This function calculates the sample size for a given power, type-I error rate and allocation rate t = n_1/N. Additionally, the actual achieved power can be simulated.
WMWssp(x, y, alpha = 0.05, power = 0.8, t = 1/2, simulation = FALSE, nsim = 10^4)
WMWssp(x, y, alpha = 0.05, power = 0.8, t = 1/2, simulation = FALSE, nsim = 10^4)
x |
prior information for the first group |
y |
prior information for the second group |
alpha |
two sided type I error rate |
power |
power |
t |
proportion of subjects in the first group; or use t = "min" to use optimal proportion rate |
simulation |
TRUE if a power simulation should be carried out |
nsim |
number of simulations for the power simulation |
Returns an object from class WMWssp containing
result |
A dataframe with the results. |
t |
The allocation rate which was used. |
alpha |
The type-I error rate which was used. |
simulation |
The achieved power in a simulation. |
power |
The power which was used. |
N |
The sample size needed. |
Brunner, E., Bathke A. C. and Konietschke, F. Rank- and Pseudo-Rank Procedures in Factorial Designs - Using R and SAS. Springer Verlag. to appear.
Happ, M., Bathke, A. C., & Brunner, E. (2019). Optimal Sample Size Planning for the Wilcoxon-Mann-Whitney-Test. Statistics in medicine, 38(3), 363-375.
# Prior information for the reference group x <- c(315,375,356,374,412,418,445,403,431,410,391,475,379) # generate data for treatment group based on a shift effect y <- x - 20 # calculate sample size ssp <- WMWssp(x, y, alpha = 0.05, power = 0.8, t = 1/2) summary(ssp)
# Prior information for the reference group x <- c(315,375,356,374,412,418,445,403,431,410,391,475,379) # generate data for treatment group based on a shift effect y <- x - 20 # calculate sample size ssp <- WMWssp(x, y, alpha = 0.05, power = 0.8, t = 1/2) summary(ssp)
This function maximizes the power of the Wilcoxon-Mann-Whitney test for a given total sample size N and type-I error rate with respect to the allocation rate t = n_1/N.
WMWssp_maximize(x, y, alpha = 0.05, N)
WMWssp_maximize(x, y, alpha = 0.05, N)
x |
a vector of prior information for the first group |
y |
a vector of prior information for the second group |
alpha |
Type I error rate |
N |
total sample size |
Returns an object from class WMWssp containing
result |
A dataframe with the results. |
t |
The optimal allocation rate. |
alpha |
The type-I error rate which was used. |
power |
The maximized power. |
N |
The total sample size which was used. |
Brunner, E., Bathke A. C. and Konietschke, F. Rank- and Pseudo-Rank Procedures in Factorial Designs - Using R and SAS. Springer Verlag. to appear.
Happ, M., Bathke, A. C., & Brunner, E. (2019). Optimal Sample Size Planning for the Wilcoxon-Mann-Whitney-Test. Statistics in medicine, 38(3), 363-375.
# Prior information for the reference group x <- c(315,375,356,374,412,418,445,403,431,410,391,475,379) # generate data for treatment group based on a shift effect y <- x - 20 # N <- 112 # calculate optimal t ssp <- WMWssp_maximize(x, y, alpha = 0.05, N) summary(ssp)
# Prior information for the reference group x <- c(315,375,356,374,412,418,445,403,431,410,391,475,379) # generate data for treatment group based on a shift effect y <- x - 20 # N <- 112 # calculate optimal t ssp <- WMWssp_maximize(x, y, alpha = 0.05, N) summary(ssp)
This function minimizes the sample size for a given power and type-I error rate with respect to the allocation rate t = n_1/N.
WMWssp_minimize(x, y, alpha = 0.05, power = 0.8, simulation = FALSE, nsim = 10^4)
WMWssp_minimize(x, y, alpha = 0.05, power = 0.8, simulation = FALSE, nsim = 10^4)
x |
a vector of prior information for the first group |
y |
a vector of prior information for the second group |
alpha |
Type I error rate |
power |
Power to detect a relative effect based on the prior information |
simulation |
TRUE if a power simulation should be carried out |
nsim |
number of simulations for the power simulation |
Returns an object from class WMWssp containing
result |
A dataframe with the results. |
t |
The optimal allocation rate for minimizing the sample size. |
alpha |
The type-I error rate which was used. |
power |
The power which was used. |
N |
The minimized sample size. |
Brunner, E., Bathke A. C. and Konietschke, F. Rank- and Pseudo-Rank Procedures in Factorial Designs - Using R and SAS. Springer Verlag. to appear.
Happ, M., Bathke, A. C., & Brunner, E. (2019). Optimal Sample Size Planning for the Wilcoxon-Mann-Whitney-Test. Statistics in medicine, 38(3), 363-375.
# Prior information for the reference group x <- c(315,375,356,374,412,418,445,403,431,410,391,475,379) # generate data for treatment group based on a shift effect y <- x - 20 # calculate optimal t ssp <- WMWssp_minimize(x, y, alpha = 0.05, power = 0.8) summary(ssp)
# Prior information for the reference group x <- c(315,375,356,374,412,418,445,403,431,410,391,475,379) # generate data for treatment group based on a shift effect y <- x - 20 # calculate optimal t ssp <- WMWssp_minimize(x, y, alpha = 0.05, power = 0.8) summary(ssp)
This function calculates the sample size for given type-I and type-II error probabilities using Noether's formula. If ties are present then prior information is needen.
WMWssp_noether(alpha, power, t, p, x = c(0), ties = FALSE)
WMWssp_noether(alpha, power, t, p, x = c(0), ties = FALSE)
alpha |
two sided type I error rate |
power |
power: detect a relative effect p at least with the specified power |
t |
proportion of subjects in the first group (between 0 and 1) |
p |
relative effect |
x |
prior information is only needed in case of ties |
ties |
TRUE if ties are possible (non continuous distribution), otherwise FALSE |
Returns an object from class WMWssp containing
result |
A dataframe with the results. |
t |
The allocation rate which was used. |
alpha |
The type-I error rate which was used. |
power |
The power which was used. |
N |
The sample size needed. |
Noether, G. E. (1987). Sample Size Determination for Some Common Nonparametric Tests. Journal of the American Statistical Association 85, 645.647.
# Prior information for the reference group x <- c(315,375,356,374,412,418,445,403,431,410,391,475,379) # generate data for treatment group based on a shift effect y <- x - 20 # this data leads to a relative effect of p = 0.349 # calculate sampe size for a balanced design ssp <- WMWssp_noether(alpha = 0.05, power = 0.8, t =1/2, p = 0.349) summary(ssp)
# Prior information for the reference group x <- c(315,375,356,374,412,418,445,403,431,410,391,475,379) # generate data for treatment group based on a shift effect y <- x - 20 # this data leads to a relative effect of p = 0.349 # calculate sampe size for a balanced design ssp <- WMWssp_noether(alpha = 0.05, power = 0.8, t =1/2, p = 0.349) summary(ssp)