Individual Diagnostic Assessment – Working with Individual Cases

Individual case diagnostics aims to arrive at the most accurate possible diagnostic judgment for an individual. Particular emphasis is placed on the uncertainty of test results that can arise from measurement error.

This is illustrated using an example from intelligence assessment: A student achieves an IQ score of 75, which could justify a recommendation to attend a special education school. However, without taking measurement error into account, the judgment could be premature and potentially inaccurate​​.

Standard error of measurement (SEM)

A central concept is the standard error of measurement (SEM), which quantifies the uncertainty of a test result. The SEM can be calculated using the standard deviation and the reliability of the test:
$$SEM = SD(X) \cdot \sqrt{1 – Rel(X)}$$
This measure indicates how much the observed score could deviate from the true score​.

Confidence intervals

Confidence intervals provide a way to visualize uncertainty. A confidence interval shows the range within which the true value lies with a certain probability. In diagnostics, these intervals are used to make the interpretation of test results more reliable​.

We calculate the confidence interval as follows:

$\text{Confidence interval} = \bar{X} \pm Z \cdot \frac{s}{\sqrt{n}}$

Explanation of the formula:

  • $\bar{X}$: Sample mean
  • $Z$: Critical value from the standard normal distribution (for 95%, $Z$ is 1.96)
  • $s$: Sample standard deviation
  • $n$: Sample size

In terms of interpretation: If we calculated infinitely many of these confidence intervals, 95% of them would contain the true value.

Practical relevance

In practice, this means that diagnosticians should always take the uncertainty of test results into account, especially when the results influence important decisions, such as a child’s educational pathway or a patient’s treatment.