simulateRandomizedDesignEffectSizes
This simulates one of four data distributions (normal, log-normal, gamma and Laplace), and finds the values of phat and Cliffs d and their variances. It assumes equal group sizes. It returns values of the effect sizes and their variance for a simulated randomized experiment with two treatments. It returns whether or not each non-parametric effect size was significant. It also returns the parametric (standardized and unstandardized) Effect Size and the whether the t-test was significant.
simulateRandomizedDesignEffectSizes( mean, sd, diff, N, type = "n", StdAdj = 0, alpha = 0.05, AlwaysTwoSidedTests = FALSE, Return.Data = FALSE )
mean: The mean used for one of the treatment groups (this is the rate for the gamma data)sd: The spread used for both treatment groups. It mus be a real value greater than 0 (this is the shape for the gamma data).diff: This is added to the parameter mean, to define the mean of the other treatment group. It can be a real value avd can take the value zero.N: this is the number of observations in each group. It must be an integer greater than 3.type: this specifies the underlying distribution used to generate the data. it takes the values 'n' for a normal distribution, 'l' for lognormal distribution,'g' for a gamma distribution, 'lap' for a Laplace distribution.StdAdj: this specifies the extent of variance instability to be introduced.alpha: the level for all statistical tests (default 0.05)AlwaysTwoSidedTests: if set to FALSE (i.e. default) the algorithms uses one-sided tests if diff!=0 and two-sided tests otherwise. If set to TRUE the algorithm always uses two-sided tests.Return.Data: if set to true the algorithm returns the data not the effect sizes (default FALSE).data frame incl. the non-parametric and parametric effect sizes and whether the effect sizes are significant at the specified alpha level. For log-normal data the function returns the effect sizes for the transformed data.
set.seed(123) as.data.frame( simulateRandomizedDesignEffectSizes( mean = 0, sd = 1, diff = 0.8, N = 10, type = "n", StdAdj = 0)) # phat varphat dfphat sigphat d vard sigd cor varcor sigCVt t.value # 1 0.75 0.01522222 17.46405 TRUE 0.5 0.06237576 TRUE 0.2631579 0.01754995 TRUE 2.095142 # t.se t.df t.lb t.ub t.sig ES Variance StdES MedDiff # 1 0.4457915 17.87244 0.1606665 Inf TRUE 0.9339963 0.9936502 0.9369759 1.260127 set.seed(123) as.data.frame( simulateRandomizedDesignEffectSizes( mean = 0, sd = 1, diff = 0.8, N = 10, type = "n", StdAdj = 0, AlwaysTwoSidedTests = TRUE)) # phat varphat dfphat sigphat d vard sigd cor # 1 0.75 0.01522222 17.46405 FALSE 0.5 0.06237576 FALSE 0.2631579 # varcor sigCVt t.value t.se t.df t.lb t.ub t.sig # 1 0.01754995 FALSE 2.095142 0.4457915 17.87244 -0.003056196 1.871049 FALSE # ES Variance StdES MedDiff # 1 0.9339963 0.9936502 0.9369759 1.260127 set.seed(456) as.data.frame( simulateRandomizedDesignEffectSizes( mean = 0, sd = 1, diff = 0.8, N = 10, type = "l", StdAdj = 0)) # phat varphat dfphat sigphat d vard sigd cor varcor # 1 0.87 0.008466667 11.1111 TRUE 0.74 0.0350497 TRUE 0.3894737 0.01039674 # sigCVt t.value t.se t.df t.lb t.ub t.sig ES Variance # 1 TRUE 3.599375 2.148297 9.312472 3.809448 Inf TRUE 7.732529 23.07591 # StdES MedDiff transttest EStrans StdEStrans VarTrans # 1 1.60969 7.77893 0.998772 1.731323 1.598065 1.173728 set.seed(123) as.data.frame( simulateRandomizedDesignEffectSizes( mean = 0, sd = 1, diff = 0.8, N = 10, type = "n", StdAdj = 0, Return.Data = TRUE)) # BaselineData AlternativeData # 1 -0.69470698 1.0533185 # 2 -0.20791728 0.7714532 # 3 -1.26539635 0.7571295 # 4 2.16895597 2.1686023 # 5 1.20796200 0.5742290 # 6 -1.12310858 2.3164706 # 7 -0.40288484 -0.7487528 # 8 -0.46665535 1.3846137 # 9 0.77996512 0.9238542 # 10 -0.08336907 1.0159416
Barbara Kitchenham and Lech Madeyski