Correlation CIs

 correlationL <- list()
  i           <- 1
  
  for (r in seq(.75, .95, .05)){     # Correlations
    
    for (n in seq(10, 1000, 10)){    # Sample sizes
      
      z      <- atanh(r)             # Fisher's transformation
      sez    <- 1 / sqrt(n - 3)      # SE of transformed variable
      lower  <- z - (1.96 * sez)
      upper  <- z + (1.96 * sez)
      lowert <- (exp(2 * lower) - 1) / (exp(2 * lower) + 1) # Back-transform
      uppert <- (exp(2 * upper) - 1) / (exp(2 * upper) + 1) # Back-transform
      
      
      correlationL[i] <- as.data.frame(c(r, n, z, sez, lower, upper, 
                                         lowert, uppert))
      
      i <- i + 1
    }
  }
  
  correlationDf <- as.data.frame(do.call(rbind, correlationL))
  
  colnames(correlationDf) <- c("Correlation", "n", "z", "sez", "lowerz", 
                               "upperz", "lowerR", "upperR")

# Plot the 95% CI for correlations at different sample sizes, all in one plot  

  ggplot(correlationDf, 
         aes(x = n, y = Correlation, ymin = lowerR, ymax = upperR, 
             group = factor(Correlation))) +
    geom_ribbon(aes(fill  = factor(Correlation)), color = "black", alpha = .5) +
    geom_line(aes(alpha = n), color = "white", show_guide = F) +
    geom_vline(x = 550, color = "red") +
    coord_cartesian(ylim = c(.6, 1)) + 
    ylab("Correlation") + 
    xlab("Sample size") +
    theme_bw() + 
    theme(text = element_text (color = "black", family = "serif"), 
          panel.border = element_blank(), 
          panel.grid.major = element_line(colour = "grey70", size = 0.2)) +
    scale_fill_brewer(name = "Correlation", palette = "Set1")