Transcript Cures 45 out of 90 people 50% Cures 4 out of 10 people

THE RISKS OF LIFE
Video Conference 5
Media & Misinformation
Newspaper Headlines
Daily Mail
“Obesity worse for cancer than smoking”
“Is anything safe to eat? Cancer report adds
bacon, ham and drink to danger list”
Guardian
“Stay trim and stop eating bacon, cancer report
declares”
The Sun
“Bacon butty cancer risk”
“Careless pork costs lives”
“Shock Cancer Alert. Save Our Bacon. Storm
as Butties Branded Killers!”
Butties Branded Killers!
OCTOBER 2007
The reason behind the
headlines
World Cancer Research Fund
(WCRF) issued a report on the
influences of nutrition and
physical activity on Cancer.
They gave 10 recommendations
for Cancer prevention
WCRF Recommendation
“Avoid processed
meats such as bacon,
ham, salami, corned
beef and some
sausages”
The Evidence
The “Convincing Evidence” states
that there is a 20% increased
risk of bowel cancer per 50g
of daily processed meat
What is this really saying?
Report
20% increased risk of bowel cancer
per 50g daily processed meat
Fact
Approximately 5 out of every 100 people
will get bowel cancer during their life.
Conclusion
Eating a huge bacon sandwich every day
increases the number of people getting bowel
cancer to 6 out of every 100.
Simpson’s Paradox
You are suffering from a terrible illness.
There are two drugs you can take to cure
this illness:
(1) Drug A
(2) Drug B
Both drugs are put on trial
Drug A
Day 1
Day 2
Total
Drug B
Drug A
Cures 63 out of 90
people
Day 1
Day 2
Total
Drug B
Drug A
Cures 63 out of 90
people
Day 1
Day 2
Total
70%
Drug B
Day 1
Day 2
Total
Drug A
Drug B
Cures 63 out of 90
people
Cures 8 out of 10
people
70%
Day 1
Day 2
Total
Drug A
Drug B
Cures 63 out of 90
people
Cures 8 out of 10
people
70%
80%
Day 1
Drug A
Drug B
Cures 63 out of 90
people
Cures 8 out of 10
people
70%
80%
Cures 4 out of 10
people
Day 2
Total
Day 1
Drug A
Drug B
Cures 63 out of 90
people
Cures 8 out of 10
people
70%
80%
Cures 4 out of 10
people
Day 2
Total
40%
Day 1
Day 2
Total
Drug A
Drug B
Cures 63 out of 90
people
Cures 8 out of 10
people
70%
80%
Cures 4 out of 10
people
Cures 45 out of 90
people
40%
Day 1
Day 2
Total
Drug A
Drug B
Cures 63 out of 90
people
Cures 8 out of 10
people
70%
80%
Cures 4 out of 10
people
Cures 45 out of 90
people
40%
50%
Day 1
Day 2
Total
Drug A
Drug B
Cures 63 out of 90
people
Cures 8 out of 10
people
70%
80%
Cures 4 out of 10
people
Cures 45 out of 90
people
40%
50%
Day 1
Day 2
Drug A
Drug B
Cures 63 out of 90
people
Cures 8 out of 10
people
70%
80%
Cures 4 out of 10
people
Cures 45 out of 90
people
40%
50%
Cures 67 out of 100
people
Total
Day 1
Day 2
Drug A
Drug B
Cures 63 out of 90
people
Cures 8 out of 10
people
70%
80%
Cures 4 out of 10
people
Cures 45 out of 90
people
40%
50%
Cures 67 out of 100
people
Total
67%
Day 1
Day 2
Drug A
Drug B
Cures 63 out of 90
people
Cures 8 out of 10
people
70%
80%
Cures 4 out of 10
people
Cures 45 out of 90
people
40%
50%
Cures 67 out of 100 Cures 53 out of 100
people
people
Total
67%
Day 1
Day 2
Drug A
Drug B
Cures 63 out of 90
people
Cures 8 out of 10
people
70%
80%
Cures 4 out of 10
people
Cures 45 out of 90
people
40%
50%
Cures 67 out of 100 Cures 53 out of 100
people
people
Total
67%
53%
Drug A is Better!
You will reach the incorrect solution if you
only consider the daily percentage results.
You are not comparing ‘like with like’.
Sports statistics, exam results are often
reported in this way and can be misleading
if the data isn’t interpreted correctly.
Football League Tables
Which is the better team?
3 points for a win and 1 point for a draw
Man Utd
Played
Win
Lose
Draw
12
8
3
1
Points
Which is the better team?
3 points for a win and 1 point for a draw
Man Utd
Played
Win
Lose
Draw
Points
12
8
3
1
25
Which is the better team?
3 points for a win and 1 point for a draw
Played
Win
Lose
Draw
Points
Man Utd
12
8
3
1
25
Arsenal
13
6
1
6
Which is the better team?
3 points for a win and 1 point for a draw
Played
Win
Lose
Draw
Points
Man Utd
12
8
3
1
25
Arsenal
13
6
1
6
24
Which is the better team?
2 points for a win and 1 point for a draw
Man Utd
Played
Win
Lose
Draw
12
8
3
1
Points
Which is the better team?
2 points for a win and 1 point for a draw
Man Utd
Played
Win
Lose
Draw
Points
12
8
3
1
17
Which is the better team?
2 points for a win and 1 point for a draw
Played
Win
Lose
Draw
Points
Man Utd
12
8
3
1
17
Arsenal
13
6
1
6
Which is the better team?
2 points for a win and 1 point for a draw
Played
Win
Lose
Draw
Points
Man Utd
12
8
3
1
17
Arsenal
13
6
1
6
18
3 points for a win and 1 point for a draw
Played Win Lose Draw Points
Man Utd
12
8
3
1
25
Arsenal
13
6
1
6
24
2 points for a win and 1 point for a draw
Played Win Lose Draw Points
Man Utd
12
8
3
1
17
Arsenal
13
6
1
6
18
Medical and
Security
Testing
Suppose there are 100 students in your year
group, and one of which has stolen another
student’s lunch money. To find the thief
everyone undergoes a lie detector test which
has an accuracy of 95%. The lie detector says
you are a thief. What is the chance you are
actually the thief?
What is the chance you are actually the thief?
17%
84%
5%
95%
Understanding Uncertainty Bayes
Theorem animation
Statistics used in Court
Sally Clark
On the 9th November 1999,
Sally Clark, was convicted of
the murder of her first two
children.
What was said in Court?
Chances of 1 child dying from SIDS
= 1 in 6,500
Chance of both children dying from SIDS
 1 


 6500 
2
= 1 in 73,000 000
What wasn’t said in court?
The birth of two children are
NOT exclusively
independent events.
What wasn’t said in court?
Statistics of two babies dying
from the same mother:
One third caused by rare but known natural causes
(not SIDS).
One third associated with child abuse.
One third true “SIDS” deaths.
2 in 3 chance of innocence, rather than a 1 in 73
million chance of innocence.
What wasn’t said in court?
Probability of a mother murdering
2 of her own children is
1 in 2,200,000,000
Much lower than the probability of
both children dying from SIDS
1 in 73,000,000
Compulsory Investigation
Using probability to understand
medical and security test
results.