The Cost of Dichotomization

“In contrast to the AUROC measure, the point biserial correlation has been shown to depend on the base rate of the dichotomous variable (Cohen, 1983; McGrath and Meyer, 2006).”

“Under certain circumstances, dichotomizing has been linked to a loss of statistical power equivalent to removing a third of the sample (Cohen, 1983; Cohen, Cohen, West, & Aiken, 2003).”

“This minimizes the potential measurement error associated with cognitive performance measures and retains information lost in categorical classifications [48,49].”

“For the T-6 graduation/elimination criterion, the data also were corrected for dichotomization of the criterion (Cohen, 1983).”

“Dichotomizing continuous variables can dramatically reduce statistical power (Cohen, 1983), which may have contributed to the lack of reliable associations between social exchange domains and depression.”

“Given that arbitrary dichotomization of a dimensional construct can lead to loss of potentially valuable information, statistical power, reliability, and validity (Cohen, 1983; Widiger, 1992), assessment instruments that measure symptoms across the full spectrum of severity hold promise of enhancing sensitivity and di…”

“If a study reported both correlational and between-groups outcomes for the same assessment, given the well-documented problems with artificial dichotomisation (J. Cohen, 1983), outcomes for the correlational comparison were selected.”

“Moreover, as Cohen (1983) has convincingly shown: “Assuming bivariate normality with correlation r, dichotomizing one variable at the mean results in the reduction in variance accounted for to .647r2 …” resulting in “reduction in statistical power equivalent to discarding 38% … of the cases under…”

“…of an attitude scale item is frequently encountered in social or political science research (Cohen, 1983); however, Cohen and Cohen (1983 as cited in Cohen, 1983) have criticized dichotomization and argued that it results in underestimating effect sizes and reducing the power of statistical tests.”

“However, studies sometimes report results with one or both variables of interest artificially dichotomized, despite known and frequently repeated arguments against this practice (e.g., Cohen, 1983; MacCallum et al., 2002; Maxwell and Delaney, 1993).”

“Median splits are almost always prejudicial (Cohen, 1983), and their use often reflects a lack of understanding of the consequences involved (MacCallum et al., 2002).”

“, low and high self-esteem) can lead to false interpretations due to a loss in variance and analytical power (Cohen, 1983; DeCoster, Iselin, & Gallucci, 2009).”

“The dichotomization of CSA may be due to theoretical differences between abused and non-abused groups, or for methodological simplicity, which limits our understanding of potential differences within the group of CSA survivors (MacCallun, Zhang, Preacher, & Rucker, 2002; Altman, Lausen, Sauerbrei, & Schumacher, 1994;…”

“In STARSCAPE, time to disease progression was a composite endpoint including death; however, its contribution to the analysis results may be limited, as it is not easy to choose cutoffs that indicate disease progression (37).”

“In order to test the above predictions of the BIA+ model, we opted for a mixed- effects analysis (Baayen, Davidson, & Bates, 2008) without dichotomization of numerical predictors for more power and precision (Baayen & Milin, 2010; Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“Since participants have some continuous sense (confidence) about their responses (Rausch, Hellmann, & Zehetleitner, 2018; Zehetleitner & Rausch, 2013), the binary response format forces them to discard this information (Cohen, 1983), which further decreases the statistical power in the direct task.”

“Dichotomizing continuous variables has been widely regarded as an inappropriate practice that generates rather than solves problems (62, 63).”

“Second, converting continuous constructs like culture and language into a few categories may result in a loss of information and biased measurement (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“Once all effect sizes of relevance to each research question had been obtained, they were averaged into composite effect sizes (Cohen’s d), with a 95% confidence interval drawn around the mean. Composite effect sizes weigh each g by the reciprocal of its variance, thus giving greater weight to studies with larger samp…”

“Moreover, such analyses may increase power (Cohen, 1983), reliability (Button et al.”

“The structural model helps to calculate the effects of mediation analysis which enhance the understanding of relationships path specified in the theoretical model of the current study (Cohen 1983).”

“For example, dichotomising continuous variables could inflate Type I (MacCallum, Zhang, Preacher, & Rucker, 2002) or Type II (Cohen, 1983) error and could also obscure the functional relationship between variables and memorial performance. Moreover, it is getting increasingly challenging to select experimental stimuli…”

“Median (or otherwise) splits also resemble person-centered analytics, but given their numerous methodological shortcomings, their use is generally not recommended (e.g., Cohen, 1983; Irwin, & McClelland, 2003; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“Significance tests were done using continuous forms of these ages because dichotomization reduces power similar to a 50% reduction in sample size (Cohen, 1983).”

“However, binary outcome measures have long been advised against in RCTs because they lack sensitivity to the differences within and among patients, resulting in reduced power to detect effects (thus requiring much larger sample sizes), and attenuated effect sizes (Cohen, 1983; DeCoster and Iselin, 2009; Kraemer and Th…”

“Within the context of quantitative research, the arbitrary dichotomization of a dimensional construct leads to a loss in measurement precision (Ruscio & Ruscio, 2002) and statistical power (Cohen, 1983; MacCallum et al. 2002), and to an increased risk of spurious statistical findings (Maxwell & Delaney, 1993).”

“When indicators of response validity are continuous, as is usually the case, they should be analyzed in that form, thereby avoiding the usual problems with categorizing continuous variables (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“…of the response times implies that the amount of information concerning individual differences in the response times is reduced (see, e.g., Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002) while one of the motivations to add the response times is to increase measurement precision…”

“Results thus suggest that HMA individuals featured significantly worse visuospatial WM than their LMA peers regardless of gender.”

