TedTest

From the Ted Talk by Mark Liddell: How statistics can be misleading

Unscramble the Blue Letters

Statistics are persuasive. So much so that people, organizations, and whole countries base some of their most important decisions on organized data. But there's a pleobrm with that. Any set of statistics might have something lurking inside it, something that can turn the results cepeotlmly upside down. For example, imagine you need to choose between two hospitals for an elderly relative's surgery. Out of each hospital's last 1000 patient's, 900 survived at haiopstl A, while only 800 survived at Hospital B. So it looks like Hospital A is the better choice. But before you make your deioscin, remember that not all patients arrive at the hospital with the same lveel of health. And if we divide each hospital's last 1000 patients into those who arrived in good health and those who arrived in poor hleath, the picture starts to look very different. Hospital A had only 100 patients who arrived in poor health, of which 30 srvieuvd. But Hospital B had 400, and they were able to save 210. So Hospital B is the better choice for patients who arvrie at hospital in poor health, with a sauvvirl rate of 52.5%. And what if your relative's health is good when she arrives at the hospital? Strangely enough, Hospital B is still the better chcoie, with a survival rate of over 98%. So how can Hospital A have a better overall survival rate if Hospital B has better survival rates for patients in each of the two groups? What we've stumbled upon is a case of Simpson's paradox, where the same set of data can appear to show opposite trends depending on how it's grouped. This often occurs when aggregated data hides a conditional variable, sometimes known as a lurking variable, which is a hidden additional factor that sinialgtfciny influences results. Here, the hidden factor is the relative proportion of paeittns who arrive in good or poor health. Simpson's padorax isn't just a hypothetical scenario. It pops up from time to time in the real world, sometimes in iamtnport contexts. One study in the UK appeared to show that smokers had a higher survival rate than nonsmokers over a twenty-year time period. That is, until dividing the participants by age group swhoed that the nonsmokers were significantly older on agverae, and thus, more likely to die during the trial period, precisely because they were living longer in gaenerl. Here, the age groups are the lurking variable, and are vital to correctly interpret the data. In another example, an analysis of Florida's death penalty cases seemed to revael no raaicl disparity in stenienncg between black and white defendants convicted of murder. But dividing the cseas by the race of the victim told a different story. In either situation, black dneftdanes were more likely to be sentenced to death. The slightly higher overall sentencing rate for white defendants was due to the fact that cases with white vimctis were more likely to elicit a death sentence than cases where the vitcim was black, and most murders occurred between people of the same race. So how do we avoid fllniag for the paradox? Unfortunately, there's no one-size-fits-all answer. Data can be grouped and divided in any number of ways, and overall numbers may sometimes give a more accurate pcturie than data divided into misleading or arbitrary categories. All we can do is celrflauy study the ataucl saitonuits the scatiistts describe and consider whether lurking virlbaaes may be present. Otherwise, we leave ourselves vulnerable to those who would use data to manipulate others and promote their own agendas.

Open Cloze

Statistics are persuasive. So much so that people, organizations, and whole countries base some of their most important decisions on organized data. But there's a _______ with that. Any set of statistics might have something lurking inside it, something that can turn the results __________ upside down. For example, imagine you need to choose between two hospitals for an elderly relative's surgery. Out of each hospital's last 1000 patient's, 900 survived at ________ A, while only 800 survived at Hospital B. So it looks like Hospital A is the better choice. But before you make your ________, remember that not all patients arrive at the hospital with the same _____ of health. And if we divide each hospital's last 1000 patients into those who arrived in good health and those who arrived in poor ______, the picture starts to look very different. Hospital A had only 100 patients who arrived in poor health, of which 30 ________. But Hospital B had 400, and they were able to save 210. So Hospital B is the better choice for patients who ______ at hospital in poor health, with a ________ rate of 52.5%. And what if your relative's health is good when she arrives at the hospital? Strangely enough, Hospital B is still the better ______, with a survival rate of over 98%. So how can Hospital A have a better overall survival rate if Hospital B has better survival rates for patients in each of the two groups? What we've stumbled upon is a case of Simpson's paradox, where the same set of data can appear to show opposite trends depending on how it's grouped. This often occurs when aggregated data hides a conditional variable, sometimes known as a lurking variable, which is a hidden additional factor that _____________ influences results. Here, the hidden factor is the relative proportion of ________ who arrive in good or poor health. Simpson's _______ isn't just a hypothetical scenario. It pops up from time to time in the real world, sometimes in _________ contexts. One study in the UK appeared to show that smokers had a higher survival rate than nonsmokers over a twenty-year time period. That is, until dividing the participants by age group ______ that the nonsmokers were significantly older on _______, and thus, more likely to die during the trial period, precisely because they were living longer in _______. Here, the age groups are the lurking variable, and are vital to correctly interpret the data. In another example, an analysis of Florida's death penalty cases seemed to ______ no ______ disparity in __________ between black and white defendants convicted of murder. But dividing the _____ by the race of the victim told a different story. In either situation, black __________ were more likely to be sentenced to death. The slightly higher overall sentencing rate for white defendants was due to the fact that cases with white _______ were more likely to elicit a death sentence than cases where the ______ was black, and most murders occurred between people of the same race. So how do we avoid _______ for the paradox? Unfortunately, there's no one-size-fits-all answer. Data can be grouped and divided in any number of ways, and overall numbers may sometimes give a more accurate _______ than data divided into misleading or arbitrary categories. All we can do is _________ study the ______ __________ the __________ describe and consider whether lurking _________ may be present. Otherwise, we leave ourselves vulnerable to those who would use data to manipulate others and promote their own agendas.

