The Cost of Dichotomization

“This is not a new idea; it has long been suggested that the use of continuous variables results in greater power (Cohen, 1983; Maxwell and Delaney, 199note3, Naggara et al., 2011; Royston et al., 2006).”

“Of some note are the (slightly) stronger associations when continuous rather than categorical variables are employed, in accord with statistical theory (Cohen, 1983).”

“6 in the explicit recognition task: The binary response format in the explicit recognition task discards information much like a dichotomization does when researchers apply it to their data (Cohen, 1983; MacCallum et al., 2002).”

“…be used for examination, but, the factorial design with continuous scales has been reported to reduce the amount of experimental variance that can be explained by experimental manipulations and lead to declines of statistical power in the parametric statistical analyses (Cohen, 1983; Baayen, 2004).”

“effect size and power, and loss of measurement reliability (Cohen, 1983; MacCallum et al., 2002).”

“These changes have led residents to suffer inconveniences such as noise in their residential areas, privacy exposure, congestion, and the general destruction of neighborhood [5,6].”

“Numerous authors have criticized researchers for splitting continuous measures into a small number of categories at arbitrary cut-points (e.g., Cohen, 1983; MacCallum et al., 2002).”

“…is undesirable because dichotomizing a continuous variable reduces the amount of information available and may result in spurious results or a failure to find significant effects (e.g., Bissonnette, Ickes, Bernstein, & Knowles, 1990; Cohen, 1983; Maxwell & Delaney, 1993; Tokowicz & Warren, 2008).”

“In general, leaving a continuous measure as continuous can increase statistical power relative to dichotomizing it (Cohen, 1983; MacCallum et al., 2002).”

“The present study adopts the latter approach to avoid the loss of prediction power associated with typologising variables (Cohen, 1983).”

“…information, introduces bias, and by not taking the uncertainty in the estimated quantities into account, can allocate a gene to the incorrect bin (Cohen, 1983; Streiner, 2002; MacCallum et al., 2002; Irwin and McClelland, 2003; Senn, 2003; Owen and Froman, 2005; Chen et al., 2007; Lazic, 2008;…”

“Because such systems display graphic (three-dimensional) cut-offs, interpretations do not depend on numerical cut-offs— which can induce false-negative and -positive results [18].”

“The strengths of the relationships between the variables were assessed using effect sizes as suggested by Cohen.”

“A dimensional scale is also preferable to a categorical measure because it can substantially increase statistical power; the high statistical costs of categorizing a quantitative variable have been demonstrated (Cohen, 1983; MacCallum et al., 2002).”

“Cohen (1983) warned, the sensitivity of the tests using this approach was reduced and few effects were evident.”

“Such dichotomization is almost never warranted (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002; Streiner, 2002) because when a dimensional score is dichotomized, information is discarded, and within the limits of sampling error, the variable produces lower magnitude associations with…”

“The latter is particularly relevant when also including additional variables, such as brain activity [1], but also helps avoiding potential biases induced by data binning in general [53,54].”

“Although, artificially creating categories will in most cases reduce statistical power (Cohen, 1983), particularly for individual difference predictor variables that are normally distributed (e.g. in a median split, some individuals may be only a few points away from fitting one category over…”

“The categorization of a continuous variable reduces measurement precision and the statistical power to detect a relationship between an independent variable and an outcome variable (Cohen, 1983).”

“However, to avoid information loss through dichotomization (Cohen, 1983), we now model RT variance as a continuous predictor instead.”

“Dichotomization of variables (for example p-value cutoffs, effect size boundaries) has been critiqued as an unnecessary step which sacrifices numerical nuance and specificity [61].”

“If a construct is distributed continuously (or graduated, to be more precise, a point made by Cohen, 1983), dichotomization can result in a substantial loss of statistical power, interfering with our ability to identify risk/protective factors for CUD symptoms.”

“Dichotomizing leads to reduction of power in the case of bivariate normality (Cohen 1983), but we know that bivariate normality does not apply to CU traits and CP; 3) The median split approach has, in the past, successfully delineated groups of children with CP who have different…”

“2007; Cohen 1983).”

“Although commonly utilized, the theoretical and statistical limitations of dichotomizing a variable with a median-split technique have been discussed in the prior literature (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“This is important because the creation of arbitrary taxa out of purely dimensional constructs results in a corresponding reduction in statistical power (Cohen 1983; MacCallum et al. 2002) and measurement precision (Ruscio and Ruscio 2002), and in some cases may produce spurious statistical findings (Maxwell and Delane…”

“Statistical power is lost: a median split has been equated to discarding one-third of the data [6].”