“Although there are concerns associated with dichotomizing continuous variables (e.g., Cohen, 1983), other studies have analyzed neighborhood density effects using regression techniques and found results that are qualitatively similar to the results obtained in studies that dichotomized the…”

“Furthermore, if AS is indeed dimensional at the latent level, any categorical classification made based on AS scores would represent an artificial dichotomization of a continuous variable and may result in distorted findings or a loss of potentially important information (Cohen, 1983).”

“…in their data analyses, which have been argued to create artificial groups, sacrifice the precision of the participants’ actual scores on the measures, and reduce statistical power (Bissonnette, Ickes, Bernstein, & Knowles, 1990a, 1990b; Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“Aside from potential loss of power (Cohen, 1983), such a dichotomization could result in spurious associations and inflated effect sizes.”

“Categorical analysis, however, brings costs, primarily in the loss of statistical power that comes from converting continuous to categorical data and the potential distortion of data (Burris 1994; Cohen 1983).”

“Second, conducting a mean or median split results in a less reliable dichotomous variable relative to the original set of continuous scores, and again is likely to attenuate the observed relations between these biculturalism scores and theoretically related variables (Cohen, 1983; Maxwell & Delaney, 1993).”

“Although most of the previous literature has classified participants into depressed vs non-depressed based upon the cut-offs for scales such as those recommended for the SDS (Zung, 1965, 1973), there is a cost to dichotomisation (Cohen, 1983) that can lead to an artefactual increase in Type II errors.”

“A continuous operationalization of neighborhood density provides greater detection power (Cohen, 1983) and more accurately characterizes the variable of interest.”

“The creation of categorical variables from continuous data results in a loss of statistical power (Cohen, 1983).”

“nd it is dichotomised into two arbitrary groups. The consensus of the statistics community is that chopping up continuous data into discrete categories is usually unnecessary and generally a bad idea [6, 7, 17, 23, 26, 30, 32, 36, 42, 44, 46]. There should also be a consensus in the biological community that the analy…”

“low anxiety sensitivity) a construct that is truly dimensional can also lead to an unnecessary loss of information (Cohen, 1983).”

“Creating arbitrary groups within continuous distributions also minimizes variability and measurement range thus affecting the power of statistical analyses used to make identification decisions (Cohen, 1983).”

“However, the effects of the alcohol influence measures on alcohol expectancies were more consistent when those measures had not been dichotomized, perhaps because of the lost information through dichotomization (Cohen, 1983).”

“All theoretical narrative indicators were treated as dimensional as opposed to ordinal or dichotomous in light of the limitations of the latter approaches (e.g., Cohen, 1983).”

“…14 The original study and this replication attempt used the same criteria to characterize a gene as silent or active, but there are many negative consequences of dichotomizing continuous variables, such as information loss, especially with a small gene set (Altman and Royston, 2006; Cohen, 1983).”

“Although cutoffs are needed for a clinical diagnosis, we were more interested in the effect of various symptom levels on benefit from extended time, and so dichotomizing the ADHD symptoms variable (even using DSM-IV cutoffs) would be statistically suboptimal (see Cohen, 1983).”

“We believe this approach allows for the creation of more representative and natural stimulus lists, and has the added advantage of avoiding the problems associated with dichotomizing continuous variables (Cohen, 1983; MacCallum, Zhang, Preacher & Rucker, 2002).”

“[5] and Cohen [10] pointed out that discretization at the median of a continuous variable leads to a loss of information, and discretization at other cut points away from the center lead to a much greater information loss.”

“As noted by Cohen (1983), dichotomisation may not represent the most accurate way to deal with age as a variable.”

“However, dichotomizing might result in loss of statistical power (Cohen, 1983; Fitzsimons, 2008).”

“Preexperimental matching on numerical covariates may lead to substantial loss of statistical power (Baayen, 2010; Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002) and may negatively affect the representativeness of the sampled items.”

“the high cost of dichotomizing continuous variables in terms of statistical power is well known (Cohen, 1983).”

“First, we prioritized dimensional scales, which enhance power compared to dichotomized scales (e.g., Cohen, 1983).”

“By default, a dichotomous indicator contains less information and therefore less statistical power to differentiate in terms of associated factors than a continuous indicator (Cohen, 1983).”

“…stage, what impact differences in methodology had on Liu et al.’s regression results, but converting a continuous variable into discrete categories reduces its variance and could have diminished the predictive power of polysemy (see Cohen, 1983, or MacCallum et al., 2002, for a related discussion).”

“Although the use of median splits in this manner has been criticized (e.g. Cohen, 1983; MacCullum, 2002), dichotomizing HRV may better capture the functional form of the HRV–EF relationship than the use of linear models representing HRV as a continuous measure (e.g., Kimhy et al., 2013).”

“Some authors have chosen to dichotomize the data (Terzis et al., 2010); however, this is generally considered an inefficient use of the available data (Cohen, 1983).”

“However, dichotomization tends to result in substantial decreases in variance and consequently in statistical power (Cohen 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“A second well-known limitation with this method is that the range restriction related to the dichotomization of a continuous distribution of IQ scores into low and high ability groups makes it difficult to find SLODR even if it is present (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“Given the statistical power that is retained when one does not artificially dichotomize a continuum, the QTL approach may provide a more powerful method for identifying susceptibility genes (Cohen, 1983).”

“In order to avoid artificial dichotomisation of variables that would be needed for nonparametric tests and can lead to distortion of the results [41], we chose a linear regression method, which also preserves loss of statistical power.”