominal type-II-risk
# H0: rho <= 0.3, H1: rho > 0.3
# alpha = 0.01, beta = 0.05, delta = 0.25

# Step 1: Determine the optimal size of subsamples (k)

sim.obj.1 <- sim.seqtest.cor(rho.sim = 0.3, k = seq(4, 16, by = 1), rho = 0.3,
                             alternative = "greater",
                             delta = 0.25, alpha = 0.05, beta = 0.05,
                             runs = 10000)

plot(sim.obj.1)

# Step 2: Determine the optimal nominal type-II-risk based on
#         the optimal size of subsamples (k) from step 1

sim.obj.2 <- sim.seqtest.cor(rho.sim = 0.55, k = 16, rho = 0.3,
                             alternative = "greater",
                             delta = 0.25, alpha = 0.05, beta = seq(0.05, 0.15, by = 0.01),
                             runs = 10000)

plot(sim.obj.2)

## End(Not run)

Print seqtest

Description

This function prints the seqtest object

Usage

## S3 method for class 'seqtest'
print(x, ...)

Arguments

Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at

References

Rasch, D., Pilz, J., Verdooren, L. R., & Gebhardt, G. (2011). Optimal experimental design with R. Boca Raton: Chapman & Hall/CRC.

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. New York: John Wiley & Sons.

Schneider, B., Rasch, D., Kubinger, K. D., & Yanagida, T. (2015). A Sequential triangular test of a correlation coefficient's null-hypothesis: 0 < \rho \le \rho0. Statistical Papers, 56, 689-699.

See Also

seqtest.mean, seqtest.prop, seqtest.cor, plot.seqtest, descript

Examples

#--------------------------------------
# Sequential triangular test for the arithmetic mean in one sample

seq.obj <- seqtest.mean(56, mu = 50, theta = 0.5,
                        alpha = 0.05, beta = 0.2, output = FALSE)

print(seq.obj)

#--------------------------------------
# Sequential triangular test for the proportion in one sample

seq.obj <- seqtest.prop(c(1, 1, 0, 1), pi = 0.5, delta = 0.2,
                        alpha = 0.05, beta = 0.2, output = FALSE)

print(seq.obj)

#--------------------------------------
# Sequential triangular test for Pearson's correlation coefficient

seq.obj <- seqtest.cor(0.46, k = 14, rho = 0.3, delta = 0.2,
                       alpha = 0.05, beta = 0.2, output = FALSE)

print(seq.obj)

Print sim.seqtest

Description

This function prints the sim.seqtest.cor object

Usage

## S3 method for class 'sim.seqtest.cor'
print(x, ...)

Arguments

Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at

References

Schneider, B., Rasch, D., Kubinger, K. D., & Yanagida, T. (2015). A Sequential triangular test of a correlation coefficient's null-hypothesis: 0 < \rho \le \rho0. Statistical Papers, 56, 689-699.

See Also

sim.seqtest.cor, plot.sim.seqtest.cor

Examples

## Not run: 

#---------------------------------------------
# Determine optimal k and nominal type-II-risk
# H0: rho <= 0.3, H1: rho > 0.3
# alpha = 0.01, beta = 0.05, delta = 0.25

# Step 1: Determine the optimal size of subsamples (k)

sim.obj <- sim.seqtest.cor(rho.sim = 0.3, k = seq(4, 16, by = 1), rho = 0.3,
                           alternative = "greater",
                           delta = 0.25, alpha = 0.05, beta = 0.05,
                           runs = 10000, output = FALSE)

print(sim.obj)

# Step 2: Determine the optimal nominal type-II-risk based on
#         the optimal size of subsamples (k) from step 1

sim.obj <- sim.seqtest.cor(rho.sim = 0.55, k = 16, rho = 0.3,
                           alternative = "greater",
                           delta = 0.25, alpha = 0.05, beta = seq(0.05, 0.15, by = 0.01),
                           runs = 10000, output = FALSE)

print(sim.obj)

## End(Not run)

Print size object

Description

This function prints the size object

Usage

## S3 method for class 'size'
print(x, ...)

Arguments

Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at

References

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. New York: John Wiley & Sons.

