Sensitivity

Sensitivity, also called true positive rate, measures a diagnostic test’s ability to detect the correct number of positive elements in a binary classification test or to diagnose the correct number of students who have a given condition. Imagine, for example, a preliminary diagnostic test that determines whether or not a student has attention-deficit/hyperactivity disorder. The sensitivity of the test would measure the number of students who are correctly diagnosed with the condition. This entry further defines sensitivity, discusses the receiver operator characteristic (ROC) and positive predictive value (PPV), and looks at the practical application of sensitivity in testing.

Sensitivity assists in avoiding false negatives or classifying something as negative when it is in fact positive (e.g., identifying students as typically functioning when they have a disability). This is also known as Type II error. Sensitivity is calculated by the following formula:

$$\begin{array}{c}\text{Sensitivity}=\frac{\left(\text{true\hspace{0.17em}positives}\right)}{\left(\text{true\hspace{0.17em}positives}\right)\text{+}\left(\text{false\hspace{0.17em}negatives}\right)}\\ =\text{probability\hspace{0.17em}of\hspace{0.17em}a\hspace{0.17em}positive\hspace{0.17em}outcome\hspace{0.17em}given\hspace{0.17em}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}that\hspace{0.17em}the\hspace{0.17em}student\hspace{0.17em}has\hspace{0.17em}the\hspace{0.17em}condition.}\end{array}$$

Sensitivity is used alongside specificity when determining the efficacy of a binary classification test also called a binomial classification test. This kind of test divides elements of a group into two classes based on a certain characteristic. Diagnostic tests are a primary example of binary classification. They determine whether or not a child has a given condition, dividing students into either the typically functioning or condition group. Sensitivity measures how accurately the test predicts positive results, and specificity measures how accurately it predicts negative results. Specificity, [Page 1508]also called true negative rate, measures a binary classification test’s ability to detect the number of negative elements that are classified as negative or a diagnostic test’s ability to identify the correct number of students who are normally functioning. In the example of the attention-deficit/hyperactivity disorder test, specificity would determine the proportion of students who do not have attention-deficit/hyperactivity disorder and are diagnosed as such by the test.

A perfect predictor would be 100% sensitive and 100% specific. A test with 100% sensitivity can correctly identify all students with a given condition, although that is unlikely. More commonly, a high, but not perfect, sensitivity score is useful in ruling out a condition when a student tests negative. For example, using a basic cognitive test to determine whether a student has a learning disorder would have high sensitivity because a high proportion of students who have learning disorders would test positive. However, imagine that this test is just the first of many tests in diagnosing a learning disorder. In that case, this test would not be very specific: A high proportion of students who do not have the learning disorder may also test positive and would be found to have no disorder with subsequent testing. A rule of thumb to go by is SnNOut (if the result of a highly sensitive [Sn] test is negative [N], it rules out the condition) and SpPIn (if the result of a highly specific [Sp] test is positive [P], it rules in the condition).