REF-1362 · Swinton et al., 2018 · Frontiers in Nutrition · Paper · PubMed · Free full text

My test went up after a block. Did it work for me?

Only if the rise beats the smallest worthwhile change by about one typical error, a rule right over 75% of the time; whether you "respond" can never be known from one test.

Main caveat: No empirical data. All worked numbers, including the 94.7% proportion of response, come from a mock data set.
thin evidenceMeasured on a mixed group

Swinton, Dolan and colleagues set out a three-step framework for interpreting individual data in nutrition and exercise interventions, with worked examples from a hypothetical randomised study of 20 participants (12 weeks of beta-alanine or placebo; sum of skinfolds, muscle carnosine and a high-intensity cycling capacity test) and spreadsheets for readers' own data.

Step 1, the baseline: every observed score is a true score plus measurement error (instrumentation noise plus biological noise such as circadian rhythm, food, sleep or motivation); the typical error (TE) is the SD of repeated tests, estimated from a group test-retest as the SD of the difference scores divided by √2 (difference scores have an SD of √2·TE), or from a published coefficient of variation; a true-score confidence interval is the observed score ± a multiple of TE, with larger multiples when the TE came from a small test-retest (for a 95% interval, 1.96 unadjusted, 2.10 if the TE came from 20 people, 2.78 from 5).

Step 2, the change: a change score has an SD of √2·TE; observed change ± TE is roughly a 50% interval, and judging an intervention successful only if that interval lies wholly beyond the smallest worthwhile change (SWC, often 0.2 × the baseline between-person SD) is correct more than 75% of the time in the long run; a test is too noisy for the purpose if its TE exceeds the gap between the expected change and the SWC.

Step 3, response: over weeks, true scores also change for reasons unrelated to the intervention (biological variability), so pre-post data cannot isolate an individual's response; responders and non-responders are theoretical constructs that can never truly be known; the spread of true response must be estimated at group level, as √(SD²intervention − SD²control), and turned into a proportion of response with a bootstrapped interval.

Our reading: this is the practical half of what REF-1274 found in VO2max trials — most of one block's spread is noise — and it supplies two things the base had only as arithmetic or practice: the √2 for a difference between two readings, and the fact that "change bigger than one typical error" is a roughly 50% interval, a lenient rule, not a 95% one.

Protocol

Design: methodological review with worked examples; n = not applicable (no participants, no new data).
Worked example: a hypothetical randomised study of 20 participants, 12 weeks of beta-alanine vs placebo; outcomes sum of 7 skinfolds, muscle carnosine (HPLC) and the CCT110% cycling capacity test; mock data, interactive calculators and spreadsheets in the supplement (maintained at github.com/sportscientist).
Statistics covered: classical test theory (observed = true + error); TE from repeated tests of one person (may need more than 10-20 tests) or a group test-retest; true-score and true-change confidence intervals with sample-size-adjusted multiples (Table 2; derivation in the appendix); SWC; intervention response SD from intervention and control arms; proportion of response by the normal model, with bootstrap intervals.
Funding and interests: grants from the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) to Dolan (2015/11328-2 and 2017/09635-0), Saunders (2016/50438-0 and 2017/04973-4) and Gualano (2013/14746-4); "The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest." No supplement maker, device maker, federation or data platform is named.

Key Results

The framework's rules (worked numbers are from the authors' mock data):

StepRule (full text)Worked example (mock data)
Typical error from a group test-retestSD of the difference scores ÷ √2carnosine: 0.74/√2 = 0.52 mmol·kg⁻¹ dm
TE from a published CVTE = CV × observed score / 100CCT110% CV 4.94% (a cited reliability study), 43.0 kJ → 2.1 kJ
95% interval multiple for a true score1.96 unadjusted; 2.10 if TE came from 20 people; 2.26 from 10; 2.78 from 511.3 ± (1.96 × 0.52) = 10.3-12.3; with TE from 5 people 9.9-12.7
SD of a change score√2 × TE—
Observed change ± TE≈ a 50% interval for the true change; for a single baseline score, observed ± TE ≈ a 70% intervalskinfolds −7.1 ± 1.35 mm = −8.45 to −5.75 → success
Success ruleinterval wholly beyond the SWC → correct > 75% of the time in the long runSWC 1.6 kJ + TE 2.2 kJ → needs ≥ 3.8 kJ; with TE 5 kJ → 6.8 kJ, more than the ~4.3 kJ expected
SWCoften 0.2 × the baseline between-person SD1.6 kJ for the cycling test
Intervention response SD√(SD²int − SD²con); needs a control group5.22 vs 1.24 → 5.07 mmol·kg⁻¹ DM
Proportion of responsearea of N(mean change, intervention SD) beyond the SWC; bootstrap CI0.947 (95% CI 88.2-100%) — mock data
Individual response"theoretical constructs that can never truly be known"—
Cited data, not mock: a time-to-exhaustion test at 75% of maximal power had a CV of 26.6%, far above the 5-15% changes in exercise capacity reported with beta-alanine; in repeated trials of the same sodium bicarbonate protocol only 1 of 15 participants improved beyond the test's normal variation on all four occasions, while 9 of 15 did so at least once.