See Also

size.mean, size.prop, size.cor

Examples

#--------------------------------------
# Two-sided one-sample test
# theta = 0.5
# alpha = 0.05, beta = 0.2

n <- size.mean(theta = 0.5, sample = "one.sample",
               alternative = "two.sided", alpha = 0.05, beta = 0.2)

print(n)

#--------------------------------------
# Two-sided one-sample test
# H0: pi = 0.5, H1: pi != 0.5
# alpha = 0.05, beta = 0.2, delta = 0.2

n <- size.prop(delta = 0.2, pi = 0.5, sample = "one.sample",
               alternative = "two.sided", alpha = 0.05, beta = 0.2)

print(n)

#--------------------------------------
# H0: rho = 0.3, H1: rho != 0.3
# alpha = 0.05, beta = 0.2, delta = 0.2

n <- size.cor(delta = 0.2, rho = 0.3, alpha = 0.05, beta = 0.2)

print(n)

Sequential triangular test for Pearson's correlation coefficient

Description

This function performs the sequential triangular test for Pearson's correlation coefficient

Usage

seqtest.cor(x, k, rho, alternative = c("two.sided", "less", "greater"),
            delta, alpha = 0.05, beta = 0.1, output = TRUE, plot = FALSE)

Arguments

Details

Null and alternative hypothesis is specified using arguments rho and delta. Note that the argument k (i.e., number of observations in each sub-sample) has to be specified. At least k = 4 is needed. The optimal value of k should be determined based on statistical simulation using sim.seqtest.cor function.

In order to specify a one-sided test, argument alternative has to be used (i.e., two-sided tests are conducted by default). That is, alternative = "less" specifies the null hypothesis, H0: \rho >= \rho.0 and the alternative hypothesis, H1: \rho < \rho.0; alternative = "greater" specifies the null hypothesis, H0: \rho <= \rho.0 and the alternative hypothesis, H1: \rho > \rho.0.

The main characteristic of the sequential triangular test is that there is no fixed sample size given in advance. That is, for the most recent sampling point, one has to decide whether sampling has to be continued or either the null- or the alternative hypothesis can be accepted given specified precision requirements (i.e. type-I-risk, type-II-risk and an effect size). The sequence of data pairs must we split into sub-samples of length k >= 4 each. The (cumulative) test statistic Z.m on a Cartesian coordinate system produces a "sequential path" on a continuation area as a triangle. As long as the statistic remains within that triangle, additional data have to be sampled. If the path touches or exceeds the borderlines of the triangle, sampling is completed. Depending on the particular borderline, the null-hypothesis is either accepted or rejected.

Value

Returns an object of class seqtest, to be used for later update steps. The object has following entries:

Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at,

References

Schneider, B., Rasch, D., Kubinger, K. D., & Yanagida, T. (2015). A Sequential triangular test of a correlation coefficient's null-hypothesis: 0 < \rho \le \rho0. Statistical Papers, 56, 689-699.

See Also

update.seqtest, sim.seqtest.cor, seqtest.mean, seqtest.prop, print.seqtest, plot.seqtest, descript

Examples

#--------------------------------------
# H0: rho = 0.3, H1: rho != 0.3
# alpha = 0.05, beta = 0.2, delta = 0.2

seq.obj <- seqtest.cor(0.46, k = 14, rho = 0.3, delta = 0.2,
                       alpha = 0.05, beta = 0.2, plot = TRUE)

seq.obj <- update(seq.obj, c(0.56, 0.76, 0.56, 0.52))

#--------------------------------------
# H0: rho <= 0.3, H1: rho > 0.3
# alpha = 0.05, beta = 0.2, delta = 0.2

seq.obj <- seqtest.cor(0.46, k = 14, rho = 0.3,
                       alternative = "greater", delta = 0.2,
                       alpha = 0.05, beta = 0.2, plot = TRUE)

seq.obj <- update(seq.obj, c(0.56, 0.76, 0.66))

Sequential triangular test for the arithmetic mean

Description

This function performs the sequential triangular test for the arithmetic mean in one- or two-samples

Usage

seqtest.mean(x, y = NULL, mu = NULL, alternative = c("two.sided", "less", "greater"),
             sigma = NULL, delta = NULL, theta = NULL, alpha = 0.05, beta = 0.1,
             output = TRUE, plot = FALSE)

Arguments

Details

For the one-sample test, arguments x, mu and the minimum difference to be detected has to be specified (i.e., argument y must not be specified). For the two-sample test, arguments x, y, and the minimum difference to be detected has to be specified. There are two options to specify the minimum difference to be detected: (1) using arguments mu, sigma and delta or (2) using arguments mu and theta. Note that it is not a requirement to know sigma in advance, i.e., theta can be specified directly. For example, theta = 1 specifies a relative minimum difference to be detected of one standard deviation.

