The Cost of Dichotomization

“Although breaking participants into two groups can lead to the loss of some of the variance accounted for by the original continuous variable (Cohen, 1983), the distribution of identification scores violated normality assumptions (Shipiro-Wilks = .94, p .0001) because of a strong negative skew…”

“…sampling points of the independent variable required by the averaging approach, regression based approaches with fewer observations of discrete values across a larger value range have larger power and allow for the test of nonlinear relationships (Cohen, 1983; MacCallum et al., 2002; Baayen, 2004).”

“Taking a continuous variable and artificially dividing it into two or more groups is a serious mistake, because you lose all the underlying continuous information for no good reason (Cohen, 1983).”

“Some previous literature has signaled important concerns about dichotomizing and trichotomizing variables due to the arbitrariness of this decision (e.g., Cohen, 1983; Irwin & McClelland, 2003; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“First, conducting group analyses when the variable of interest is actually continuous reduces statistical power and increases the chance of a Type I error (Altman & Royston, 2006; Cohen, 1983).”

“Fourth, factorial analysis of variance (ANOVA) requires categorical independent variables; continuous variables such as word frequency must be converted to categorical variables, which may reduce statistical power and reliability (see Cohen, 1983; Humphreys, 1978; Maxwell & Delaney, 1993).”

“However, it does not take into account overall effects of RWA, and dichotomization of RWA loses information (Cohen, 1983).”

“Dichotomization of continuous behaviour is known to result in a significant loss of information and thus of statistical power (Cohen, 1983).”

“…loss of measurement precision (Ruscio & Ruscio, 2002), an increased risk for spurious findings (i.e., Type I error; MacCallum, Zhang, Preacher, & Rucker, 2002; Maxwell & Delaney, 1993), as well as loss of statistical power and attendant risk for Type II errors (Cohen, 1983; MacCallum et al., 2002).”

“(Cohen, 1983) especially when dichotomization is used (Zhao and Kolonel, 1992; MacCallum et al.”

“…variables can not only lead to a decrease in statistical power, increased potential for spurious finding, and a reduced ability to detect complex and/ or non-linear relationships (see Cohen, 1983; Young, 2016), but also have more general implications for interpretation and theory formation.”

“Because of their continuous nature (27,28), severity scales allow more precise (longitudinal) associations of depression or anxiety with lipid or obesity values than associations based on dichotomous diagnoses.”

“Simulations by Cohen (1983) suggest that dichotomization reduces the bivariate R2 by 35% if the predictor variable is dichotomized at the median, and Irwin and McClelland (2003) estimate a 42% reduction in R2 if the dichotomization is at the 70th percentile, which is where positive hooks (6+/7)…”

“Although such prevalence analyses are merely a simpler, dichotomized (thus less powerful; Cohen, 1983) version of our magnitude analyses, they provide a slightly different and potentially more intuitive metric.”

“, Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002; Maxwell & Delaney, 1993) as it lowers the information concerning individual differences (i.e., in age), affecting the power to detect a possible effect of that variable (i.e., a differentiation effect). In addition, to investigate the age differentiation hypot…”

“However, it is preferable to avoid such dichotomization which may at once lead to a loss of relevant information and to an oversimplification of the data (Cohen 1983).”

“In addition, when the explanatory variable is subject to measurement error the downwards bias in the estimator of its regression coefficient – the so-called ‘regression dilution’ – is well understood.(26,28,32,33) However, the magnitude of any power loss due to measurement error, that is the size of the reduction of t…”

“The issues have been discussed at length in the statistical literature (Cohen, 1983; Karabinus, 1975; McGrath & Meyer, 2006), but are presumably not well understood in many areas of psychology judging by the persistent and continued use of correlations on such data, without mention of this issue.”

“However, using a median split to dichotomize Vocabulary Knowledge, a continuous measure, would have diminished the statistical power of our analysis (Cohen, 1983; Humphreys, 1978; Maxwell & Delaney, 1993).”

“Despite evidence associating the MetS to increased risk of developing CVD, using the commonly applied definitions [12, 13], the use of dichotomized variables to create a clustered risk score ignores the continuous nature of risk and substantially decreases the available information and power of statistical analysis [1…”

“Even small amounts of measurement error lead to unreliability in detection of specific individuals as a member of a category (Cohen, 1983).”

