The Cost of Dichotomization

“Although one could simply dichotomize the probabilities to facilitate such an analysis, numerous studies have documented significant problems with this practice (e.g., Cohen, 1983; Maxwell & Delaney, 1993; MacCallum et al., 2002; Streiner, 2002; Young, 2016).”

“Although it would be possible to collapse such variability into a smaller number of categories (e.g., with a median split) for a factorial analysis of variance (ANOVA), such techniques would greatly reduce statistical power (Cohen, 1983).”

“Cohen (1983) has demonstrated the loss of power that occurs when multiple-valued scales are reduced to dichotomies.”

“This approach implies artificially transforming dimensional constructs into subcategories, which could over-shadow the intertrial variability within categories (Cohen 1983), and lead to ecological fallacy (Freedman 2001), by assuming that the average value across trials holds for individual trials.”

“Outside of controlled experiments, artificial binning of naturally occurring continuous variation will also reduce statistical power and tend to downwardly bias effect sizes (e.g. Cohen, 1983 ; MacCallum et al., 2002 ).”

“58,59 Moving forward from traditional risk factor research “Field of risk factors is relatively well ploughed” as Kayes and Galea have stated.”

“However, their focus, and much of the focus of the statistical community (Cohen, 1983; MacCallum et al., 2002), is on issues with dichotomization.”

“Thus, a three-level random effects model was used to estimate the overall relationship between Roux, 2021 ), due to well-documented issues with artifi - cal dichotomization (Cohen, 1983).”

“Second, using cut-off points reduces available information by transforming a numerical variable into a dichotomous one, reducing statistical power (49) .”

“Dichotomising a Likert scale may sacrifice data variability and analytical power (Cohen 1983), yet Likert-type responses frequently avoid negative ratings, clustering around average scores.”

“This practice can compromise measurement reliability, statistical power, the accuracy and magnitude of individual differences correlations, and the precision of measurements of the underlying latent construct (Cohen, 1983; Fedorov et al., 2009; MacCallum et al., 2002).”

“An example of PR’s calming effect on the autonomic nervous system is the alleviation of sleeping difficulties, which may occur due to hyper-arousal states [16].”

“The main problem for prediction is that dichotomising a numerical outcome implies a loss of information equivalent to discarding a certain proportion of the data [2], although it might simplify the understanding and communication of results [6,7] or increase robustness against contamination [25].”

“BMI scores were analyzed as continuous variable to maximize statistical power [19, 20].”

“While the correlations were all less than .2, dichotomizing variables can result in an intense range restriction which attenuates correlation values (Cohen, 1983).”

“If these choice options can be analyzed in an ordinal scale, researchers do not have to dichotomize response data at the risk of reducing measurement information and introducing errors (Cohen, 1983).”

“Reducing data from a continuous scale such as the SDS into a dichotomous variable always reduces the power of the analysis (35).”

“Age was purposely conceptualized as a continuous variable, which increases experimental power and avoids the loss of variance resulting from the use of categorical age groups (Cohen, 1983).”

“Moreover, the use of median splits leads to a considerable loss of the variance accounted for by the original variable (Cohen, 1983).”

“A point-biserial correlation (rpb) describes the relationship between dichotomous variables (i.e., correct vs incorrect) and continuous variables (i.e., test score; Cohen, 1983; Dungan, 1996; Randolph, McCrea, & Barr, 2005).”

“In addition, such a paradigm incurs lower statistical power since only two data points can be analyzed (Cohen, 1983).”

“This choice was motivated by a substantial methodological literature demonstrating that continuous or graded response scales preserve more information, increase sensitivity, and avoid distortions associated with dichotomization (e.g., Cohen, 1983; Dawes, 2008; Simms et al., 2019).”

“Dichotomizing variables that are continuous in nature sacrifices statistical power (Cohen, 1983) and reduces reliability (Markon et al., 2011), increasing the risk of Type II errors.”

“…Type D effect showed dichotomous approach often tends to produce false-positive effects when only NA or SI is related to the outcome (Lodder, 2020 a, b; Lodder et al., 2021), as well as reduce the information about individual differences on these personality traits (J. Cohen., 1983; Lodder, 2020).”

“While a categorization of skewed continuous measures has been a common practice in reviewed studies [12-15], splitting a continuous measure into two or more categories has long been known to come at a cost of losing statistical power and residual confounding [58-60].”

“However, binarizing continuous responses are known to have lower statistical power than analyzing them continuously (e.g., Cohen, 1983; Fedorov et al., 2009; MacCallum et al., 2002).”

“Although the conversion of a continuous handedness score into discrete categories is of great importance for comparative studies, this issue is still the subject of ongoing debate (e.g., Chisnall, 2012; Cohen, 1983; Dinsdale, Reddon, & Hurd, 2011; Irwin & McClelland, 2003; Streiner, 2002).”

“Consequently, artificially dichotomizing a variable has numerous costs (Cohen, 1983; Irwin & McClelland, 2003; MacCallum et al., 2002).”

“Using a pass-fail criterion also results in reducing the variance of the criterion, thus making it more difficult to find a correlation (Cohen, 1983).”