In order to specify a one-sided test, argument alternative has to be used (i.e., two-sided tests are conducted by default). For the one-sample test, alternative = "less" specifies the null hypothesis, H0: \mu >= \mu.0 and the alternative hypothesis, H1: \mu < \mu.0; alternative = "greater" specifies the null hypothesis, H0: \mu <= \mu.0 and the alternative hypothesis, H1: \mu > \mu.0. For the two-sample test alternative = "less" specifies the null hypothesis, H0: \mu.1 >= \mu.2 and the alternative hypothesis, H1: \mu.1 < \mu.2; alternative = "greater" specifies the null hypothesis, H0: \mu.1 <= \mu.2 and the alternative hypothesis, H1: \mu.1 > \mu.2.

The main characteristic of the sequential triangular test is that there is no fixed sample size given in advance. That is, for the most recent sampling point, one has to decide whether sampling has to be continued or either the null- or the alternative hypothesis can be accepted given specified precision requirements (i.e. type-I-risk, type-II-risk and a minimum difference to be detected). The (cumulative) test statistic Z.m on a Cartesian coordinate system produces a "sequential path" on a continuation area as a triangle. As long as the statistic remains within that triangle, additional data have to be sampled. If the path touches or exceeds the borderlines of the triangle, sampling is completed. Depending on the particular borderline, the null-hypothesis is either accepted or rejected.

Value

Returns an object of class seqtest, to be used for later update steps. The object has following entries:

Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at,

References

Rasch, D., Pilz, J., Verdooren, L. R., & Gebhardt, G. (2011). Optimal experimental design with R. Boca Raton: Chapman & Hall/CRC.

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. New York: John Wiley & Sons.

See Also

update.seqtest, seqtest.prop, seqtest.cor, print.seqtest, plot.seqtest, descript

Examples

#--------------------------------------
# Two-sided one-sample test
# H0: mu = 50, H1: mu != 50
# alpha = 0.05, beta = 0.2, theta = 0.5

seq.obj <- seqtest.mean(56, mu = 50, theta = 0.5,
                        alpha = 0.05, beta = 0.2, plot = TRUE)

# alternative specifiation using sigma and delta
seq.obj <- seqtest.mean(56, mu = 50, sigma = 10, delta = 5,
                        alpha = 0.05, beta = 0.2, plot = TRUE)

seq.obj <- update(seq.obj, x = c(54, 52, 46, 49))
seq.obj <- update(seq.obj, x = c(46, 49, 51, 45))
seq.obj <- update(seq.obj, x = c(51, 42, 50, 53))
seq.obj <- update(seq.obj, x = c(50, 53, 49, 53))

#--------------------------------------
# One-sided one-sample test
# H0: mu <= 50, H1: mu > 50
# alpha = 0.05, beta = 0.2, theta = 0.5

seq.obj <- seqtest.mean(c(56, 53), mu = 50, alternative = "greater",
                        theta = 0.5, alpha = 0.05, beta = 0.2, plot = TRUE)

# alternative specifiation using sigma and delta
seq.obj <- seqtest.mean(c(56, 53), mu = 50, alternative = "greater",
                        sigma = 10, delta = 5, alpha = 0.05, beta = 0.2, plot = TRUE)

seq.obj <- update(seq.obj, x = c(67, 52, 48, 59))
seq.obj <- update(seq.obj, x = c(53, 57, 54, 62))
seq.obj <- update(seq.obj, x = 58)

#--------------------------------------
# Two-sided two-sample test
# H0: mu.1 = mu.2, H1: mu.1 != mu.2
# alpha = 0.01, beta = 0.1, theta = 1

seq.obj <- seqtest.mean(53, 45, theta = 1,
                        alpha = 0.01, beta = 0.01, plot = TRUE)

