Transcript Pathophysiology of Disease * USSJT7-30-1

Practice & Communication of Science
Measurement
@UWE_KAR
What is Measurement?
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Assigning comparative labels to things to help
explain their relationships…
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sounds a bit abstract…
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…but things/relationships is all there is…
…and that’s all that science is about!
so measurement is rather central to science
Measurements are typically, but not exclusively,
numerical
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not all types of measurement are equivalent
four different levels of measurement
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nominal, ordinal, interval and ratio
Nominal Scales
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The ‘lowest’ level of measurement
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nominal implies ‘names’
Just labels to stick things into categories and
separate them
No implicit order
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eg yes/no
shirt numbers of footballers
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1 – goalie, 10 – striker (but not ‘10x better’!)
can serve to separate and provide some info
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if refer to #10, it’s likely to be about a striker not a
goalie
blue, yellow, red, green etc
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no implicit order (though underlying spectrum has)
Ordinal Scales
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The measurements can be ‘ordered’ (ranked)
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the order of finishers in a race (first, second, etc)
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but time between each can vary dramatically
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equal gaps not implied
the Likert scale (1  5)
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agree strongly, agree, neutral, disagree, disagree
strongly
again, the ‘gaps’ between each are not equal
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agree - neutral doesn’t ‘equal’ neutral - disagree
Interval Scales
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The ‘gaps’ (intervals) between units of
measurement are equal
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the Centigrade scale
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the temp difference between 20 and 30 C is the
same as between 10 and 20 C
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there is no absolute reference point
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0 C is arbitrary
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though they might not ‘feel’ that way!
water’s freezing point used to define the baseline
Much more common in science
Ratio Scales
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An interval scale that has an absolute reference
point
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the Kelvin temperature scale
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for our everyday lives, time is a ratio scale
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0 K is -273.16 C
the reference point is absolute
absolute zero (0 K) is, well, absolute!
zero time is absolute
like interval scales, ratio scales common in science
These measurement scales are important as
they determine the types of datahandling/statistics that can be performed
Summaries of Data
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Scientists seldom take single measurements
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need repeated measurements to…
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minimise error
permit extrapolation to the general case
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eg my eyes are blue
32 out of 100 subjects studied had blue eyes
32% of the general population have blue eyes
Data is plural (datum is singular)
Could just report all measurements…
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contains unadulterated ‘info’ about what you did
but doesn’t carry a ‘message’ about the findings
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can’t see the wood for the trees
Summaries of Data
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Here is a set of ordered data…
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Mode
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the central value in the ordered data (19)
Mean
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the most common value(s) of a list of data (18)
Median
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17, 18, 18, 18, 19, 19, 20 21, 21
sum of values/sample size (171 / 9 = 19)
Range (or maybe Maximum and Minimum)
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highest minus lowest (21 – 17 = 4)
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starts to indicate variability, but biased by extremes
Indicating Variability
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This is an important aspect of measurement
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Need a way to summarise data both in terms of
‘central tendency’ and ‘spread’
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17, 18, 18, 18, 19, 19, 20 21, 21 and
18, 19, 19, 19, 19, 19, 19, 19, 20 and
19, 19, 19, 19, 19, 19, 19, 19, 19
all have the same mean
mean and standard deviation
median and quartiles
Measures of variation covered in detail
elsewhere
Summary
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Measurements are labels assigned to things
to explain relationships
Four levels…
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Nominal – names; no inherent order
Ordinal – ordered; ‘gaps’ not equal
Interval – ordered; ‘gaps’ are equal
Ratio – ordered; equal gaps; absolute ref point
Summaries of data needed to ease
interpretation – eg mode, mean, median, range
Need indicators of ‘spread’ as well as ‘centre’
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eg range, max, min, standard deviation
Practice & Communication of Science
Probability
@UWE_KAR
What is Probability?
