Breaking Up is Hard to Do: The Heartbreak of Dichotomizing Continuous Variables David L. Streiner Nour Kteily PSY 1950

The Danger of Dichotomizing Reduced statistical power Increased probability of type II error Difficulty reinterpreting data once definitions have changed

The Rationale for Dichotomizing Outcomes 1) “Clinicians have to make dichotomous decisions to treat or not to treat, so it makes sense to have a binary outcome” 2) “Physicians find it easier to understand results when they are expressed in proportions or odds ratios rather than beta weights and other indices”

Striener’s Retort 1) Confuses measurement with decision making. 2) Many ‘binary’ disorders could actually be seen as a continuum. 3) All research using the old dichotomy becomes much more difficult to interpret if the definition of the dichotomy changes. 4) Many treatments for ‘binary’ disorders actually fall along a continuum.

Example 1 Scale dichotomized- scores below 15 considered normal; above 15 = ‘case’ If treat scores in Group 1 and Group 2 continuously: Mean G1 = Mean G2 = t(18)= 2.16, p = If treat dichotomously: G1: 9 normal, 1 ‘case’ G2: 4 normal, 6 ‘cases’ Fisher’s test: P = 0.057

Example 2 40 subjects, measured on 4 variables A-D Testing correlations (continuous), you would get 4 significant correlations (upper triangle) at p<0.01 level If you dichotomize the data using median splits, you get only 2 significant correlations (lower triangle). Run regression with A as the dependent variable and B-D as the predictors: Variables kept as continua: R 2 = Variables dichotomized: R 2 = 0.211

Issues with Dichotomizing 1) Magnitude of the effects were lower when considering outcomes as dichotomous versus continuous. 2) Findings that were significant using continuous variables were not significant using dichotomous variables. Why? Dichotomizing results in a ‘tremendous’ loss of information Misclassification Signal/Noise ratio Taken together, these issues result in decreased statistical power and increased probability of type II error

It’s Not All Bad There are actually a few cases, based on statistical not clinical considerations, when we should divide variables into a dichotomy or ordinal data. 1) J-shaped distributions 2) Non-linear relationships

Conclusion Gather data as continua whenever possible Unless your variable deviates considerably from normality, avoid decreased power and increased type II error - don’t dichotomize!