# alternative specifiation using sigma and delta
seq.obj <- seqtest.mean(57, 45, sigma = 10, delta = 10,
                        alpha = 0.01, beta = 0.01, plot = TRUE)

seq.obj <- update(seq.obj, x = c(58, 54, 56), y = c(45, 41, 42))
seq.obj <- update(seq.obj, x = c(56, 50, 49), y = c(42, 45, 50))
seq.obj <- update(seq.obj, x = c(62, 57, 59))
seq.obj <- update(seq.obj, y = c(41, 39, 46))
seq.obj <- update(seq.obj, x = 67)
seq.obj <- update(seq.obj, y = 40)
seq.obj <- update(seq.obj, y = 36)

#--------------------------------------
# One-sided two-sample test
# H0: mu.1 <= mu.2, H1: mu.1 > mu.2
# alpha = 0.01, beta = 0.1, theta = 1

seq.obj <- seqtest.mean(53, 45, alternative = "greater", theta = 1,
                        alpha = 0.01, beta = 0.01, plot = TRUE)

# alternative specifiation using sigma and delta
seq.obj <- seqtest.mean(57, 45, alternative = "greater",sigma = 10, delta = 10,
                        alpha = 0.01, beta = 0.01, plot = TRUE)

seq.obj <- update(seq.obj, x = c(58, 54, 56), y = c(45, 41, 42))
seq.obj <- update(seq.obj, x = c(56, 50, 49), y = c(42, 45, 50))
seq.obj <- update(seq.obj, x = c(62, 57, 59))
seq.obj <- update(seq.obj, y = c(41, 39, 46))

Sequential triangular test for the proportion

Description

This function performs the sequential triangular test for the proportion in one- or two-samples

Usage

seqtest.prop(x, y = NULL, pi = NULL, alternative = c("two.sided", "less", "greater"),
             delta, alpha = 0.05, beta = 0.1, output = TRUE, plot = FALSE)

Arguments

Details

For the one-sample test, arguments x, pi, and delta has to be specified (i.e., argument y must not be specified). For the two-sample test, arguments x, y, pi, and delta has to be specified

In order to specify a one-sided test, argument alternative has to be used (i.e., two-sided tests are conducted by default). For the one-sample test, alternative = "less" specifies the null hypothesis, H0: \pi >= \pi.0 and the alternative hypothesis, H1: \pi < \pi.0; alternative = "greater" specifies the null hypothesis, H0: \pi <= \pi.0 and the alternative hypothesis, H1: \pi > \pi.0. For the two-sample test alternative = "less" specifies the null hypothesis, H0: \pi.1 >= \pi.2 and the alternative hypothesis, H1: \pi.1 < \pi.2; alternative = "greater" specifies the null hypothesis, H0: \pi.1 <= \pi.2 and the alternative hypothesis, H1: \pi.1 > \pi.2.

The main characteristic of the sequential triangular test is that there is no fixed sample size given in advance. That is, for the most recent sampling point, one has to decide whether sampling has to be continued or either the null- or the alternative hypothesis can be accepted given specified precision requirements (i.e. type-I-risk, type-II-risk and an effect size). The (cumulative) test statistic Z.m on a Cartesian coordinate system produces a "sequential path" on a continuation area as a triangle. As long as the statistic remains within that triangle, additional data have to be sampled. If the path touches or exceeds the borderlines of the triangle, sampling is completed. Depending on the particular borderline, the null-hypothesis is either accepted or rejected.

Value

Returns an object of class seqtest, to be used for later update steps. The object has following entries:

Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at,

References

Rasch, D., Pilz, J., Verdooren, L. R., & Gebhardt, G. (2011). Optimal experimental design with R. Boca Raton: Chapman & Hall/CRC.

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. New York: John Wiley & Sons.