“In this article, the issue is addressed from a life transition perspective (Elias, 1989).According to Elias (1989), transition between school grades is understood as a set of demands that require adaptive effort in five domains or tasks: (a) adjustment to changes in role definitions and expected behaviors; (b) reestab…”

“…allows for creating two sufficiently distinct groups of participants that differ in terms of their reading skill, the median split technique may have drawbacks such as artificially creating an experimental variable (also see Cohen, 1983, for a discussion of the effectiveness of the median split).”

“It should be stressed that the practice of dichotomising data from continuous scores into more discrete categories is not without criticism, as it can lead to unreliable results (Cohen, 1983).”

“Additionally, for simple counts, they require dichotomizing outcomes to a present/absent status, which results in a loss of information regarding the severity of each risk factor and reduced statistical power (Cohen, 1983; Royston, Altman, & Sauerbrei, 2006).”

“…Interview für DSM-IV [Wittchen et al., 1997]) sowie die Dichotomisierung der kontinuierlichen Variable Distanz zum Wohnort in Kilometern, die häufig kritisch betrachtet wird, da dies zu einer Reduktion der Teststärke und damit einer konservativeren Signifikanzaussage führen kann [Cohen, 1983].”

“, binarizing into high versus low) such as reduced power, increased chances of finding spurious effects, and the inability to detect non-linear relationships (Cohen, 1983; MacCallum et al., 2010).”

“As the above factorial analysis was conducted using a median split of the optimism variable, we may have lost considerable statistical power (Cohen, 1983).”

“Dichotomisation is a statistical procedure by which an originally continuous variable is transformed into a categorical binary variable based on where individuals fall relative to a cut-off point (Cohen, 1983).”

“analysis, dichotomizing the adverse impact ratio may have serious and unexpected consequences under certain circumstances (Cohen 1983; Maxwell and Delany 1993).”

“Unlike other studies [15, 23] the relationship between age and satisfaction was not statistically significant.”

“Appendix B.7 gives the smooth-integral calculation and the remainder it leaves unbounded; agreement in particular models, such as the Gaussian computations of Appendix E.2, does not establish the expansion in general.”

“Although a binary scoring sys-tem incurs a notable loss of statistical power in comparison to a continuous score (Cohen 1983), the gain in classification accuracy (compared to measures such as the IQR or beat- to-tap consistency when used with phase-based responders with high IBI variability)…”

“This approach provides a more accurate representation of central tendency for skewed data and is commonly used in studies with non-parametric characteristics due to its empirical robustness and lower sus - ceptibility to outliers [12,13].”

“For such distributions, a median split minimizes misclassification bias and is optimal for group comparisons, aligning with established practice in exploratory research [39, 40].”

“Lack of variability has long been noted as a potential source of correlational attenuation (Bland & Altman, 2011; Cohen, 1983; Goodwin & Leech, 2006; Hunter & Schmidt, 1990).”

“Input frequency, based on the Gachon Learner Corpus, was treated as a continuous variable to avoid data loss associated with categorization (Cohen 1983).”

“Additionally, a dummy variable may result in a loss of variation and statistical power (e.g. Cohen, 1983).”

“Although TFI scores are often used as a dichotomous variable in regression analyses (i.e., at/ above 70% of maximum total score vs. below 70%), Cohen (1983) outlined that dichotomization substantially reduces statistical power, meaning it is unlikely that dichotomizing would be more sensitive to…”

“In addition, erroneously treating data as either categorical or continuous negatively impacts statistical power as well as the precision of the estimated associations when using attachment as predictor (Cohen, 1983, 1988; Fraley & Spieker, 2003).”

“This approach of predicting the future level of a variable while accounting for predictions from initial levels (e.g., stability), yields one marker of change in that variable: increases or decreases in its fi nal state relative to predictions based upon initial levels (Cohen & Cohen, 1983).”

“Reducing continuous variables to categorical variables through a median split reduces reliability, statistical power, and effect sizes (Cohen, 1983; Markon et al., 2011).”

“In fact, dichotomising a variable can reduce statistical power by the same amount as would discarding a third of the data or more [37].”

“All else being equal, dimensional analyses offer more power than categorical analyses (49,50); moreover, transdiagnostic fear is likely a more cohesive construct than categorical diagnosis of SP.”

“We were aware of the cost of dichotomization and accepted the concomitant loss of variance, reduction in statistical power and influence on effect sizes (Cohen, 1983; Preacher et al., 2005) as potential limitations to our approach.”

“…analyses, for example, It is important to note that concerns regarding loss of power from dichotomizing relate to the case of bivariate normality (Cohen, 1983), but using continuous measure of CP and CU can generate problems if modelled together, given the absence of bivariate normality—high CU…”

“On the one hand, dichotomization has been observed to result in a large reduction of statistical power (12,13).”

“Moderation analysis also has the advantage of using continuous variables (in this case, mathematical skills) and thus avoids the lack of power associated with artificially categorizing participants in groups (Cohen, 1983), as would have been the case were we to have used an ANOVA.”

“Apart from tautological tests being silly and cluttering research reports with useless prose, carving up continuous variables into high and low groups is almost invariably a bad idea (e.g., Cohen 1983; MacCallum et al. 2002; Maxwell & Delaney 1993).”