The Cost of Dichotomization

“Prior work has noted the sizable loss in power resulting from categorizing continuous data (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

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

“We expected that a continuous variable produces more variance, while the dichotomization of variables reduces variance, which, in turn, results in a reduction in statistical power (Cohen, 1983).”

“Further, measurement of injection use as a dichotomous variable decreases both measurement precision[27] and statistical power.[28, 29] Despite these limitations, the association between this behavior and suicide attempts was robust across several series of analyses in a theoretically consistent manner.”

“Additionally, the categorical measure of readiness to change was replaced with a continuous measure to increase statistical power (see Cohen, 1983).”

“We used Cohen’s (1988) formula for estimating effect size associated with valence: f 2 = (R(2)ab − R(2)a)/(1− R(2)ab).”

“The current statistical literature assessing the practice of dichotomization is largely negative, pointing out the adverse consequence of dichotomization for either efficiency (Cox, 1957; Cohen, 1983; Delpizzo and Borghes, 1995; Weinberg, 1995; MacCallum et al., 2002; Senn, 2003; Royston, Altman, and Sauerbrei, 2006;…”

“Consequently, researchers with causal or explanatory aims should attempt, where possible to measure risks on interval scales in order to obtain accurate measurements [73,74].”

“First, research conducted within each subgroup has a lower statistical power than the full sample [61].”

“Moreover, applying a categorical structure to individual differences that vary continuously can compromise the power to detect significant links between attachment and internalizing symptoms [83].”

“Therefore, statistical power can be enhanced by studying the broader distribution than by dichotomizing the same distribution into cases and controls [12,13].”

“However, the practice of median splits has been heavily criticized in the literature because it leads to loss of information, power, and effect size (Cohen, 1983; Irwin & McClelland, 2003; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“The median split technique (Cohen, 1983) was used to select the 16 hours of”

“In all statistical association tests, dichotomizing a continuous variable decreases statistical power [24, 25].”

“More specifically, the slopes representing the relationship between pain intensity and pain-related disability were calculated at different conventional values of the moderator ( 1 SD, M, 1 SD; e.g., Aiken, West, & Reno, 1991; Cohen, 1983).”

“The power gains of quantitative versus dichotomous outcome specifications are well documented (Cohen, 1983), and it has been demonstrated that focusing solely on clinical diagnoses in psychiatric GWAS dramatically decreases power to detect effects (van der Sluis et al., 2013).”

“First, discarding all values from the middle of the distribution necessarily distorts the distribution of the data (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“…vs. categorical and specific vs. general adversity types) and often involved the generation of (artificial) groups from a continuous variable ( Cohen, 1983 ) by median-split dichotomization ( Jovanovic et al., 2020 ; Lange et al., 2019 ) or by applying cut-offs - that may vary even for a…”

“Hierarchical regression is one of the most useful tools for examining the interaction effect because it allows a researcher to base variables’ entry order according to their casual priority (Cohen, 1983).”

“However, it is also important to note that this advice followed articles one (Hunter & Schmidt, 1990) and two (Cohen, 1983) decades prior that essentially delivered the same cautions, and itself was followed by further research attempting to understand why researchers might dichotomize a continuous…”

“…amounts of observations per cell (Pinheiro & Bates, 2000), or (2) due to dichotomization of continuous variables, such as foveal load (Baayen, 2004; Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002), and (3) the models allow us to include both participants and items as crossed random…”

“First, if there is a desire to measure the change of WVOs within populations across time or space, a continuous scale would be more sensitive to detection of that change (Cohen 1983).”

“Second, dichotomizing a continuous measure will substantially reduce the statistical power of the analysis (Cohen, 1983).”

“However, it has been criticized for decades because it loses information, results in biased estimates, and reduces power (e.g., Cohen, 1983; Edwards & Lambert, 2007; MacCallum et al., 2002; Maxwell & Delaney, 1993).”

“For moderation, the hierarchical regression technique has been used as it has been considered one of the best techniques for analyzing the interaction between variables (Cohen, 1983).”

“The negative consequences of falsedichotomization within the general linear model (GLM) framework are well-documented (Cohen, 1983; Maxwell & Delaney, 1993), and the aspects of this practice that create problems for the GLM may also apply to mixture models.”

“A major drawback of the CQCA technique derives from the quantitization step as transforming qualitative data into quantitative carries the risk of losing critical information and analytical power contained in the raw qualitative data (Chi 1997; Cohen 1983; Driscoll and Appiah-Yeboah 2007).”

“’’ This dichotomization makes the longitudinal changes easy to interpret but reduces statistical power (Cohen, 1983) somewhat.”

“attenuate correlations and reduce statistical power necessary to detect significant relationships (Cohen, 1983) and cut points are often arbitrary (Decker, Melde, & Pyrooz, 2013).”

“…we split up the experiment in two halves and assess how the and conditions compare Major Minor to the condition at either side of the experimental lists (This None procedure is statistically suboptimal (see Cohen, 1983), but may be more familiar to readers that are not used to regression designs).”

“Although collapsing response options is seldom a wise psychometric decision (Cohen, 1983), this particular type of reporting is commonly used in organizational survey research (Rogelberg et al., 2002).”

“While dichotomizing continuous variables can reduce effect sizes by up to 30% and cause other issues with parametric analyses, dichotomization of categorical variables does not have the same computational consequences (Cohen, 1983; Royston et al., 2006).”

“However, such dichotomization is particularly associated with information loss and reduction of statistical power (22).”

“However, the multiple-group analysis with its reduction in variance (Cohen, 1983) did not indicate a clear difference in associations between the group with low and high attitude importance (B ¼ .848, SE ¼ .157, p < .001; B ¼ .855, SE ¼ .095, p < .001, respectively).”

