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  • When dichotomising variables, what information is lost in the process?
  • How does a dichotomisation help in the analyses?
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  • $\begingroup$ Gelman and Park have an article which compares the practice of creating three categories from a continues variable, as opposed to two. Usually it is best to leave the variable continuous for the reasons explained by others below. $\endgroup$ Oct 7 '11 at 21:49
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What information is lost: It depends on the variable. Generally, by dichotomizing, you're asserting that there is a straight line of effect between one variable and another. For example, consider a continuous measure of exposure to a pollutant in a study on cancer. If you dichotomize it to "High" and "Low", you assert that those are the only two values that matter. There is a risk of cancer in high, and there is one in low. But what if the risk rises steadily for awhile, then flattens out, then rises again before finally spiking at high values? All of that is lost.

What you gain: It's easier. Dichotomous variables are often much easier to deal with statistically. There are reasons to do it - if a continuous variable falls into two clear groupings anyway, but I tend to avoid dichotomizing unless its a natural form of the variable in the first place. It is often also useful if your field is dichotomizing things anyway to have a dichotomized form of a variable. For example, many consider CD4 cell count of less than 400 to be a critical threshold for HIV. As such, I'd often have a 0/1 variable for Above/Below 400, though I would retain the continuous CD4 count variable as well. This helps cohere your study with others.

I'll disagree slightly with Peter. While dividing a continuous variable up into categories is often far more sensible than a crude dichotomization, I'm rather opposed to quantile categorization. Such categorizations are very difficult to give meaningful interpretations. I think your first step should be to see if there are biologically or clinically well supported categorization one can use, and only once those options are exhausted should you use quantiles.

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  • $\begingroup$ Hi @epigrad. I think quantile regression has a fairly easy interpretation; it is very similar to regular OLS regression, except to substitute "XXX percentile" for "mean". $\endgroup$
    – Peter Flom
    Oct 5 '11 at 21:57
  • $\begingroup$ @PeterFlom Sorry, I should have been more clear. I find them hard to compose as a clinically/biologically relevant interpretation, when compared to categories constructed from clinical/biological evidence. This is admittedly field-specific bias on my part. $\endgroup$
    – Fomite
    Oct 5 '11 at 22:01
  • $\begingroup$ Oh, OK, @epigrad, that makes sense. And I will edit my answer to include this case. $\endgroup$
    – Peter Flom
    Oct 5 '11 at 22:34
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    $\begingroup$ It seems that EpiGrad and @PeterFlom interpret "quantile regression" differently. EpiGrad talks about dividing the X variable into groups defined by quantiles, while Peter Flom talks about modeling, say, the 90th quantile of the response instead of its mean. $\endgroup$
    – Aniko
    Oct 6 '11 at 15:24
  • $\begingroup$ @Aniko That may be possible too. I had assumed (probably incorrectly) that Peter meant categorizing the data into quantiles and using that in a regression model. A common (and irksome) tendency in my field. That may not be the case. $\endgroup$
    – Fomite
    Oct 6 '11 at 17:43
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Dichotimization adds magical thinking to data analysis. This is very rarely a good idea.

Here is an article by Royston, Altman and Sauerbrei on some reasons why it is a bad idea.

My own thoughts: if you dichotomize a dependent variable, say, birth weight at 2.5 kg (this is done all the time) then you are treating babies who are born at 2.49 kg just like those born at 1.5 kg, and babies born at 2.51 kg just like those who are 3.5 kg. This does not make sense.

A better alternative is often quantile regression. I wrote about this for NESUG recently. That paper is here

One exception to the above is when the categories are substantively motivated; for example, if you are working with driving behavior, it will be sensible to categorize based on the legal age for driving.

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    $\begingroup$ Beautifully said Peter. I can't imagine a situation where dichotomization in analysis is a good idea. $\endgroup$ Oct 5 '11 at 22:35
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    $\begingroup$ Hi Peter, dichotimizing continous variables into caregorical reduces statistical power. That would be an inevitable downside, right? $\endgroup$
    – unicorn
    Sep 27 '20 at 3:38
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I liked and support both @Epigrad's and @Peter's answers. I just wanted to add, that, binning interval variable into binary one makes (potentially) metrical variable just ordinal one. With binary variable it is improper to calculate mean or variance (despite that some people do), and, as I've noted elsewhere, some multivariate analyses become theoretically or logically inapplicable. For example, I think it is not correct to use centroid/Ward hierarchical clustering or factor analysis with binary variables.

Clients of investigation often force us to dichotomise variables at output because thinking in terms of few classes rather than one continuous trait is simpler, information seems less foggy and (falsely) more bulky.

There are, however, cases when dichotomization may be warranted. For example where there is strong bimodality or when analysis (e.g. MAMBAC or other) show presence of 2 latent classes.

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  • $\begingroup$ I'm having a hard time understanding your argument. And if a client wants us to engage in bad statistical practice we should think twice. Note: trichotomise isn't a word. Dichotomization = dicho (two) + tomous (cut), so it would be tritomize/tritomise if used. $\endgroup$ Oct 6 '11 at 21:01
  • $\begingroup$ Passage on client was a lament, not argument. As for the Greek, you are right; I removed the word. $\endgroup$
    – ttnphns
    Oct 7 '11 at 3:47
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    $\begingroup$ Thanks. I try, as much as humanly possible, to translate statistical laments into corrective action, though an intensive education process with the client. $\endgroup$ Oct 7 '11 at 15:48

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