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compute_mod_power <- function(n_groups, effect_sizes, variance, i2, overall_effect, study_size, k, c_alpha_b){
df_b <- n_groups-1
df_w <- k-n_groups
## between groups
#fixed_weight_c <- sum(rep(1/variance, k/n_groups))
fixed_weight_c <- sum(rep(1/variance, k/n_groups))
fixed_lambda_b <- sum(fixed_weight_c*(effect_sizes-overall_effect)^2)
##within-groups
#fixed_weight_w <-1/variance
#fixed_var_w <- round(sqrt(1/sum(rep(fixed_weight_w,study_size/n_groups))),2)
tau2 <- (i2*variance)/(1 - i2) # calculate tau2
## between groups
random_weight_b <- sum(rep(1/(variance+tau2),k/n_groups))
random_lambda_b <- sum(random_weight_b*(effect_sizes-overall_effect)^2)
#mod power list
mod_power_list <- data.frame(fixed_power_b = (1 - pchisq(c_alpha_b,df_b,fixed_lambda_b,lower.tail = TRUE)),
random_power_b = (1 - pchisq(c_alpha_b,df_b,random_lambda_b,lower.tail = TRUE)))
}
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