Describing Categorical Data

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Describing Categorical Data

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How many, out of how many?

A categorical column cannot be averaged. The session starts from that fact rather than from a list of percentages to memorise.

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What you will be able to do at the end of today

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Act I · Counting, and the Three Things It Turns Into

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Four words, and they are not synonyms

Count, proportion, percentage, and rate get used as if they were the same sentence. They are not. The rest of the afternoon is about keeping the denominator in the sentence so the word you print still means something.

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Prevalence needs a place and a time

A prevalence is a proportion with an address. ‘Hypertension is 18.7%’ is not yet a finding. ‘Among these adults, in this district, in these years’ is.

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Missing values, worked

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Collapsing categories is the same trade as a threshold

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An order without a distance

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Act II · Out of How Many? The Question the Number Does Not Answer

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One table, two denominators, one row header between them

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Percentages inside subgroups

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The same 44.5%, in two sentences

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Both sentences are worth saying, and they are for different people

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Where the denominator usually goes missing

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A percentage of a small denominator is mostly noise

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Act III · Two Columns at Once, and the Three Percentages in Every Cell

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Crossing two categorical columns

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One cell, three percentages, all of them correct

Row, column, and overall: three different denominators, three true percentages, three different sentences. The question is never ‘which number is right?’ It is ‘which sentence were you trying to say?’

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So which percentage do you print?

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The footnote that decides the sentence

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You already read a table this way: sensitivity and specificity

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Act IV · When the Comparison Is Not a Fair One

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The crude number and the stratum numbers disagree

Hospital A looks safer until you notice who was sent there. A crude percentage can reverse once the same patients are compared inside the same stratum. That is not a trick. It is why a Table 1 is read before a headline.

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What a reversal does, and does not, license

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Comparing two populations as if they had the same patients

Standardization is not advanced material smuggled into description. It is the move that lets two percentages talk to each other when the people underneath them are not the same mix.

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Did hypertension rise, or did Bangladesh get older?

The crude figures move. The obvious objection is age. The session answers it in one sum, with the standardized figures computed in the room, so a rising headline has to survive a fairer comparison.

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Comparing a percentage with somebody else’s

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Act V · What a Percentage Hides, and How to Check

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Reading a Table 1, in order

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Auditing a table before you believe it

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A percentage on its own is a claim with the evidence removed

The session closes on a habit, not a formula. If the denominator is not in the sentence, the number is not finished. That habit is what Session 3.5 then makes you produce yourself.

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The same percentage, from three different studies

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Common traps, collected

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Close

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Before the next session