“In general, median splits, as practice for dichotomizing a continuous variable, have a long tradition of being criticized for the loss of information and reduction in power (e.g., Cohen, 1983).”

“…large portion of the distribution of data, or the potential to overestimate the relationships between variables (see, for example, Humphreys, 1978; Cohen, 1983; Preacher et al, 2005), this methodology can be a useful heuristic for establishing that individual differences are real and meaningful,…”

“First, while Fitzsimons (2008) suggested using spotlight analysis instead of dichotomizing continuous variables, he did not exactly spell out in any easy way how to do it. Jaccard et al. (1990); Aiken and West (1991) and Irwin and McClelland (2001) give more detail but either researchers find their articles hard to co…”

“To do so, we introduce a novel analytic technique that has been developed in the field of physics that is not biased due to information loss incurred in artificially dichotomizing an underlying continuous variable (Aguinis, Pierce, & Culpepper, 2009; Cohen, 1983).”

“For example, most studies examine only one age group’s perceptions of developmental transitions (Barrett and Von Rohr, 2008) or ignore certain groups (e.g., middle-aged adults) entirely by comparing only extreme groups of younger and older adults (Cohen, 1983; Freund and Isaacowitz, 2013).”

“…word frequency into high and low conditions), which can misrepresent continuous variables, conceal potential nonlinearities, decrease power and effect size (Baayen, 2004; Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002), and increase the likelihood of Type I error (Maxwell & Delaney, 1993).”

“, defect counts in this case) into two classes often leads to a significant loss of information [2], [11], [34] and introduces undesired false positives or false negatives [5].”

“Dichotomization of continuous variables is associated with losses of information and may thus decrease statistical power (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“In contrast, the dichotomization artifact is introduced after data are collected and then scores are split (e.g., at the median) creating ‘‘high’’ and ‘‘low’’ categories (Cohen, 1983), so dichotomization is a data-analysis artifact.”

“Furthermore, dichotomizing can result in the underestimation of effect sizes, reduce statistical power, and increase false ‐ positives (Cohen, 1983; MacCallum et al., 2002).”

“It is worth noting that regression designs provide several advantages over factorial designs, such as allowing to determine how large the contribution of each independent variable is and avoiding the loss of information associatedwith the categorization of continuous variables [38].”

“Much as artificially dividing continuous personality variables into categories using a median split sacrifices real and meaningful variation (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002), dichotomizing personality variables such as anxiety into ‘‘short’’ and ‘‘long’’ timeframes may sacrifice the opportunit…”

“Further, predictors measured on a continuous scale tend to provide more information for detection of significant effects (Cohen, 1983; Cohen & Cohen, 1983; Gradstein, 1986; Maxwell & Delaney, 1993).”

“In the present manuscript, we improved upon their analyses by examining whether age, treated as a continuous variable (see Cohen, 1983), moderates the associations between social investment and trait development—including whether it does so in a curvilinear fashion.”

“Cox (1957), Cohen (1983), van Belle (2008), Fedorov, Mannino, and Zhang (2009)).”

“As Cohen (1983) pointed out, “Since methods are available for making use of all the original scaling information” (p. 249), dichotomizing variables is just a convenient practice that is “neither appropriate nor justifiable” (p. 252).”

“Artificially dichotomizing variables may also attenuate correlations with their true value, thereby causing a downward distortion in the mean correlation (Cohen, 1983).”

“However, these factors were not normally distributed across the studies so we decided to adopt a simple dichotomized approach to enable us to compare the highest against the lowest for both dose and duration [15].”

“Once we consider the issue from this point of view, it is not surprising that OSC provides a better fit to RT data than the transparency predictor; the latter just happens to be a dichotomization of the former, and it is well known that, when dealing with naturally continuous variables, a continuous indicator has to b…”

“In addition, dichotomizing ‘‘hides’’ variability within categories, has the potential to attenuate statistical power, and can lead to spurious findings (Cohen 1983; Irwin and McClelland 2003; Maxwell and Delaney 1993).”