See Also

update.seqtest, seqtest.mean, seqtest.cor, print.seqtest, plot.seqtest, descript

Examples

#--------------------------------------
# Two-sided one-sample test
# H0: pi = 0.5, H1: pi != 0.5
# alpha = 0.05, beta = 0.2, delta = 0.2

seq.obj <- seqtest.prop(c(1, 1, 0, 1), pi = 0.5, delta = 0.2,
                        alpha = 0.05, beta = 0.2, plot = TRUE)

seq.obj <- update(seq.obj, x = c(1, 1, 1, 1, 1, 0, 1, 1, 1))
seq.obj <- update(seq.obj, x = c(0, 1, 1, 1))
seq.obj <- update(seq.obj, x = c(1, 1))

#--------------------------------------
# One-sided one-sample test
# H0: pi <= 0.5, H1: pi > 0.5
# alpha = 0.05, beta = 0.2, delta = 0.2

seq.obj <- seqtest.prop(c(1, 1, 0, 1), pi = 0.5,
                        alternative = "greater", delta = 0.2,
                        alpha = 0.05, beta = 0.2, plot = TRUE)

seq.obj <- update(seq.obj, x = c(1, 1, 1, 1, 1, 0, 1, 1, 1))
seq.obj <- update(seq.obj, x = c(0, 1, 1, 1))

#--------------------------------------
# Two-sided two-sample test
# H0: pi.1 = pi.2 = 0.5, H1: pi.1 != pi.2
# alpha = 0.01, beta = 0.1, delta = 0.2

seq.obj <- seqtest.prop(1, 0, pi = 0.5, delta = 0.2,
                        alpha = 0.01, beta = 0.1, plot = TRUE)

seq.obj <- update(seq.obj, x = c(1, 1, 1, 0), y = c(0, 0, 1, 0))
seq.obj <- update(seq.obj, x = c(0, 1, 1, 1), y = c(0, 0, 0, 0))
seq.obj <- update(seq.obj, x = c(1, 0, 1, 1), y = c(0, 0, 0, 1))
seq.obj <- update(seq.obj, x = c(1, 1, 1, 1), y = c(0, 0, 0, 0))
seq.obj <- update(seq.obj, x = c(0, 1, 0, 1))
seq.obj <- update(seq.obj, y = c(0, 0, 0, 1))
seq.obj <- update(seq.obj, x = c(1, 1, 1, 1))

#--------------------------------------
# One-sided two-sample test
# H0: pi.1 <=  pi.1 = 0.5, H1: pi.1 > pi.2
# alpha = 0.01, beta = 0.1, delta = 0.2

seq.obj <- seqtest.prop(1, 0, pi = 0.5, delta = 0.2,
                        alternative = "greater",
                        alpha = 0.01, beta = 0.1, plot = TRUE)

seq.obj <- update(seq.obj, x = c(1, 1, 1, 0), y = c(0, 0, 1, 0))
seq.obj <- update(seq.obj, x = c(0, 1, 1, 1), y = c(0, 0, 0, 0))
seq.obj <- update(seq.obj, x = c(1, 0, 1, 1), y = c(0, 0, 0, 1))
seq.obj <- update(seq.obj, x = c(1, 1, 1), y = c(0, 0))

Simulation of the sequential triangular test for Pearson's correlation coefficient

Description

This function performs a statistical simulation for the sequential triangular test for Pearson's correlation coefficient.

Usage

sim.seqtest.cor(rho.sim, k, rho, alternative = c("two.sided", "less", "greater"),
                delta, alpha = 0.05, beta = 0.1, runs = 1000,
                m.x = 0, sd.x = 1, m.y = 0, sd.y = 1,
                digits = 3, output = TRUE, plot = FALSE)

Arguments

Details

In order to determine the optimal k, simulation is conducted under the H0 condition, i.e., rho.sim = rho. Simulation is carried out for a sequence of k values to seek for the optimal k where the empirical alpha is as close as possible to the nominal alpha. In order to determine optimal beta (with fixed k), simulation is conudcted under the H1 condition, i.e., rho.sim = rho + delta or rho.sim = rho - delta. Simulation is carried out for a sequencen of beta values to seek for the optimal beta where the empirical beta is as close as possible to the nominal beta.

In order to specify a one-sided test, argument alternative has to be used (i.e., two-sided tests are conducted by default). Specifying argument alternative = "less" conducts the simulation for the null hypothesis, H0: \rho >= \rho.0 with the alternative hypothesis, H1: \rho < \rho.0; specifying argument alternative = "greater" conducts the simluation for the null hypothesis, H0: \rho <= \rho.0 with the alternative hypothesis, H1: \rho > \rho.0.

Value

Returns an object of class sim.seqtest.cor with following entries:

Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at,

References

Schneider, B., Rasch, D., Kubinger, K. D., & Yanagida, T. (2015). A Sequential triangular test of a correlation coefficient's null-hypothesis: 0 < \rho \le \rho0. Statistical Papers, 56, 689-699.

