# wp.crt2arm: Statistical Power Analysis for Cluster Randomized Trials with... In WebPower: Basic and Advanced Statistical Power Analysis

## Description

Cluster randomized trials (CRT) are a type of multilevel design for the situation when the entire cluster is randomly assigned to either a treatment arm or a contral arm (Liu, 2013). The data from CRT can be analyzed in a two-level hierachical linear model, where the indicator variable for treatment assignment is included in second level. If a study contains multiple treatments, then mutiple indicators will be used. This function is for designs with 2 arms (i.e., a treatment and a control). Details leading to power calculation can be found in Raudenbush (1997) and Liu (2013).

## Usage

 ```1 2``` ```wp.crt2arm(n = NULL, f = NULL, J = NULL, icc = NULL, power = NULL, alpha = 0.05, alternative = c("two.sided", "one.sided")) ```

## Arguments

 `n` Sample size. It is the number of individuals within each cluster. `f` Effect size. It specifies either the main effect of treatment, or the mean difference between the treatment clusters and the control clusters. `J` Number of clusters / sides. It tells how many clusters are considered in the study design. At least two clusters are required. `icc` Intra-class correlation. ICC is calculated as the ratio of between-cluster variance to the total variance. It quantifies the degree to which two randomly drawn observations within a cluster are correlated. `power` Statistical power. `alpha` significance level chosed for the test. It equals 0.05 by default. `alternative` Type of the alternative hypothesis (`"two.sided"` or `"one.sided"`). The default is "two.sided". The option "one.sided" can be either "less" or "greater".

## Value

An object of the power analysis.

## References

Liu, X. S. (2013). Statistical power analysis for the social and behavioral sciences: basic and advanced techniques. Routledge.

Raudenbush, S. W. (1997). Statistical analysis and optimal design for cluster randomized trials. Psychological Methods, 2(2), 173.

Zhang, Z., & Yuan, K.-H. (2018). Practical Statistical Power Analysis Using Webpower and R (Eds). Granger, IN: ISDSA Press.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43``` ```#To calculate the statistical power given sample size and effect size: wp.crt2arm(f = 0.6, n = 20, J = 10, icc = 0.1, alpha = 0.05, power = NULL) # Cluster randomized trials with 2 arms # # J n f icc power alpha # 10 20 0.6 0.1 0.5901684 0.05 # # NOTE: n is the number of subjects per cluster. # URL: http://psychstat.org/crt2arm #To generate a power curve given a sequence of sample sizes: res <- wp.crt2arm(f = 0.6, n = seq(20,100,10), J = 10, icc = 0.1, alpha = 0.05, power = NULL) res # Cluster randomized trials with 2 arms # # J n f icc power alpha # 10 20 0.6 0.1 0.5901684 0.05 # 10 30 0.6 0.1 0.6365313 0.05 # 10 40 0.6 0.1 0.6620030 0.05 # 10 50 0.6 0.1 0.6780525 0.05 # 10 60 0.6 0.1 0.6890755 0.05 # 10 70 0.6 0.1 0.6971076 0.05 # 10 80 0.6 0.1 0.7032181 0.05 # 10 90 0.6 0.1 0.7080217 0.05 # 10 100 0.6 0.1 0.7118967 0.05 # # NOTE: n is the number of subjects per cluster. # URL: http://psychstat.org/crt2arm #To plot the power curve: plot(res) #To calculate the required sample size given power and effect size: wp.crt2arm(f = 0.8, n = NULL, J = 10, icc = 0.1, alpha = 0.05, power = 0.8) # Cluster randomized trials with 2 arms # # J n f icc power alpha # 10 16.02558 0.8 0.1 0.8 0.05 # # NOTE: n is the number of subjects per cluster. # URL: http://psychstat.org/crt2arm ```

WebPower documentation built on May 1, 2019, 8:19 p.m.