Enter the individual test scores, individual criterion measures, mean of the test scores, and mean of the criterion measures into the calculator to determine the validity coefficient.

Validity Coefficient Formula

The following formula is used to calculate the validity coefficient. 

VC = Σ((X - Mx) * (Y - My)) / sqrt((Σ(X - Mx)^2 * Σ(Y - My)^2))

Variables:

  • VC is the validity coefficient
  • X represents the individual test scores
  • Y represents the individual criterion measures
  • Mx is the mean of the test scores
  • My is the mean of the criterion measures

What is a Validity Coefficient?

A validity coefficient is a statistical measure used in psychometrics to determine the extent to which a test, scale, or measurement tool accurately measures what it is intended to measure. It is a correlation coefficient between the test scores and the criterion measure, ranging from -1 to +1. A higher absolute value indicates a stronger relationship and thus a more valid test. It is used to assess the validity of a test and to make predictions based on test scores.

How to Calculate Validity Coefficient?

The following steps outline how to calculate the Validity Coefficient.

  1. First, gather the individual test scores (X) and individual criterion measures (Y).
  2. Next, calculate the mean of the test scores (Mx) and the mean of the criterion measures (My).
  3. Next, subtract the mean of the test scores (Mx) from each individual test score (X) and subtract the mean of the criterion measures (My) from each individual criterion measure (Y).
  4. Multiply the differences obtained in step 3 for each pair of X and Y.
  5. Sum up all the products obtained in step 4.
  6. Next, calculate the sum of the squared differences between the test scores (X) and the mean of the test scores (Mx).
  7. Calculate the sum of the squared differences between the criterion measures (Y) and the mean of the criterion measures (My).
  8. Multiply the results obtained in steps 6 and 7.
  9. Take the square root of the product obtained in step 8.
  10. Finally, divide the sum of the products obtained in step 5 by the square root obtained in step 9.
  11. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

VC: validity coefficient

X: individual test scores

Y: individual criterion measures

Mx: mean of the test scores

My: mean of the criterion measures