See Also

seqtest.cor, plot.sim.seqtest.cor, print.sim.seqtest.cor

Examples

## Not run: 

#---------------------------------------------
# Determine optimal k and nominal type-II-risk
# H0: rho <= 0.3, H1: rho > 0.3
# alpha = 0.01, beta = 0.05, delta = 0.25

# Step 1: Determine the optimal size of subsamples (k)

sim.seqtest.cor(rho.sim = 0.3, k = seq(4, 16, by = 1), rho = 0.3,
                alternative = "greater",
                delta = 0.25, alpha = 0.05, beta = 0.05,
                runs = 10000, plot = TRUE)

# Step 2: Determine the optimal nominal type-II-risk based on
#         the optimal size of subsamples (k) from step 1

sim.seqtest.cor(rho.sim = 0.55, k = 16, rho = 0.3,
                alternative = "greater",
                delta = 0.25, alpha = 0.05, beta = seq(0.05, 0.15, by = 0.01),
                runs = 10000, plot = TRUE)

## End(Not run)

Sample size determination for testing Pearson's correlation coefficient

Description

This function performs sample size computation for testing Pearson's correlation coefficient based on precision requirements (i.e., type-I-risk, type-II-risk and an effect size).

Usage

size.cor(rho = NULL, delta,
         alternative = c("two.sided", "less", "greater"),
         alpha = 0.05, beta = 0.1, output = TRUE)

Arguments

Value

Returns an object of class size with following entries:

Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at,

References

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. New York: John Wiley & Sons.

Rasch, D., Pilz, J., Verdooren, L. R., & Gebhardt, G. (2011). Optimal experimental design with R. Boca Raton: Chapman & Hall/CRC.

See Also

seqtest.cor, size.mean, size.prop, print.size

Examples

#--------------------------------------
# H0: rho = 0.3, H1: rho != 0.3
# alpha = 0.05, beta = 0.2, delta = 0.2

size.cor(rho = 0.3, delta = 0.2, alpha = 0.05, beta = 0.2)

#--------------------------------------
# H0: rho <= 0.3, H1: rho > 0.3
# alpha = 0.05, beta = 0.2, delta = 0.2

size.cor(rho = 0.3, delta = 0.2, alternative = "greater", alpha = 0.05, beta = 0.2)

Sample size determination for testing the arithmetic mean

Description

This function performs sample size computation for the one-sample and two-sample t-test based on precision requirements (i.e., type-I-risk, type-II-risk and an effect size).

Usage

size.mean(theta, sample = c("two.sample", "one.sample"),
          alternative = c("two.sided", "less", "greater"),
          alpha = 0.05, beta = 0.1, output = TRUE)

Arguments

Value

Returns an object of class size with following entries:

Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at,

References

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. New York: John Wiley & Sons.

Rasch, D., Pilz, J., Verdooren, L. R., & Gebhardt, G. (2011). Optimal experimental design with R. Boca Raton: Chapman & Hall/CRC.

See Also

seqtest.mean, size.prop, size.cor, print.size

Examples

#--------------------------------------
# Two-sided one-sample test
# H0: mu = mu.0, H1: mu != mu.0
# alpha = 0.05, beta = 0.2, theta = 0.5

size.mean(theta = 0.5, sample = "one.sample",
          alternative = "two.sided", alpha = 0.05, beta = 0.2)

#--------------------------------------
# One-sided one-sample test
# H0: mu <= mu.0, H1: mu > mu.0
# alpha = 0.05, beta = 0.2, theta = 0.5

size.mean(theta = 0.5, sample = "one.sample",
          alternative = "greater", alpha = 0.05, beta = 0.2)

#--------------------------------------
# Two-sided two-sample test
# H0: mu.1 = mu.2, H1: mu.1 != mu.2
# alpha = 0.01, beta = 0.1, theta = 1

size.mean(theta = 1, sample = "two.sample",
          alternative = "two.sided", alpha = 0.01, beta = 0.1)

#--------------------------------------
# One-sided two-sample test
# H0: mu.1 <= mu.2, H1: mu.1 > mu.2
# alpha = 0.01, beta = 0.1, theta = 1

size.mean(theta = 1, sample = "two.sample",
          alternative = "greater", alpha = 0.01, beta = 0.1)

Sample size determination for testing the proportion

Description

This function performs sample size computation for the one-sample and two-sample test for proportions based on precision requirements (i.e., type-I-risk, type-II-risk and an effect size).

