PHIL2420 Lecture Notes - Lecture 7: Ronald Fisher, Rare Disease, Daniel Kahneman
1 Jun 2018
School
Department
Course
Professor
PHIL 2420
Critical Thinking
April 26, 2018
WEEK 7
How to Lie with Statistics
Inspiration – How to Lie with Statistics by Darrel Huff, 1954
Or… how to get the wrong idea
HIV
• Suppose you test positive
• The test is 99% accurate
• What are the odds you actually have HIV?
o Not as bad as you think
o Depends on how common HIV+ is
o Currently, rate is 1:1000 in Australia
False negatives kill you.
Type 1 & Type 2 error
1. False positive
a. Alarm goes off but there is no danger. False alarm.
b. Boy who cried wolf
2. False negative
a. Alarm fails to go off but there is danger. Faulty alarm.
HIV Test
for 100,000
people total
Reality (1:1000)
HIV+
HIV-
Total
Test
99% accurate
+
99
True Positive
Correct
999
False Positive
Type I error
1098
Diagnosed HIV+
-
1
False Negative
Type II error
98,901
True Negative
Correct
98,902
Total
100
99,900
100,000
• 1 in 1000 is HIV+
o So… total of HIV+ column = 100, total of HIV- column = 99,9900
• Test is 99% accurate
o 99 / 100 (100x.99) will be accurately diagnosed positive
o HIV+ column will be as shown
find more resources at oneclass.com
find more resources at oneclass.com
o 999 / 99,990 (99900x.99) will be accurately diagnosed as negative
o HIV- column will be as shown
• Total diagnosed HIV+
o = 99 + 999
o = 1098
• The ratio of number truly diagnosed positive (99) to the total diagnosed positive
91098) is 99 / 1098
o 99 / 1098 is a little less than 0.0902
• Odds of actually being HIV+ by a 99% accurate test is only about 9%
• Total of the HIV- row is 98,902
o 98901 / 98902 > 0.999
o If you are diagnosed HIV-, there is nearly a 100% chance you are HIV-
• Totals should add up to 100,000
Keep in Mind
• Rare VS Serious
o Picked a rare disease
o The rarity of the disease is the relevant issue
o We not really care about rare trivial diseases
• False (+) / False (-) asymmetry
o Typical tests have different rates for false positive and false negative
o It does not affect the main message
Take Home Lesson 1
The odds of the person actually having a disease she is diagnosed with depends
on the accuracy of the diagnosis and how common the disease is.
• Surveyed doctors, 90% don’t know about the chart
Why bother testing?
• To find out you’re off the hook
• Odds of testing positive twice
o Test again with the same test
Sensitivity and Selectivity
• More sensitive test – less likely to yield false negative
o Better for serious conditions
• More selective test – less likely to yield false positive
o Better if conditions require dangerous/expensive treatment (surgery)
Conditional Probability
• Odds of A given B
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Inspiration (cid:1688)how to lie with statistics(cid:1689) by darrel huff, 1954. Hiv: suppose you test positive, the test is 99% accurate, what are the odds you actually have hiv, not as bad as you think, depends on how common hiv+ is, currently, rate is 1:1000 in australia. Type 1 & type 2 error: false positive, alarm goes off but there is no danger. False alarm: boy who cried wolf, false negative, alarm fails to go off but there is danger. Total: 1 in 1000 is hiv, test is 99% accurate. If you are diagnosed hiv-, there is nearly a 100% chance you are hiv- The odds of the person actually having a disease she is diagnosed with depends on the accuracy of the diagnosis and how common the disease is: surveyed doctors, 90% don"t know about the chart. Why bother testing: to find out you"re off the hook, odds of testing positive twice, test again with the same test.
