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Statistics are persuasive.

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So much so that people, organizations,[br]and whole countries

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base some of their most important [br]decisions on organized data.

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But there's a problem with that.

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Any set of statistics might have something[br]lurking inside it,

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something that can turn the results[br]completely upside down.

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For example, imagine you need to choose[br]between two hospitals

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for an elderly relative's surgery.

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Out of each hospital's [br]last 1000 patient's,

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900 survived at Hospital A,

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while only 800 survived at Hospital B.

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So it looks like Hospital A [br]is the better choice.

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But before you make your decision,

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remember that not all patients[br]arrive at the hospital

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with the same level of health.

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And if we divide each hospital's[br]last 1000 patients

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into those who arrived in good health[br]and those who arrived in poor health,

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the picture starts to look very different.

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

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of which 30 survived.

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

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So Hospital B is the better choice

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for patients who arrive [br]at hospital in poor health,

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with a survival rate of 52.5%.

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

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Strangely enough, Hospital B is still[br]the better choice,

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with a survival rate of over 98%.

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So how can Hospital A have a better[br]overall survival rate

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

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

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

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depending on how it's grouped.

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This often occurs when aggregated data[br]hides a conditional variable,

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sometimes known as a lurking variable,

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which is a hidden additional factor[br]that significantly influences results.

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Here, the hidden factor is the relative[br]proportion of patients

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who arrive in good or poor health.

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Simpson's paradox isn't just[br]a hypothetical scenario.

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It pops up from time [br]to time in the real world,

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sometimes in important contexts.

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One study in the UK appeared to show

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that smokers had a higher survival rate[br]than nonsmokers

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over a twenty-year time period.

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That is, until dividing the participants[br]by age group

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showed that the nonsmokers [br]were significantly older on average,

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and thus, more likely[br]to die during the trial period,

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precisely because they were living longer[br]in general.

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Here, the age groups [br]are the lurking variable,

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and are vital to correctly [br]interpret the data.

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In another example,

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an analysis of Florida's [br]death penalty cases

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seemed to reveal [br]no racial disparity in sentencing

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between black and white defendants[br]convicted of murder.

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

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In either situation,

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black defendants were more likely[br]to be sentenced to death.

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The slightly higher overall sentencing [br]rate for white defendants

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was due to the fact [br]that cases with white victims

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were more likely [br]to elicit a death sentence

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than cases where the victim was black,

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and most murders occurred between[br]people of the same race.

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So how do we avoid [br]falling for the paradox?

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

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

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and overall numbers may sometimes[br]give a more accurate picture

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than data divided into misleading[br]or arbitrary categories.

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

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and consider whether lurking variables[br]may be present.

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

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to manipulate others[br]and promote their own agendas.