Usage

size.prop(pi = NULL, delta, sample = c("two.sample", "one.sample"),
          alternative = c("two.sided", "less", "greater"),
          alpha = 0.05, beta = 0.1, correct = FALSE, output = TRUE)

Arguments

Value

Returns an object of class size with following entries:

Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at,

References

Fleiss, J. L., Levin, B., & Paik, M. C. (2003). Statistical methods for rates and proportions (3rd ed.). New York: John Wiley & Sons.

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. New York: John Wiley & Sons.

Rasch, D., Pilz, J., Verdooren, L. R., & Gebhardt, G. (2011). Optimal experimental design with R. Boca Raton: Chapman & Hall/CRC.

See Also

seqtest.prop, size.mean, size.cor, print.size

Examples

#--------------------------------------
# Two-sided one-sample test
# H0: pi = 0.5, H1: pi != 0.5
# alpha = 0.05, beta = 0.2, delta = 0.2

size.prop(pi = 0.5, delta = 0.2, sample = "one.sample",
          alternative = "two.sided", alpha = 0.05, beta = 0.2)

#--------------------------------------
# One-sided one-sample test
# H0: pi <= 0.5, H1: pi > 0.5
# alpha = 0.05, beta = 0.2, delta = 0.2

size.prop(pi = 0.5, delta = 0.2, sample = "one.sample",
          alternative = "less", alpha = 0.05, beta = 0.2)

#--------------------------------------
# Two-sided two-sample test
# H0: pi.1 = pi.2 = 0.5, H1: pi.1 != pi.2
# alpha = 0.01, beta = 0.1, delta = 0.2

size.prop(pi = 0.5, delta = 0.2, sample = "two.sample",
          alternative = "two.sided", alpha = 0.01, beta = 0.1)

#--------------------------------------
# One-sided two-sample test
# H0: pi.1 <=  pi.1 = 0.5, H1: pi.1 > pi.2
# alpha = 0.01, beta = 0.1, delta = 0.2

size.prop(pi = 0.5, delta = 0.2, sample = "two.sample",
          alternative = "greater", alpha = 0.01, beta = 0.1)

Update seqtest

Description

This function updates the seqtest object

Usage

## S3 method for class 'seqtest'
update(object, x = NULL, y = NULL, initial = FALSE,
       output = TRUE, plot = TRUE, ...)

Arguments

Author(s)

Takuya Yanagida takuya.yanagida@univie.ac.at

References

Rasch, D., Pilz, J., Verdooren, L. R., & Gebhardt, G. (2011). Optimal experimental design with R. Boca Raton: Chapman & Hall/CRC.

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. New York: John Wiley & Sons.

Schneider, B., Rasch, D., Kubinger, K. D., & Yanagida, T. (2015). A Sequential triangular test of a correlation coefficient's null-hypothesis: 0 < \rho \le \rho0. Statistical Papers, 56, 689-699.

See Also

seqtest.mean, seqtest.prop, seqtest.cor,

Examples

#--------------------------------------
# Sequential triangular test for the arithmetic mean in one sample

seq.obj <- seqtest.mean(56, mu = 50, theta = 0.5,
                        alpha = 0.05, beta = 0.2, plot = TRUE)

seq.obj <- update(seq.obj, x = c(54, 52, 46, 49))

#--------------------------------------
# Sequential triangular test for the proportion in one sample

seq.obj <- seqtest.prop(c(1, 1, 0, 1), pi = 0.5, delta = 0.2,
                        alpha = 0.05, beta = 0.2, plot = TRUE)

seq.obj <- update(seq.obj, x = c(1, 1, 1, 1, 1, 0, 1, 1, 1))

#--------------------------------------
# Sequential triangular test for Pearson's correlation coefficient

seq.obj <- seqtest.cor(0.46, k = 14, rho = 0.3, delta = 0.2,
                       alpha = 0.05, beta = 0.2, plot = TRUE)

seq.obj <- update(seq.obj, c(0.56, 0.76, 0.56, 0.52))