LYRICFLUENT
LYRICFLUENTHow Statistics Can Be Misleading Lyrics by Addison Anderson Addison Anderson
Below, you will find the lyrics for How Statistics Can Be Misleading by Addison Anderson.
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
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