Concept Architecture
Concept
Theoretically, Standardised Response Mean (SRM) is a statistical measure of responsiveness that quantifies the magnitude of change in an outcome measure over time relative to the variability of that change. It is used to assess an instrument's ability to detect clinically meaningful change and is widely applied in psychometrics, health-related quality of life research, and health economics when evaluating patient-reported outcome measures.
Mathematically, the Standardised Response Mean is calculated as the mean change in scores divided by the standard deviation of those change scores. Unlike Cohen's d, which standardises using the baseline or pooled standard deviation, the SRM standardises using the variability of individual changes, thereby reflecting both the magnitude and consistency of change within a population.
In practice, the SRM is calculated from paired baseline and follow-up measurements for each individual. Change scores are computed, their mean and standard deviation are estimated, and the resulting SRM is interpreted as an effect size. Larger absolute values indicate greater responsiveness of the instrument to changes in health status over time.
Purpose
Used to quantify the responsiveness of health outcome measures by standardising the average change in scores relative to the variability of individual changes.
Mathematical Formulae
Primary Formula
SRM = ???SD?
where:
- ?? = mean change score
- SD? = standard deviation of the change scores
Supporting Formulae
Change score:
?? = X?,follow-up ? X?,baseline
Mean change:
?? = (1?n)????�??
Standard deviation of change scores:
SD? = �[????�(?? ? ??)�?(n ? 1)]
Related Mathematical Methods
- Effect size analysis
- Responsiveness assessment
- Paired-sample analysis
- Standard deviation estimation
- Longitudinal outcome measurement
Example
A study evaluates an HRQoL instrument before and after treatment in 100 patients.
- Mean change in score = 8.0
- Standard deviation of change scores = 10.0
SRM = 8.0?10.0 = 0.80
An SRM of 0.80 indicates a large degree of responsiveness according to conventional effect size interpretation.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| AVERAGE | =AVERAGE(C2:C101) | Calculates the mean change score. |
| STDEV.S | =STDEV.S(C2:C101) | Calculates the standard deviation of change scores. |
| AVERAGE/STDEV.S | =AVERAGE(C2:C101)/STDEV.S(C2:C101) | Computes the Standardised Response Mean. |
| COUNT | =COUNT(C2:C101) | Confirms the number of paired observations included in the analysis. |
VBA (Optional)
Automate calculation of change scores, estimate the Standardised Response Mean for multiple outcome measures, and generate responsiveness summary reports.
Sources
- Liang MH, Fossel AH, Larson MG. Comparisons of five health status instruments for orthopaedic evaluation. Medical Care. 1990;28(7):632?642.
- Husted JA, Cook RJ, Farewell VT, Gladman DD. Methods for assessing responsiveness: A critical review and recommendations. Journal of Clinical Epidemiology. 2000;53(5):459?468.
- Streiner DL, Norman GR, Cairney J. Health Measurement Scales: A Practical Guide to Their Development and Use.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
- NICE. Health Technology Evaluation Manual.
Related Concepts (2)
Library
Publications
1
NICE DSU Technical Support Document 8: An Introduction to the Measurement and Valuation of Health for NICE Submissions — Brazier, Rowen, TSD 8 ed., 2011 (NICE Decision Support Unit (University of Sheffield))
An introduction to the measurement and valuation of health for NICE submissions — the QALY, health-state utility values, generic preference-based measures, and the requirements of the NICE reference case.
Frequently Asked Questions (6)
What is the standardised response mean?
A responsiveness statistic calculated as the mean score change over time divided by the standard deviation of that change, unlike an effect size.
Source: Guyatt et al. 2002
How should a standardised response mean be interpreted?
The statistic expresses observed change in standard deviation units of that change, so larger values indicate that a measure detected change more clearly relative to the variability of the change. Values are read against conventional benchmarks for small and large effects, so a low figure signals weak responsiveness and a high one strong, though these labels are rules of thumb rather than fixed rules. Interpretation therefore depends on the sample and the comparison intended. Husted and colleagues (2000) discuss interpreting responsiveness statistics.
Source: Husted et al. 2000
How is the standardised response mean calculated?
The standardised response mean is calculated by taking the mean of the changes in scores between two time points across a group of patients and dividing it by the standard deviation of those changes. The numerator captures the average change, and the denominator its variability, so the ratio measures the change in units of its own spread. It is computed from the change scores of patients expected to have changed, over the period of interest.
Source: Guyatt et al. 2002
How does the standardised response mean differ from the effect size?
Both relate change to variability, but they use different denominators: the effect size divides the mean change by the standard deviation of the baseline scores, while the standardised response mean divides it by the standard deviation of the change scores. The standardised response mean thus reflects the variability of change rather than of baseline status. The two can give different values, so which is reported is stated, since they gauge responsiveness in slightly different ways.
Source: Guyatt et al. 2002
How is the standardised response mean used?
The standardised response mean is used to quantify and compare the responsiveness of health outcome measures, indicating how well each detects change relative to its variability, which helps in selecting an instrument for evaluating treatment. A higher value suggests a measure better able to register change. It is one of several responsiveness statistics, used alongside the effect size and anchor-based comparisons to judge whether a measure can capture the changes an intervention produces.
Source: Guyatt et al. 2002
What are the limitations of the standardised response mean?
The standardised response mean depends on the variability of change in the sample, which differs between populations and settings, so a measure's value is not fixed and comparisons require similar conditions. It reflects the magnitude of change occurring, not only the measure's properties, so a small observed change gives a small value regardless of the measure. It also does not indicate whether the change detected is clinically meaningful, which requires the minimal important difference.
Source: Guyatt et al. 2002
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 2 Sep 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-EE-HU-074
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