How statistics can be misleading - Mark Liddell

Translator: Victoria Méndez Reviewer: traduceTED USC

Statistics are persuasive.

As estatísticas son moi convincentes,

tanto que persoas, organizacións e mesmo países enteiros

So much so that people, organizations, and whole countries

base some of their most important decisions on organized data.

basean algunhas das súas decisións máis importantes en datos organizados.

But there's a problem with that.

Pero hai un problema:

Any set of statistics might have something lurking inside it,

calquera conxunto de estatísticas pode ter información oculta,

something that can turn the results completely upside down.

datos que cambian totalmente as conclusións obtidas.

For example, imagine you need to choose between two hospitals

Por exemplo, imaxina que tes que elixir entre dous hospitais

for an elderly relative's surgery.

para a operación dun familiar ancián.

Out of each hospital's last 1000 patient's,

Dos últimos 1000 pacientes de cada hospital,

900 survived at Hospital A,

no hospital A sobreviviron 900,

while only 800 survived at Hospital B.

mentres que só 800 no hospital B.

Parece que o hospital A é a mellor opción.

So it looks like Hospital A is the better choice.

But before you make your decision,

Pero, antes de tomar unha decisión,

remember that not all patients arrive at the hospital

pensa que non todos os pacientes chegan ao hospital

with the same level of health.

co mesmo nivel de saúde.

And if we divide each hospital's last 1000 patients

E se dividimos os últimos 1000 pacientes de cada un dos hospitais

into those who arrived in good health and those who arrived in poor health,

entre os que gozaban de boa saúde ao chegar e os que non,

the picture starts to look very different.

o panorama cambia radicalmente.

Hospital A had only 100 patients who arrived in poor health,

Ao hospital A só chegaran 100 pacientes con mala saúde,

of which 30 survived.

dos que 30 sobreviviron.

But Hospital B had 400, and they were able to save 210.

Pero ao hospital B chegaran 400, e puideron salvar a 120.

So Hospital B is the better choice

Entón, o hospital B é a mellor opción para aqueles que chegan mal de saúde,

for patients who arrive at hospital in poor health,

with a survival rate of 52.5%.

cunha taxa de supervivencia do 52,2 %.

And what if your relative's health is good when she arrives at the hospital?

E que pasaría se o teu familiar gozase de boa saúde ao chegar ao hospital?

Strangely enough, Hospital B is still the better choice,

Sorprendentemente, o hospital B segue a ser a mellor opción,

with a survival rate of over 98%.

cunha taxa de supervivencia do 98 %.

So how can Hospital A have a better overall survival rate

Como é que o hospital A ten un índice xeral de supervivencia maior

if Hospital B has better survival rates for patients in each of the two groups?

se o hospital B ten mellores resultados para cada un dos dous grupos?

What we've stumbled upon is a case of Simpson's paradox,

Estamos ante un exemplo do paradoxo de Simpson,

where the same set of data can appear to show opposite trends

onde o mesmo conxunto de datos mostra tendencias opostas

depending on how it's grouped.

dependendo de como se agrupen.

This often occurs when aggregated data hides a conditional variable,

Isto sucede normalmente cando un estudo agocha unha variable condicionada

sometimes known as a lurking variable,

denominada variable ou factor de confusión,

which is a hidden additional factor that significantly influences results.

que é un factor adicional oculto que altera significativamente o resultado.

Here, the hidden factor is the relative proportion of patients

Neste caso, o factor influínte é a proporción de pacientes

who arrive in good or poor health.

que chegan con boa ou mala saúde.

Simpson's paradox isn't just a hypothetical scenario.

O paradoxo de Simpson non é só un caso hipotético.

It pops up from time to time in the real world,

Aparece de cando en vez en situacións da vida real,

sometimes in important contexts.

ás veces mesmo en contextos importantes.

One study in the UK appeared to show

Un estudo en Gran Bretaña mostraba que a taxa de supervivencia dos fumadores

that smokers had a higher survival rate than nonsmokers

era maior que a dos non fumadores nun período de vinte anos.

over a twenty-year time period.

That is, until dividing the participants by age group

Isto era así ata que, ao dividir os participantes por grupo de idade,

showed that the nonsmokers were significantly older on average,

os non fumadores eran, de media, significativamente maiores

and thus, more likely to die during the trial period,

e, polo tanto, era máis probable que morresen durante o estudo

precisely because they were living longer in general.

precisamente porque xa viviran máis tempo, en xeral.

Here, the age groups are the lurking variable,

Aquí, os grupos de idade son o factor de confusión

and are vital to correctly interpret the data.

e son vitais para interpretar os datos de xeito adecuado.

In another example,

Noutro exemplo,

an analysis of Florida's death penalty cases

unha análise dos casos de pena de morte en Florida

seemed to reveal no racial disparity in sentencing

mostraba ausencia de racismo á hora de ditar sentenza

between black and white defendants convicted of murder.

entre persoas brancas e negras condenadas por asasinato.

But dividing the cases by the race of the victim told a different story.

Porén, ao dividir os casos segundo a raza da vítima, os resultados cambiaban.

In either situation,

En calquera situación,

black defendants were more likely to be sentenced to death.

os acusados negros eran máis propensos a que os sentenciasen.

The slightly higher overall sentencing rate for white defendants

A media xeral era lixeiramente maior para os acusados brancos

was due to the fact that cases with white victims

precisamente porque, nos casos en que a vítima era branca,

were more likely to elicit a death sentence

a sentenza era case sempre de pena de morte,

than cases where the victim was black,

non coma nos casos con vítimas negras,

e a maioría de asasinatos producíranse entre xente da mesma raza.

and most murders occurred between people of the same race.

So how do we avoid falling for the paradox?

Entón, como evitamos caer no paradoxo?

Unfortunately, there's no one-size-fits-all answer.

Lamentablemente, non hai unha única resposta correcta.

Data can be grouped and divided in any number of ways,

Os datos poden agruparse e dividirse de moitísimos xeitos diferentes

and overall numbers may sometimes give a more accurate picture

e as observacións globais ás veces dan unha imaxe máis axeitada

than data divided into misleading or arbitrary categories.

que as resultantes de dividir os datos en categorías arbitrarias ou confusas.

All we can do is carefully study the actual situations the statistics describe

Todo canto podemos facer é estudar con coidado as situacións reais descritas

e considerar se hai variables de confusión que alteren a información.

and consider whether lurking variables may be present.

Otherwise, we leave ourselves vulnerable to those who would use data

Doutro xeito, quedamos vulnerables ante aqueles que usarán os datos

to manipulate others and promote their own agendas.

para manipular os demais e promover os seus intereses propios.