Table 1 Calculation formulas for distribution-based methods

Standard deviation method (SD)

\(S{D}_{baseline}=\sqrt{{\sum \left({x}_{0}-{\overline{x} }_{0}\right)}^{2}/\left(n-1\right)}\)

\(MCID=0.5*\text S{D}_{basline}\)  

\({x}_{0}\) is the baseline score for patients before intervention, \(\overline{{x }_{0}}\) is the mean score of patients before intervention, and n is the sample size, \(S{D}_{baseline}\) is the standard deviation of score before intervention.

MCID is 0.5SD of baseline data.

Effect size method (ES)

\(ES=\frac{\overline{{x }_{1}}-\overline{{x }_{0}}}{\sqrt{\sum {({x}_{0}-\overline{{x }_{0}})}^{2}/(n-1)}}\)

\(MCID=ES*S{D}_{baseline}\)

\(\overline{{x }_{1}}\) is the mean score after intervention.

MCID is the calculation result when the baseline data is 0.2, 0.5, and 0.8 respectively.

Standardized response mean method (SRM)

\(SRM=\frac{\overline{{x }_{1}}-\overline{{x }_{0}}}{\sqrt{\sum {({d}_{i}-\overline{d })}^{2}/(n-1)}}\)

\(MCID=\text SRM*S{D}_{d}\)  

\({d}_{i}\) is the change of scores before and after intervention,

\(\overline{d }\) is the mean of the changed score.

MCID was calculated when the data were 0.2, 0.5 and 0.8 after intervention.

Standard error of measurement method (SEM)

\(SEM=\text{}\sqrt{1-r*S{D}_{basline}}\)  

\(MCID=SEM*X\)  

r is the reliability coefficient, generally using test–retest reliability coefficient. If the test–retest reliability coefficient is unknown, the Cronbach coefficient can be replaced.

Reliability change index method (RCI)

\(RCI=\sqrt{2*SEM}\)

\(MCID=X*S{D}_{baseline}*\sqrt{2(1-r)}\)