Solution

average
showed
survival
paradox
hospital
completely
victims
situations
problem
survived
actual
health
choice
variables
important
reveal
statistics
significantly
falling
picture
victim
racial
defendants
level
cases
sentencing
carefully
decision
arrive
general
patients

Original Text

Statistics are persuasive. So much so that people, organizations, and whole countries base some of their most important decisions on organized data. But there's a problem with that. Any set of statistics might have something lurking inside it, something that can turn the results completely upside down. For example, imagine you need to choose between two hospitals for an elderly relative's surgery. Out of each hospital's last 1000 patient's, 900 survived at Hospital A, while only 800 survived at Hospital B. So it looks like Hospital A is the better choice. But before you make your decision, remember that not all patients arrive at the hospital with the same level of health. And if we divide each hospital's last 1000 patients into those who arrived in good health and those who arrived in poor health, the picture starts to look very different. Hospital A had only 100 patients who arrived in poor health, of which 30 survived. But Hospital B had 400, and they were able to save 210. So Hospital B is the better choice for patients who arrive at hospital in poor health, with a survival rate of 52.5%. And what if your relative's health is good when she arrives at the hospital? Strangely enough, Hospital B is still the better choice, with a survival rate of over 98%. So how can Hospital A have a better overall survival rate if Hospital B has better survival rates for patients in each of the two groups? What we've stumbled upon is a case of Simpson's paradox, where the same set of data can appear to show opposite trends depending on how it's grouped. This often occurs when aggregated data hides a conditional variable, sometimes known as a lurking variable, which is a hidden additional factor that significantly influences results. Here, the hidden factor is the relative proportion of patients who arrive in good or poor health. Simpson's paradox isn't just a hypothetical scenario. It pops up from time to time in the real world, sometimes in important contexts. One study in the UK appeared to show that smokers had a higher survival rate than nonsmokers over a twenty-year time period. That is, until dividing the participants by age group showed that the nonsmokers were significantly older on average, and thus, more likely to die during the trial period, precisely because they were living longer in general. Here, the age groups are the lurking variable, and are vital to correctly interpret the data. In another example, an analysis of Florida's death penalty cases seemed to reveal no racial disparity in sentencing between black and white defendants convicted of murder. But dividing the cases by the race of the victim told a different story. In either situation, black defendants were more likely to be sentenced to death. The slightly higher overall sentencing rate for white defendants was due to the fact that cases with white victims were more likely to elicit a death sentence than cases where the victim was black, and most murders occurred between people of the same race. So how do we avoid falling for the paradox? Unfortunately, there's no one-size-fits-all answer. Data can be grouped and divided in any number of ways, and overall numbers may sometimes give a more accurate picture than data divided into misleading or arbitrary categories. All we can do is carefully study the actual situations the statistics describe and consider whether lurking variables may be present. Otherwise, we leave ourselves vulnerable to those who would use data to manipulate others and promote their own agendas.

Frequently Occurring Word Combinations

ngrams of length 2

collocation	frequency
survival rate	4
white defendants	2

Important Words

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