Mechanisms

Measured: nothing new; the cited figures above are from other studies.
Authors' interpretation: an observed change mixes measurement error (instrumentation and biological noise) with biological variability (real change unrelated to the intervention); with only pre and post data, an individual's response cannot be isolated, and even a true non-response on one occasion does not predict the next. Researchers should estimate the proportion of response in a group with a control arm, or factors associated with response.
Inference: the base's line that "a change no larger than about the test's typical error is no change" (SYNTH-93) corresponds, by this paper's arithmetic, to a roughly 50% interval: a change just beyond one TE passes a rule that, applied routinely, is right more than 75% of the time in the long run; it is not a probability for this athlete, and not proof.A stricter reading (a 90-95% interval) needs a change of about 2.3-2.8 typical errors (our arithmetic: 1.64-1.96 × √2).
Inference: the sodium bicarbonate result is a direct demonstration that one person's "response" does not repeat reliably, matching the barely reproducible individual VO2max response in REF-498.

Practical Application

My test went up after a block. Did it work for me? Only if the rise beats the smallest worthwhile change by about one typical error, a rule right over 75% of the time; whether you "respond" can never be known from one test.
Get the noise first: run a test-retest of the athlete's own test, or take a published coefficient of variation for the same protocol and population (the authors' recommendation; C+, methods review). A test whose typical error is larger than the gap between the expected gain and the smallest worthwhile change cannot judge the block; standardise it or choose another test (SYNTH-53).
Two readings carry √2 × the noise: the SD of a change score is √2 times the typical error (full text), the basis of the base's "about 1.4 times" (SYNTH-93).
Never call an athlete a non-responder from one block: responder status is a theoretical construct for one person; spread of true response needs a control group (REF-1274, REF-430). Not from this paper; the base's own practice: judge a lever over 2-3 blocks on the same benchmark (SYNTH-42).
What it is good for as a source: the arithmetic and decision rules for reading an individual change against noise. What it does not show: the noise of any particular test (use REF-1278, REF-752) or whether real responders exist (that is REF-1274's question); its worked numbers are mock data.

Limitations

No empirical data. All worked numbers, including the 94.7% proportion of response, come from a mock data set; they illustrate the method and must not be quoted as findings.
Normal-model assumptions. The intervals and the proportion of response assume normally distributed errors and responses and a typical error that is the same across people and across the intervention (the authors' stated assumptions).
Confidence intervals are long-run properties. The authors warn that an interval from one data set should not be read probabilistically; a single athlete's "75% likely" is a statement about the procedure, not about that athlete.
Smallest worthwhile change is a choice. The 0.2 × between-person SD default is a convention; the authors ask for the SWC to be set before the intervention.
Nutrition-oriented examples. Beta-alanine, skinfolds and carnosine; the logic transfers to power tests, but the numbers do not. A small slip in the mock example: the cycling test's typical error is 2.1 kJ in section 1.2 and 2.2 kJ in section 2.2; it does not affect the method.
Funding and interests: FAPESP research grants to three authors; no conflicts declared. No supplement maker, device maker, federation or data platform is named.
How this entry was checked and changed
Why this level

a methods review without systematic method; the batch rule keeps B+ for the leading group, and a group working on individual response (the first author is also an author of REF-1274) is not shown to be one, unlike REF-430 and REF-441; its rules are classical-test-theory arithmetic derived in the paper, so the grade does not weaken the √2 or the interval multiples; read from the full text (open access, CC BY 4.0). It reports no empirical data: every worked number is from a mock data set, so none of them is a finding

Full text (checked 2026-10-28)
Difference scores are described by a normal distribution with mean 0 and standard deviation equal to √(2)TE; the TE estimate is the standard deviation of the difference scores divided by √(2) (full text)
For the muscle carnosine data, the standard deviation of the difference scores was 0.74 mmol·kg^−1dm; hence the estimate of TE is 0.74/√(2) = 0.52 (full text)
Typical error multiples for a 95% confidence interval: 1.96 non-adjusted; adjusted for a test-retest of 20 people 2.10, of 10 people 2.26, of 5 people 2.78 (Table 2; full text)
With (OSpost − OSpre) ± TE the multiple is 0.71, which approximately equates to a 50% CI (full text)
If interventions are deemed a success only if observed score change ± TE lie to the desired side of the 0 line, the proportion of times an intervention will correctly be identified as a success will be greater than 75% in the long-run (full text)
Constructing CIs with the observed score plus/minus the estimated TE for baseline scores provides approximate 70% true score CIs (full text)
A SWC of 1.6 kJ and a TE of 2.2 kJ require an observed improvement of at least 1.6 + 2.2 = 3.8 kJ; with a TE of 5 kJ, at least 1.6 + 5 = 6.8 kJ (full text)
Standard deviations of observed score change from the control and intervention group of 1.24 and 5.22 give an intervention response SD of 5.07 (full text)
The proportion of response estimate was 0.947, with a 95% CI of 88.2–100% (mock data; full text)
A time-to-exhaustion test at 75% of previously determined maximal power output had a CV of 26.6%, far in excess of the 5-15% changes in exercise capacity shown with beta-alanine supplementation (full text)
Only 1 out of 15 participants improved on all four occasions above the normal variation of the test, whereas 9 out of 15 improved on at least one occasion (full text)
ED (2015/11328-2 & 2017/09635-0), BS (2016/50438-0 & 2017/04973-4), and BG (2013/14746-4) were all supported by research grants from FAPESP; no conflicts declared (full text)