This document discusses simple tools for understanding risks and moving from innumeracy to insight. It explains that confusing numerical representations like single event probabilities, conditional probabilities, and relative risks can lead to misunderstanding and inappropriate actions. Using natural frequencies and clearly specifying the reference class can help diminish confusion. Conditional probabilities are more difficult for people to understand than natural frequencies, which refer to the same class of observation. The document also discusses how framing risks as absolute reductions rather than relative risks can avoid misunderstanding. Clarifying the reference class, using transparent representations like natural frequencies, and being aware of negative versus positive framing are some ways to help people better understand statistical risks.

1. Simple tools for understanding risks:
from innumeracy to insight
An article by:
Gerd Girenzer and Adrian Edwards
Presented by:
Muhammad Husnul Khuluq
F131877

2. What does it
mean?
DO I have a
cancer?
Bad
Presentation
Confused/
Misperception
Inappropriate
Action
Confusing numerical
representations
1. Single event probabilities
2. Conditional probabilities
3. Relative risks

3. This medicine,
however, might have
30% to 50% chance of
developing a sexual
problem
Oh, NO!
I’ll have 30-
50% sexual
problems.
Different reference classes (in mind)
results in ambiguity
Of every 10
people who take
fluoxetine, three
to five will
experience a
sexual problem
Better Representation
Specify the reference class
Use frequency statement
OR

4. The probability that a woman has
a breast cancer 0.8%.
If she has breast cancer, the
probability that a mammogram
will show a positive result is 90%.
If a woman does not have breast
cancer, the probability of a
positive result is 7%.
If a woman has a positive result,
what is the probability that she
actually has breast cancer?
8 out of 1000 women have breast
cancer.
Of these 8 women with breast
cancer, 7 will have a positive
result on mammography.
Of the 992 women who do not
have breast cancer, some 70 will
have a positive mammogram.
If a group of women have positive
mammograms, how many of them
actually have breast cancer?
sensitivityspecificity
positive
predictive
Conditional probabilities Natural frequencies
Presenting three conditional probabilities is likely
becoming a trouble for understanding the information
Natural frequencies refer only to the same class of
observation. Therefore, confusion could be
diminished.

5. Conditional probabilities VS natural frequencies
The doctors who were
given natural frequencies
tend to estimate more
precisely than those who
were given conditional
probabilities

6. Women aged over 50 years are
told that undergoing
mammography screening reduces
their risk of dying from breast
cancer by 25%
Women in high risk groups are told
that bilateral prophylactic
mastectomy reduces their risk of
dying from breast cancer by 80%
Of 1000 who DO NOT undergo
mammography 4 will die from
breast cancer
Of 1000 who DO mammography, 3
will die from breast cancer
Of 100 who DO NOT undergo
mastectomy, 5 will die from breast
cancer
Of 100 who DO mastectomy, 1 will
die from breast cancer
Absolute risks reduction
People tend to misunderstand the relative risks like
(for the 1st case), of 1000 who do the test, 25% will
save and 75% others will die from breast cancer

7. Confusing Factors and
How to Avoid it
For each case of confusing numerical
representation, misunderstanding of
the reference class always exists
Clarify the reference class first.
OR
Use transparent representations like
natural frequencies
Negative framing (negative-oriented
information) tend to worry the
patients very much and negate to
undertake the treatment
Use negative frame for communicating
clinical risk that the patient might still
choose whether to take or not
Use positive frame to persuade patient
for risky treatment
The use of verbal explanation tend
to confuse the patients
Manipulate the way of representing
statistical information.
The use of pictorial representation or
chart might be helpful for patients to
understand the information

8. Strength Weakness
The article is well structured,
completed with examples, and
charts
The important point are
highlighted, so people will not
loose the content
Less explanation of the example
given. So it becomes less readable
for people who are not familiar with
the terms
No explanation why statistical
innumeracy is ignored (whereas in
the beginning they it is given as a
problem)
Thank you very much for
your attention