Table 2

Common statistical techniques for determining change in cognitive test score

Statistical techniqueReferenceAccounts forCalculationExtra data required
*Although RCIs allow for regression to the mean, they do not account for it statistically, as regression techniques do.
X1  =  baseline score; X2  =  retest score; SD  =  standard deviation; SEdiff  =  standard error of the difference; r  =  test-retest reliability coefficient; Y  =  predicted post-concussion score; X  =  slope of the regression equation; C  =  intercept of the regression equation; B  =  assessment number; μ  =  group mean; M  =  score of matched control subject; SEM  =  standard error of measurement; ƒ  =  value of multiple regression predictor; RCI, reliable change index.
Simple change scoreMitrushina & Satz28X2−X1
“True change” coreMaassen29Measurement error Regression to mean(X2−X1r2Test reliability
Standard deviation indexKneebone et al30(X2−X1)/μSD1Control group SD
Standard error of measurement indexJacobson et al31Measurement error Regression to mean(X2−X1)/μSEM1Control group SEM
Cohen’s dBenedict & Zgaljardic15(X2−X1)/SD1
Simple regressionMcSweeney et al14Regression to meanY = BX+C. Y is then compared with actual post-injury scoreControl group baseline mean Control group follow up mean
Multiple regressionTemkin et al26Regression to meanY = BX+C+ƒAge+ƒEducation+.... Y is then compared with actual post-injury scoreControl group baseline mean
Variables such as age, education, socioeconomic, and history of concussionControl group follow up mean
Variables such as age, education, socioeconomic status, history of concussion
RCIJacobson & Traux32Measurement error(X2−X1)/SEdiffTest reliability
Regression to mean*Control group SD
Modified RCI 1Chelune et al33Measurement error(X2−X1)−(μ2−μ1)/SEdiffControl group baseline mean
Regression to mean*Control group follow up mean
Practice effectsTest reliability
Control group SD
Modified RCI 2Zegers & Hafkenschield23Measurement error((X2−X1)r)+((μ2−μ1)1−r)/(√μr√(1−μr)SD)Control group baseline mean
Regression to mean*Control group follow up mean
Practice effectsTest reliability
Control group SD