Lab exercise 3

Please upload your completed .pdf file on Moodle by 23:59pm.

1. Import the two data sets from the following links into the RStudio, and name the two objects as data1 and data2.

• test1.txt
• test2.txt

2. Suppose you want to create a function that returns the criterion-related validity. Complete the following code chunk.

cr_val <- function(test1, test2){
  # total scores of the two tests
  total1 <- 
  total2 <- 
  # the Pearson correlation between the total scores
  rho_xy <- 
    
  return()
}

3. Complete the following code chunk to create a function that calculates the correlation between the true scores of two tests after correcting for attenuation.

true_cor <- function(test1, test2){
  # validity
  rho_xy <- 
  # reliability of the two tests
  rho_xx <- 
  rho_yy <- 
  # correlation between the true scores
  rho_txty <- 
    
  return(rho_txty)
}

hints:

• Inside the true_cor() function body, you can use cr_val() and coeff_alpha() functions to obtain \(\rho_{XY}\), \(\rho_{XX'}\), \(\rho_{YY'}\).

• You need to include a code chunk defining a function (e.g., coeff.alpha) before using it. Otherwise, it will return an error message when knitting.

• The correlation between the true scores \(\rho_{T_X T_Y}\) is:

\[\rho_{T_X T_Y} = \frac{\rho_{XY}}{\sqrt{\rho_{XX'}} \sqrt{\rho_{YY'}}}\]