“However, dichotomizing continuous variables to create groups, as is the case with the current moderators, reduces power (J. Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“Tables 1 and 2 summarize descriptive statistics and correlations among all attitude measures and performance criteria (all correlations are uncorrected for criterion attenuation and dichotomization; Cohen, 1983).”

“Birth year was used as a proxy for birth cohort and entered as a continuous variable (Cohen, 1983; MacCullum, Zhang, Preacher, & Rucker, 2002).”

“…(or collapsing) alone can lead to negative consequences such as reduced effect size and power, loss of information on individual differences, and the possible introduction of spurious effects (e.g., Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002; Taylor, West, & Aiken, 2006).”

“These outcomes are a typical result of dichotomizing: correlations lose size, and this loss is larger as splitting departs from the mean (e.g., Cohen, 1983): in the lower prevalence conditions, dichotomization was applied further from the mean, and therefore, predictive utility was lower.”

“38 Substantial time can be necessary to explore the harmonized data and conduct preliminary analysis.”

“…be valuable because artificially reducing continuous constructs into arbitrary dichotomies reduces measurement precision and statistical power (Cohen, 1983; MacCallum et al.,2002), losing meaningful variability which could decrease accuracy in clinical risk assessments and research designs…”

“Because they can offer polychotomous answers, pattern recognition-oriented methods prevent dichotomization-related errors (24).”

“Indeed, dichotomizing a continuous outcome variable can reduce power to detect effects by the same amount as would discarding one third of available data (Cohen, 1983).”

“Dichotomization is a statistical procedure by which a measure that originally was continuous is transformed into a categorical variable on the basis of where individuals fall relative to a cutoff point (Cohen, 1983).”

“The problems associated with dichotomizing a continuous variable are well documented (J. Cohen, 1983) and include such pitfalls as a loss of variance and potentially inaccurate statistical conclusions.”

“Several studies suggest that information can be lost when a “coarse” response scale of nine or fewer fig- ures is used to represent a near continuous or “fine” variable (Russell, Pinto, & Bobko, 1991; Russell & Bobko, 1992; Cohen, 1993; Bobko & Russell, 1994).”

“We made use of multiple regression in order to avoid the problems known to arise when continuous predictors are dichotomised for the purposes of analysis of variance (Cohen, 1983 ; MacCallum, Zhang, Preacher, & Rucker, 2002 ).”

“62, considering it was based on dichotomous items [39].”

“This dimensional strategy is recommended to avoid artificial boundaries and artifacts associated with historical diagnostic criteria, increase relevance to preclinical forms of disease, and improve statistical power (Cohen, 1983; Royston et al., 2006; Yee et al., 2015).”

“Type I errors have also been shown to be induced by binning in other ways [6], [14].”

“Second, categorizing continuous data results in loss of valuable information captured by variables used to calculate allostatic load (Altman, Lausen, Sauerbrei, and Schumacher, 1994; Cohen, 1983).”

“Such an artificial dichotomization of the cognitive outcome ignores the intrinsically continuous nature of resilience and has potential limitations, including loss of power, spurious statistical significance and decrease in reliability (Cohen 1983).”

“Dichotomization reduces statistical power considerably (Cohen, 1983), and is an imprecise reflection of the measured construct.”

“MRA technique allows functional form of relationships between the variables (Stanley & Doucouliagos, 2012; Cohen, 1983).”

“…from splitting the data, and the fact that this interaction is ultimately continuous rather than categorical in nature, inferential statistics were not run on the subsetted data to avoid a Type II error in testing for effects of grammaticality or grammatical phrase frequency (see Cohen, 1983).”

“, determining what age span each bin covers) and can, in principle, increase the probability of finding spurious associations if the split points do not align with the actual distribution of values in the population (Cohen, 1983; MacCallum et al., 2002).”

“Second, dichotomising variables adds error, reduces power, and can lead to underestimating effect sizes (Cohen, 1983).”

“Most variables showed considerable skew, but we followed Cohen (1983) and MacCallum, Zhang, Preacher, and Rucker (2002) in analysing them as continuous, untransformed variables.”

“For these methods, designed to be applied to continuous variables, discretization does not improve clinical credibility and would likely hinder performance [51, 52].”

