PHIL2420 Lecture Notes - Lecture 6: Fallacy, Mesothelioma, Standard Deviation
1 Jun 2018
School
Department
Course
Professor
PHIL 2420
Critical Thinking
April 19, 2018
WEEK 6
Probability & Statistical Inference
Statistical Reasoning
The rule of statistical inference enable us to evaluate how likely data is to reflect
reality.
Probability – statistical reasoning is based on an analysis of the probabilities of random
events
Random process
• Small correlation with where coin starts and ends up
• We’re biased a little bit
• Real randomness may not really exist
Coin toss
• How likely to be all heads?
o 1 coin – 50%, or 1:2
o 2 coins – 25%, or 1:4
Typical tosses
• 10 coins – 4, 4, 5, 6, 5, 4, 3 . . .
• 100 coins – 46, 54, 48, 45 . . .
• 1000 coins – 486, 501, 489, 537 . . .
Law of Large Numbers
• The larger the number of flips, the less likely that the proportion of heads will be
far from 50%
• John Kerrich’s Experiment – 5067/1000 heads
• When number gets bigger, proportion of heads to tails gets smaller
Cancer statistics
• Is NT safer than NSW?
• NT – 700 cases / year
• NSW – 40,000 cases / year
• 55 cases in NT make them equal
• It takes 3200 cases in NSW
Take Home Lesson 1
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Be careful when comparing statistics from samples of different sizes. Statistics of
small populations are more sensitive to random fluctuations.
Law of Averages
Deviation of 50/50 goes down the more you try to flip the coin
• Given 8 heads in a row, what is likelihood that next toss will be heads?
• 50%
• It is tempting to believe that after observing a run of 8 or 10 or 100 heads that the
next throw will INEVITABLY (or most likely) be tails
Independence of Events
The coin has NO MEMORY of how it landed in the past.
Gambler’s Fallacy / Take Home Lesson 2
There is no Law of Averages.
Common Sense
1. Tails must be slightly more likely, in order to correct the existing imbalance
2. Each throw is independent
What makes all those trials converge on 50/50 in the long run?
Dilution of the Unlikely
• The law of large numbers works not by balancing out prior unlikely outcomes
• It is by diluting their effect on the average in the long term
• EXAMPLE
o A run of 8 heads does not make tails more likely
o 8 heads in a row becomes less important when we flip the coin 8008 times
o the results of a run of 8 heads will be diluted as more tosses are made
How large is large?
• LOLN – The more flips, the less likely the proportion of heads will be far from
50%
• What is the relationship between the number of flips and discrepancy from
expectation
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