Brand Equity Meta-Analysis

You can find additional information for my meta-analysis on this page.

To incorporate prior research to your new correlation between brand equity and brand performance, you only need three values:

1. The new correlation: r_new
2. The new sample size: n_new
3. Your desired alpha level: alpha

You can copy the same code into R and it should run smoothly without any packages.

n_new              <- 200
r_new              <- 0.5
alpha              <- 0.05

update_correlation <- function(n_new, r_new, alpha) {
    n_meta             <- 50205
    r_meta             <- 0.206
    
    # Variance
    var_xi         <- 1 / (n_new + n_meta)
    format(var_xi, scientific = FALSE)
    
    # mean
    mu_xi          <- var_xi * (n_meta * atanh(r_meta) + n_new * (atanh(r_new)))
    format(mu_xi, scientific  = FALSE)
    
    # confidence interval
    upper_xi       <- mu_xi + qnorm(1 - alpha / 2) * sqrt(var_xi)
    lower_xi       <- mu_xi - qnorm(1 - alpha / 2) * sqrt(var_xi)
    
    # rho
    mean_rho       <- tanh(mu_xi)
    upper_rho      <- tanh(upper_xi)
    lower_rho      <- tanh(lower_xi)
    
    # return a list
    return(
        list(
            "mu_xi" = mu_xi,
            "var_xi" = var_xi,
            "upper_xi" = upper_xi,
            "lower_xi" = lower_xi,
            "mean_rho" = mean_rho,
            "upper_rho" = upper_rho,
            "lower_rho" = lower_rho
        )
    )
}


new_cor = update_correlation(n_new = n_new, r_new = r_new, alpha = alpha)


# new correlation
new_cor$mean_rho

## [1] 0.2072927

# lower confident interval
new_cor$lower_rho

## [1] 0.1989229

# upper confident interval
new_cor$upper_rho

## [1] 0.2156322