assessing the effect of visualizations on bayesian reasoning through crowdsourcing
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Assessing the Effect of Visualizations on Bayesian Reasoning through Crowdsourcing
Jean-Daniel Fekete
Pierre Dragicevic
Luana Micallef
0% - 30% 30% - 60% 60% - 100%
The probability that a woman at age 40 has breast cancer is 1%.
The probability that the disease is detected by a mammography is 80%.
The probability that the test misdetects the disease although the patient does not have it is 9.6%.
If a woman at age 40 is tested as positive, what is the probability that she indeed has breast cancer?
ATTENTION
The probability that a woman at age 40 has breast cancer is 1%.
The probability that the disease is detected by a mammography is 80%.
The probability that the test misdetects the disease although the patient does not have it is 9.6%.
If a woman at age 40 is tested as positive, what is the probability that she indeed has breast cancer?
0% - 30% 30% - 60% 60% - 100%
The probability that a woman at age 40 has breast cancer is 1%.
The probability that the disease is detected by a mammography is 80%.
The probability that the test misdetects the disease although the patient does not have it is 9.6%.
If a woman at age 40 is tested as positive, what is the probability that she indeed has breast cancer?
0% - 30% 30% - 60% 60% - 100%
7.8%P ( Cancer | Positive Mammography ) =
95 doctors out of 100
said the answer is between 70% to 80%
Why the correct answer is so low
P ( cancer | +ve mammography )
=
P ( +ve mammography | cancer)
P (+ve mammography | cancer) + P (+ve mammography | cancer)
Bayes’ Theorem
women without cancer
women with cancer
The probability that a woman at age 40 has breast cancer is 1%.
women without cancer
women with cancer
The probability that the disease is detected by a mammography is 80%.
The probability that the test misdetects the disease although the patient does not have it is 9.6%.
If a woman at age 40 is tested as positive, what is the probability that she indeed has breast cancer?
7.8%
Can such visualizations facilitate Bayesian reasoning
Proposed Visualizations
contingency table
bar-grain boxes Bayesian boxes trees
signal detection curves
Euler diagram frequency grid
+
Euler diagram + glyphs
Previous Studies
Mainly in Psychology
Claim that
Bayesian problem representation impacts comprehension
but …
Inconsistent findings
Most effective Bayesian problem representation? UNCLEAR
Inconsistent and sometimes inappropriate diagram designs
Diagrams do not match textual information
(Sloman et al., 2003)
Area-Proportional Not Area-Proportional
and the subjects …
Specific background usually highly-focused university students
Specific age group
Sometimes,
specific department
carried out as part of their course
so … cannot generalize their findings to
a more diverse population of laypeople
Our Work
Assessing the Effect of Visualizations on Bayesian Reasoning through Crowdsourcing
to identify…
- the most effective visualization for the crowd
- whether hybrid visualizations are helpful
- the link between the visualizations and different spatial and numeracy abilities
but…
how appropriate is
Amazon MTurk
Used and evaluated for research and InfoVis
Demographics of workers are well-understood
Captures aspects of real-world problem solving better
- a large diverse population with different backgrounds, education, occupations, age, gender
- workers carry out tasks rapidly but accurately to improve their rating
- reduces experimental biases, as demand characteristics
http://www.eulerdiagrams.org/eulerGlyphs
Experiment
168 workers with MTurk approval rate ≥ 95%
Demographics
25 min
$1
3 Bayesian problemsclassics in Psychology
in natural frequencies format
followed by
objective and subjective numeracy tests
paper folding spatial abilities test
brief questionnaire
Results
We failed to replicate previous findings
subjects’ accuracy was remarkably lower
visualizations exhibited no measurable benefit
even though …
reasonably confident with their answer
overall
12% exact answers
6%
no visualization
14% 11% 11%
21% 7% 14% 21%
no vis V0
V1
V2
V3
V4
V5
V6Answer errors for all three Bayesian problems combined
per visualization type (N = 24 each)
21% exact
6% exact
12% 40% - 80%our study
exact answers
previous studies
Thus
we failed to demonstrate measurable
benefits from visualizations to
facilitate Bayesian reasoning.
Qualitative Feedback
53 out of the 168 subjects
participated
89% ‘somehow’ used the diagram
Most found the diagram very useful
BUT
Various did not understand the diagram
Some doubted the diagram’s credibility
However
must understand and trust the diagram
the answer is in the visualization
women without cancer
women with cancer
The probability that the disease is detected by a mammography is 80%.The probability that the test misdetects the disease although the patient does not have it is 9.6%.If a woman at age 40 is tested as positive, what is the probability that she indeed has breast cancer?
7.8%
How
either
help them understand and relate the diagram to the text
or
force them to get the answer from the diagram
change the text
Another Experiment
480 workers with MTurk approval rate ≥ 95%
did not participate in experiment 1
1 Bayesian problemthe Mammography problem
10 out of every women at age forty who participate in routine screening have breast cancer.
8 of every 10 women with breast cancer will get a positive mammography.
95 out of every 990 women without breast cancer will also get a positive mammography.
classic
10 out of every women at age forty who participate in routine screening have breast cancer (compare the red dots in the diagram below with the total number of dots).
8 of every 10 women with breast cancer will get a positive mammography (compare the red dots that have a black border with the total number of red dots).
95 out of every 990 women without breast cancer will also get a positive mammography (compare the blue dots that have a black border with the total number of blue dots).
with instructions
10 out of every women at age forty who participate in routine screening have breast cancer.
8 of every 10 women with breast cancer will get a positive mammography.
95 out of every 990 women without breast cancer will also get a positive mammography.
without numbers
A small minority of women at age forty who participate in routine screening have breast cancer.
A large proportion of women with breast cancer will get a positive mammography.
A small proportion of women without breast cancer will also get a positive mammography.
without numbers
10 out of every women at age forty who participate in routine screening have breast cancer.
8 of every 10 women with breast cancer will get a positive mammography.
95 out of every 990 women without breast cancer will also get a positive mammography.
classic
Results
The Most Effective Textual Representation
A small minority of women at age forty who participate in routine screening have breast cancer.
A large proportion of women with breast cancer will get a positive mammography.
A small proportion of women without breast cancer will also get a positive mammography.
without numbers
exact answers
+no visualization
3.3% exact answers
classic text
+5% exact answers
classic text
5% exact answers
+
text with instructions
1 exact answer (N=120)
+
text without numbers
Answer errors for the Mammography Bayesian problemper presentation type (N = 120 each)
classic + no vis
classic + vis
with instructions + vis
without numbers + vis
Conclusion
Using crowdsourcing, we assessed
6 visualizations and text alone for
3 classic Bayesian problems
We failed to replicate previous findings
subjects’ accuracy was remarkably lower
visualizations exhibited no measurable benefit
A follow-up experiment confirmed …
simply adding a visualization to a textual Bayesian
problem does not help
diagrams can help but numerical values have to be removed and the text should be used to merely set the scene
We need …
novel visualization that holistically combine
text and visualization and promote the use of estimation rather than calculation
more studies in settings that better capture real-life rapid decision making
To …
facilitate reasoning of statistical information
for both layman and professionals
ThanksJean-Daniel
FeketePierre
DragicevicLuana Micallef
error = log10answergiven
answerexpected
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