Tuberculin skin test

A diagnostic test with a very high sensitivity but very low specificity has the following problem:

  1. It will be very expensive to administer
  2. It will correctly identify all negative cases.
  3. It will label a big proportion of healthy people as sick (false-positives).
  4. It will miss a big proportion of true cases (label them as negatives).
  5. Specificity is the single most important characteristic of a test.

The tuberculin skin test is a screening test to identify people who have been exposed to tuberculosis.  A small amount of protein is injected into a bubble under the skin, after which the arm is examined for evidence of an inflammatory reaction (as evidence by redness and raising of the skin).  The lesion that develops is then measured by a healthcare provider who then judges the result as being positive or negative based on their results.  The majority of individuals who have had latent infection, active disease, successfully treated tuberculosis, or have been vaccinated tuberculosis vaccination will test positive.

New nurses are trained on this technique; the results of a recent student are compared with her instructor (shown below).  What is the percent agreement?