“This was not the case, however, which is consistent with the expected loss of statistical power typically associated with dichotomizing continuous distributions ( Cohen, 1983; MacCallum et al., 2002)— unless there are clear-cut violations of normality in the data.”

“…even if the underlying functional form of accentedness is linear, discretization of a continuous variable can lead to a loss of statistical power (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002). hts reserved. uded as part of the first author's dissertation. sity of Alberta, 2-40…”

“Dichotomizing continuous variables is known to attenuate associations or even create spurious relationships (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“As a result, studies that dichotomize these initial attitude or preference measures will have less power to detect true selective exposure effects (see Cohen, 1983, for a discussion of the effect of dichotomization of research variables on achieved statistical power).”

“Such dichotomization severely compromises a study’s statistical power [135,136] and decreases the likelihood of detecting subtle, yet potentially meaningful, differences.”

“Most commonly, the dichotomization of dimensional scales reduces statistical power, making the detection of effects more difficult (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“…and psychological research that has clearly demonstrated the deleterious effects that scale coarseness and artificial dichotomization of a scale have for the magnitude of relations between coarsened/dichotomized scales and other variables (Aguinis, Pierce, & Culpepper, 2009; Cohen, 1983).”

“As if dichotomization of qualitative data into quantitative data is not criticized enough, the dichotomization of Likerttype scaled items, though frequently encountered in survey research whereby interval variables are reduced to dichotomies, is also vigorously criticized due to the loss of considerable amount of info…”

“We examined this attenuation and found in line with previous research (Cohen 1983; MacCallum, Zhang, Preacher, & Rucker, 2002) that the attenuation factor is constant across our simulation conditions as long as the dichotomization always occurs at the same percentile.”

“…fi nding, as one may expect severe anxiety to be more strongly related to parenting than milder anxiety, is that anxiety disorders were assessed as a categorical variable in the coded studies, as a result of which the power is lower compared to when continuous measures are used (Cohen, 1983).”

“We identified key concerns with logistic regression in physical activity and obesity research (Table 1), issues which also apply to other research fields [8, 9].”

“Thus, restrictions on the number of categories used for the SES variable decreased the correlation between SES and academic achievement (for explanations of this see Cohen, 1983; Hunter & Schmidt, 1990).”

“…and thus not comparable between studies, it has also been shown that the practice of dichotomizing a continuous variable leads to decreased statistical power, higher occurrence of false positives, or an overestimation of effect sizes depending on the data set (Cohen, 1983; MacCallum et al., 2002).”

“Based on statistical considerations (Cohen, 1983; Maxwell & Delaney, 1993), tertile scores were computed to create reasonably equal-sized groups with low levels of neuroticism (n1⁄4 136) and conscientiousness (n1⁄4 139), medium levels of neuroticism (n1⁄4 140) and conscientiousness (n1⁄4 119), and high levels of neuro…”

“Including continuous variation is more powerful than a median split (Cohen, 1983) and also yields more accurate estimates of effect size and lower rates of Type I error (MacCallum, Zhang, Preacher, & Rucker, 2002; Preacher, Rucker, MacCallum, & Nicewander, 2005).”

“Although it would be possible to divide reading time into a categorical variable for use in an ANOVA (e.g., with a median split), such dichotomization greatly reduces statistical power by discarding the variation within each category (Cohen, 1983).”

“Problems associated with artificially dichotomizing continuous data have long been known (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“In general, a criticism of this method has been that dichotomizing leads to less powerful and less accurate statistical tests (e.g. Cohen, 1983; Maxwell and Delaney, 1993).”

“…the continuous measures of the strategy variables (rather than dichotomize or truncate them) following recommended statistical procedures that prioritize continuous measures when possible in order to maximize the variability of the data (Cohen, 1983; MacCallum, Zhang, Preacher, & Rucker, 2002).”

“Nevertheless, our version of accuracy retains a different, arguably richer, source of information because ratings were allowed to be continuous (Cohen, 1983).”

“This required data reduction, as using individual PRISE items as GWAS outcomes would provide minimal statistical power, given the presence of substantial measurement error in self-report measures combined with the inherently weak statistical power of dichotomous outcomes.(30,33) Given the limitations of using individu…”