“As such, they suggest that using mood episode status in place of quantitative symptom severity measures in research and clinical decision making necessarily involves a loss of meaningful information and statistical power (Cohen, 1983).”

“Such a practice could reduce statistical power [40,41], obscure the conceptual nature of the construct, disguise potential non-linear relationships between depressive symptoms and other variables of interest [42], potentially create spurious statistically significance, and increase Type I errors”

“Although nonparametric tests based on discretizing a continuous covariate avoid modeling assumptions, there may be reduced power to detect the covariate effect (Cohen, 1983; Morgan and Elashoff, 1986; Selvin, 1987).”

“383,391,392 Challenges related to the design of clinical trials have the potential to impede the future development of novel, safe, and effective treatments for childhood myopia.”

“We adopted this typical approach of an at least moderate exposure cut-off from the literature for our main analyses, despite the well-known statistical disadvantages of artificially dichotomizing variables that are (presumably) dimensional in nature ( Cohen, 1983 ).”

“10,23,30 Considering the various classification schemes, the dichotomization of groups for analysis, and the influence of lower extremity mechanics leading up to SFC, 14 it is necessary to further investigate the effect of pitching style (spectrum of TF vs DD) on performance and injury risk.”

“All analyses were conducted with the continuous variable for action-state orientation, looking at action-state orientation on a spectrum rather than treating it as a categorical variable [19, 67].”

“(2021) to apply correlation-based procedures to AA-depression data rather than ANOVA procedures that rely upon dichotomy (with its inherent limitations upon statistical outcomes: Cohen, 1983).”

“This is problematic because the methodology of the median split can be accompanied by a reduction in test strength (Cohen, 1983) and also because it may happen that the variance concerning prior knowledge is not particularly high in the sample (Heemsoth and Kleickmann, 2018).”

“Numerous authors have suggested that dichotomization biases parameter estimates and reduces power (Cohen, 1983; DeCoster et al., 2009; MacCallum et al., 2002).”

“Rather than use transformations to reduce skew or dichotomize the outcome variable which reduced statistical power (Cohen, 1983), we followed recommendations outlined by Atkins & Gallop (2007) and utilized a negative binomial distribution and log link function to account for the nonnormality in the completed rape outc…”

“It has been frequently pointed out that dichotomizing continuous variables is a poor statistical practice that reduces power and obscures individual differences (e.g., Cohen, 1983; MacCallum, 2002).”

“The parameter values for a, b, and c’ were 0, .35, .96, and 1.46, which correspond to effect sizes of zero, small, medium, and large after adjusting for dichotomization (Cohen 1983, 1988).”

“See, e.g., Cox (1957) ; Cohen (1983) ; van Belle (2008) , and Fedorov et al. (2009) for more comprehensive discussions on problems associated with discretizing continuous variables.”

“analyses reflect the same overall trend as the correlational analysis but may be restricted by the dichotomisation of CASI-4 SP item responses into two subsets of response rather than the full range of four responses (Cohen, 1983).”

“Furthermore, from a statistical perspective, there are often costs to dichotomizing continuous variables (e.g., Cohen, 1983), and the use of a binary measure may dampen power to detect effects.”

“…to a quantitative measure of frequency of use, entails a very discernible loss of information that in turn can result in a significant loss of statistical power (Altman and Royston, 2006; Cohen, 1983; Cox, 1957; Fedorov et al., 2009; MacCallum et al., 2002; Royston et al., 2006; Streiner, 2002).”

“While this statistical approach is often used in psychology, Cohen suggests that dividing a sample into two groups leads to loss of the power of the sample [40].”

“A weakness of this latter approach is that acculturationgap groups are typically created by dichotomizing continuous measures of acculturation level, which is problematic because cut-points are arbitrary (in the sense that they are based on the given distribution of scores) and dichotomization of continuous data typic…”

“Such structure prevents errors associated with (cut-off mediated) false-negatives and false-positives [32].”

“Indeed dichotomizing our target-distracter similarity variable, something necessary for performing the conventional ANOVA, reduces the overall statistical power of the comparison (Cohen, 1983), and can produce misleading results (MacCallum et al.”

“Alternatively, using a repeated measures ANOVA would, under certain assumptions, account for the within-subject dependence, but would require us to transform the continuous variable of interest (QoL) to a categorical variable, a procedure which is discouraged (Cohen, 1983; Maxwell and Delaney, 1993).”