A score moves from 42 to 46. Has the person improved? You can say the recorded score increased by four points. To say more, you need to know the direction of the scale, the measurement procedure, the uncertainty in repeat measurements and what the change means to the person.
Those questions are often collapsed into one cutoff. They should stay separate. A detectable change concerns measurement error; an important change concerns meaning. De Vet and colleagues explain the distinction and why a threshold based on measurement variability cannot by itself establish what people consider important. de Vet et al., 2006.
This is an interpretation exercise for PT students. The scale, numbers and person described below are fictional.
Start with the measurement conditions
Imagine a made-up activity questionnaire scored from 0 to 100, with higher scores indicating greater reported ability. A person records 42 at the first visit and 46 at a later visit.
Before doing calculations, check whether the same version of the questionnaire, instructions, assistance and scoring procedure were used. If one score came from a translated version with different validation evidence, or one session involved substantial prompting, that context belongs in the record. A difference between numbers is easy to calculate; comparability requires more attention.
Now assume this exercise has comparable administration and a relevant estimate of the standard error of measurement, or SEM, of two points. That value is supplied for the fictional example. It must not be borrowed for a real instrument.
Work through detectable change
A commonly used individual-level 95% minimal detectable change calculation is:
MDC95 = 1.96 × √2 × SEM
With SEM = 2, the result is approximately 5.54 points. MDC explanation and formula.
For this calculation, assume independent measurement errors with the same variance at both visits, no systematic change in measurement bias, and an approximately normal error difference. Each error variance is SEM², so the variance of their difference is 2 × SEM² and its standard deviation is √2 × SEM. Multiplying by 1.96 gives the stated two-sided 95% threshold. Correlated errors, unequal precision or a different measurement design require reconsidering that calculation; the formula is not universal.
The observed four-point increase is smaller than the example’s MDC95. A careful interpretation is that the change does not exceed this estimated measurement-error threshold. That is different from saying “nothing changed” or “the person’s account is wrong.” The instrument may not distinguish a modest change reliably under these conditions.
Suppose the later score were 49 instead. The seven-point increase would exceed 5.54. You would have more support for a change beyond the specified measurement-error threshold, assuming the estimate applies. You still would not know whether the change was important or caused by a particular intervention.
Put importance beside detectability
Now imagine that separate work for this fictional instrument, in a comparable population and context, identified three points as a candidate threshold for a minimally important change. That value is deliberately invented for the exercise.
The four-point change exceeds the example’s importance threshold but falls below its detectable-change threshold. This is not a mathematical contradiction. One threshold describes meaning and the other describes measurement uncertainty.
The lesson is not to choose whichever threshold gives the more appealing conclusion. It is to explain the tension: “The observed increase is large enough to meet the illustrative importance threshold, but it remains within the example’s measurement-error limit.” The next discussion should consider the person’s account, other relevant observations and whether the measurement approach can capture changes of interest.
A seven-point increase would exceed both illustrative thresholds. Even then, calling the intervention effective from this person’s before-and-after scores alone would add a causal claim that the calculation has not established.
Read the label carefully
Research papers use terms such as minimal important change, minimal clinically important difference and smallest detectable change. Check how each paper defines and estimates the term. An individual change threshold, a difference between group averages and a threshold derived in another population are not automatically interchangeable.
For example, a value estimated after one type of intervention may not transfer cleanly to people with a different starting severity or follow-up period. Record the population, method and time interval next to a threshold in your notes. A bare number loses the conditions that make it interpretable.
Do not confuse SEM with the standard error of a group mean. Both involve uncertainty, but they answer different questions. When a paper abbreviates a quantity, read the definition before inserting it into a formula.
A worked discussion note
For the initial fictional example, a student might write:
The activity score increased by four points under comparable administration. Using the supplied SEM of two points gives an illustrative MDC95 of about 5.54, so the change does not exceed that measurement-error threshold. Its importance requires separate interpretation, including the person’s priorities. These scores alone do not establish the cause of change.
The note names the observed fact, the calculation, the limit and the missing judgement. It also gives an educator something concrete to correct if the assumptions are wrong.
Test the distinction
A fictional measure has an appropriate individual MDC95 of six points. A person’s score improves by eight points, but the task they most want to resume remains unchanged. Can the student write “meaningful recovery achieved”?
No. The numerical change exceeds the supplied detectability threshold. The case does not establish meaningful recovery, and it gives a reason to investigate whether the measure captures the person’s priority. The next useful question concerns the relationship between the questionnaire and that specific task.
For your next assignment, keep three columns: observed change, uncertainty and importance. Fill each from an identified source or case fact. If one is unknown, leave it unknown. That is a stronger interpretation than using one familiar acronym to answer all three questions.
Sources and further reading
- de Vet and colleagues 2006 — Detectable and important change — Distinction between measurement error and important change, including the MDC formula.