“In contrast, measures that aim to sort individuals into SAD or non-SAD groups are contraindicated given that dichotomization of a continuous variable results in a loss of potentially important data (Cohen, 1983).”

“There is no reason to do this and all that will happen is the amount of variance explained in a dependent variable will be decreased (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“However, because W is binary we use the result in Cohen (1983) stating that for the case with two normally distributed variables, such asW ∗ and Z∗, in which one is dichotomized into equally sized groups, cor(W,Z∗) = 0.798 · cor(W ∗,Z∗).”

“In the sensitivity analysis, more variance in health literacy was explained when cognitive impairment was measured by the two component scores rather than the overall dichotomous classification, which is not surprising as dichotomizing may lead to loss of information [35].”

“…the underlying variation in attachment-related individual differences is important because many methodologists have highlighted the problems that can arise when researchers assign people to groups for the purpose of statistical analysis (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“That analytic strategy creates artificial groups and sacrifices the precision of the participants’ actual scores on the measures (Bissonnette, Ickes, Bernstein, & Knowles, 1990a, 1990b; Cohen, 1983).”

“Dichotomization has also long been objected to by methodologists on grounds that it has lower statistical power (Cohen, 1983).”

“The Perceived Stress Scale − 10 (PSS; Cohen 48 ) is a widely used psychometric questionnaire consisting of 10-items, assessing stress of which four are worded positively and six are worded negatively, assessing stress.”

“Reducing the continuous NA and SI measures to two or four personality types reduces the information about individual differences on these personality traits and this practice is associated with a loss in statistical power up to 60% [16].”

“One possible contributor to this decline has to do with the smaller effect sizes typical for dichotomous versus dimensional variables (Cohen 1983).”

“…of mania, there are concerns associated with potentially incorrectly conceptualizing mania as a categorical construct, including statistical problems (e.g. attenuated statistical power ; Cohen, 1983), spurious psychiatric co-morbidity (Haslam, 2003) and inappropriate denial of treatment services.”

“, [47, 48]) do not apply in a person-centered analytic framework.”

“Technically, categorization always implies a loss of information, and it usually leads to misleading results [1] [2] [3] [4].”

“Although having a larger number of groupings allows students’ differences to be modelled at a higher level of granularity than, say, a division at the median, it is sub-optimal to categorise a continuous variable as this can result in a loss of statistical power (Cohen, 1983).”

“Importantly, the current approach should have higher power as it is based on a continuous measure rather than dichotomization (Cohen, 1983).”

“This dichotomization of a continuous variable, however, is known to result in a significant loss of information and thus of statistical power (Cohen, 1983).”

“Based on statistical theory, the cost of loss of measurement information due to the dichotomization of a single predictor in the context of multiple regression analysis translates into underestimated effect sizes and a reduction of power in statistical hypothesis tests.(23,24) In practice, dichotomization of a quantit…”

“As per Cohen (1983), the relationship between narrative transportation and advertising behaviour is lower when the prior online purchase experience (POPE) is higher (β = 0.401, t = 6.597 p 0.05).”

“In addition, we used constraint (entropy) and word predictability (log cloze probability) as continuous rather than categorical predictors in the statistical analysis, which maximises statistical power (Cohen, 1983).”

“Further, themedian split discards the precision of the original continuous measure, and may underestimate the relationship and decrease statistical power (Cohen, 1983; Humphreys and Fleishman, 1974; Irwin and McClelland, 2003; Maxwell and Delaney, 1993).”

“Reducing continuous constructs into arbitrary dichotomies results in a corresponding reduction in measurement precision (Ruscio & Ruscio, 2002) and statistical power (Cohen, 1983; MacCallum et al., 2002), and in some cases may yield spurious statistical findings (Maxwell & Delaney, 1993).”

“…as an Australian, the Phase 1 identification measure was included as a covariate in all of the main analyses.2 Results were analyzed using hierarchical moderated multiple regression analyses and all predictors were mean-centered prior to conducting the analyses (Aiken & West, 1991; Cohen, 1983).”

“To maximize power, age was entered as a continuous variable in the regression equation, rather than dichotomized into two (younger and older) groups (Cohen 1983; Keith 2006).”

“It is difficult to interpret these mixed findings because most past research has used analytic techniques such as median splits or cluster analysis which prevent a powerful test of interactions by collapsing the variance in goal orientation dimensions into two groups (see Cohen 1983 for discussion of the conceptual an…”

“According to traditional conventional standards for effect sizes, our reported relationship between telework and WIF did not meet the criteria for classification as even a small effect (Cohen, 1983).”

“Statistically, dichotomizing a continuous variable reduces power [10].”

“Since participants have a continuous sense about their responses (i.e., confidence; cf. Zehetleitner & Rausch, 2013), the dichotomization in the direct task also discards information (Cohen, 1983).”

“This procedure has been criticized in the literature for various statistical limitations such as a loss of power, loss of effect size, loss of measurement reliability, and subjectivity with regard to cutoff points (Cohen, 1983; Gebhardt, Rose, & Mitte, 2014).”

“…transforming a continuous variable into a categorical variable (with a median split) reduces statistical power and may lead to spurious conclusions (Cohen, 1983; DeCoster, Iselin, & Gallucci, 2009; Fitzsimons, 2008; Irwin & McClelland, 2003; MacCallum, Zhang, Preacher, & Rucker, 2002; Maxwell &…”

“This trend is somewhat expected given the typical dichotomized scale of the graduate/attrite criterion, which tends to lead to underesti‐ mated correlation coefficients (Cohen, 1983).”

“‘low’ frequency, as in many previous studies), thereby avoiding loss of power and other problems [73,74].”