How statistics can be misleading - Mark Liddell

Kako statistika može da bude varljiva - Mark Lidel (Mark Liddell)

Prevodilac: Milenka Okuka Lektor: Mile Živković

Statistics are persuasive.

Statistika je uverljiva,

So much so that people, organizations, and whole countries

toliko da ljudi, organizacije i čitave države zasnivaju

base some of their most important decisions on organized data.

neke od svojih najvažnijih odluka na organzovanim podacima.

But there's a problem with that.

Međutim, tu imamo problem.

Any set of statistics might have something lurking inside it,

Svaki statistički skup može da ima nešto skriveno u sebi,

something that can turn the results completely upside down.

nešto što može u potpunosti da preokrene rezultate.

For example, imagine you need to choose between two hospitals

Na primer, zamislite da morate da izaberete između dve bolnice

for an elderly relative's surgery.

zbog operacije starijeg rođaka.

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

Od poslednjih 1000 pacijenata iz svake bolnice,

900 survived at Hospital A,

u bolnici A je preživelo 900,

while only 800 survived at Hospital B.

dok je u bolnici B preživelo svega 800.

So it looks like Hospital A is the better choice.

Pa se čini da je bolnica A bolji izbor.

But before you make your decision,

No, pre nego što se odlučite,

remember that not all patients arrive at the hospital

zapamtite da svi pacijenti ne stižu u bolnicu

with the same level of health.

istog zdravstvenog stanja.

And if we divide each hospital's last 1000 patients

A ako podelimo poslednjih 1000 pacijenata iz svake bolnice

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

na one koji su stigli dobrog zdravlja i one koji su stigli lošeg zdravlja,

the picture starts to look very different.

slika počinje da izgleda veoma drugačije.

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

Bolnica A je imala samo 100 pacijenata koji su stigli lošeg zdravlja,

of which 30 survived.

od kojih je 30 preživelo.

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

Međutim, bolnica B je imala 400 takvih i uspeli su da spase 210.

So Hospital B is the better choice

Pa je bolnica B bolji izbor

for patients who arrive at hospital in poor health,

za pacijente koji stižu u bolnicu lošeg zdravlja,

with a survival rate of 52.5%.

sa stopom preživelih od 52,5%.

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

A šta ako je zdravlje vašeg rođaka dobro kad stigne u bolnicu?

Strangely enough, Hospital B is still the better choice,

Zvuči čudno, ali bolnica B je i dalje bolji izbor,

with a survival rate of over 98%.

sa stopom preživelih preko 98%.

So how can Hospital A have a better overall survival rate

Pa, kako može bolnica A da ima bolju ukupnu stopu preživelih,

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

ako bolnica B ima bolje stope preživelih u obe grupe pacijenata?

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

Ono na šta smo nabasali je slučaj Simpsonovog paradoksa,

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

gde ista grupa podataka može da pokaže suprotne trendove,

depending on how it's grouped.

u zavisnosti od toga kako su grupisani.

This often occurs when aggregated data hides a conditional variable,

Ovo se često dešava kad skup podataka skriva uslovnu varijablu,

sometimes known as a lurking variable,

koju ponekad zovu skrivenom varijablom,

which is a hidden additional factor that significantly influences results.

a to je skriveni dodatni faktor koji značajno utiče na rezultate.

Here, the hidden factor is the relative proportion of patients

Ovde je skriveni faktor, relativna srazmera pacijenata

who arrive in good or poor health.

koji stižu dobrog ili lošeg zdravlja.

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

Simpsonov paradoks nije prosto hipotetičan scenario.

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

S vremena na vreme se pojavljuje u stvarnom svetu,

sometimes in important contexts.

ponekad u bitnim kontekstima.

One study in the UK appeared to show

Jedno istraživanje u Britaniji je pokazalo

that smokers had a higher survival rate than nonsmokers

da pušači imaju veću stopu preživelih od nepušača

over a twenty-year time period.

tokom perioda od 20 godina.

That is, until dividing the participants by age group

Sve dok učesnici u istraživanju nisu podeljeni po starosnim grupama,

showed that the nonsmokers were significantly older on average,

tada se pokazalo da su nepušači u proseku značajno stariji

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

i stoga je bila veća verovatnoća da će da umru tokom istraživanja,

precisely because they were living longer in general.

baš zbog toga što su inače živeli duže.

Here, the age groups are the lurking variable,

Ovde su starosne grupe skrivena varijabla

and are vital to correctly interpret the data.

i od suštinskog su značaja za pravilno tumačenje podataka.

In another example,

U drugom primeru,

an analysis of Florida's death penalty cases

analiza slučajeva smrtne kazne u Floridi

seemed to reveal no racial disparity in sentencing

nije se činilo da otkriva rasnu nejednakost kod presuda

between black and white defendants convicted of murder.

između crnih i belih prestupnika osuđenih na smrt.

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

Međutim, podela slučajeva prema rasi žrtve, govorila je nešto drugo.

In either situation,

U oba slučaja,

black defendants were more likely to be sentenced to death.

crni prestupnici su češće osuđivani na smrt.

The slightly higher overall sentencing rate for white defendants

Sveukupno nešto veća stopa osuđenih belih prestupnika

was due to the fact that cases with white victims

je bila posledica činjenice da slučajevi sa belim žrtvama

were more likely to elicit a death sentence

češće uzrokuju smrtnu kaznu

than cases where the victim was black,

od slučajeva gde je žrtva crnac,

and most murders occurred between people of the same race.

a većina ubistava se dešavala među ljudima iste rase.

So how do we avoid falling for the paradox?

Pa, kako da izbegnemo podleganje ovom paradoksu?

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

Nažalost, ne postoji univerzalno rešenje.

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

Podaci se mogu grupisati i podeliti na bezbroj načina,

and overall numbers may sometimes give a more accurate picture

a sveukupne cifre mogu ponekad da daju tačniju sliku

than data divided into misleading or arbitrary categories.

od podataka podeljenih u varljive ili proizvoljne kategorije.

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

Sve što možemo da učinimo je da izučavamo stvarne situacije koje statistika opisuje

and consider whether lurking variables may be present.

i da pazimo na prisustvo skrivenih varijabli.

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

U suprotnom, podložni smo uticaju onih koji će da iskoriste podatke

to manipulate others and promote their own agendas.

kako bi manipulisali drugima i promovisali sopstvene ciljeve.