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We cannot know everything about everything
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So uncertainty is a central feature of science
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uncertainty in observations/measurements 
uncertainty in explanations 
uncertainty in predictions
Probability is a way of quantifying (un)certainty
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we cannot measure everything
our measurements are prone to error
scale of 0  1 (or 0%  100%)
Probability reflects random influences
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‘randomness’ reflects our lack of knowledge
Randomness  Predictable Rules
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Individual outcomes cannot be predicted, but
repeated runs are very predictable
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eg individual coin-toss  H or T
‘infinite’ repeats  50:50 H:T (if fair)
Modelling a system in terms of probabilities can
be done through observation or from theory
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Throwing dice
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theory
Red vs Blue in sport
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observation
(Hill & Barton)
Frequencies and Probabilities
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Red and Blue football teams
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in 140 matches, Red won 60 and drew 30
relative frequency = 60/140
probability of red winning (in the future) is also
60/140 = 0.429
For throwing a die
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relative frequency of getting a ‘3’ is 1/6
probability is also 1/6 = 0.167
Combining Probabilities
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For independent events, eg probability of
throwing a five and then a two
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multiply the individual probabilities
P(A and B) = P(A) x P(B)
eg 1/6 x 1/6 = 1/36 = 0.028
For incompatible events, eg probability of
throwing a five or a two
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add the individual probabilities
P(A or B) = P(A) + P(B)
eg 1/6 + 1/6 = 1/3 = 0.333
Probability and common sense
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In playing the lottery, which choice of numbers
is more likely to win?
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I won the lottery last week; the chances of me
winning the lottery this week are…
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3, 5, 15, 27, 29, 44
1, 2, 3, 4, 5, 6
less, the same, greater?
I won the lottery last week; the chances of me
winning the lottery twice in a row are…
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less, the same, greater?
Probability and common sense
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What are the chances of two people on a
football field sharing the same birthday?
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For 23 people, prob of not sharing b’day with
previously considered people is…
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1%, 11%, 21%, 31%, 41%, 51%
person 1 : 365/365
person 2 : 364/365
…
person 23 (includes ref!) : 343/365
Multiply them all together  0.493
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1 – 0.493 = 0.507 = 51%
Probability and common sense
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Linda is thirty-one, single, outspoken and very
bright
She studied political science at Uni; she was
concerned with discrimination and social
justice, and took part in CND demonstrations
Which of the following statements about Linda
is more likely?
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Linda works as an estate agent
Linda works as an estate agent and is active in the
feminist movement
Probability is context-sensitive
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In tossing a coin ten times, which sequence is
most probable?
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HTTHHTHTHT
HHHHHHHHHH
In coin-tossing, which sequence is more
probable?
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A mix of heads and tails
10 heads in a row
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1 in 1024
Probability is context-sensitive
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Derren Brown can toss a coin heads 10x in a
row
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Incredible motor control over ‘random’ variables?
Probability can be counter-intuitive
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Flip a coin three times to get HH or HT
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Are the two outcomes equally probable?
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HHH  HH first
HHT  HH first
HTH  TH first
HTT
TTT
TTH  TH first
THT  TH first
THH  TH first
Probability can be counter-intuitive
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Defendant’s DNA match was 1 in 1 billion
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Lab’s false positive error rate (not disclosed) is 1%
What is the probability of the defendant being
falsely convicted on that evidence?
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1
1
1
1
in 1 billion
billion x 1% = 1 in 10 million
billion x 99% = 1 in 990,000,000
in 100.000000001
Probability can be counter-intuitive
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The Monty Hall conundrum
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You are on a game show
You have a choice of three doors
Behind one is a car, behind other two are goats
You choose a door
The host (who knows where the goats are) opens
one to show you a goat
Should you now change the door you have chosen?
Probability can be counter-intuitive
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A mother gives birth to twins (not identical)
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What is the chance they will be of different sexes?
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25%
33%
50%
A mother gives birth to twins (not identical)
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One is a girl
What is the chance that they will both be girls?
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25%
33%
50%
Conditional Probability
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Previous questions not conditional/conditional…
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What is the chance that they will both be girls?
Cond - A mum gives birth to twins (not identical).
What is the chance that they will both be girls if
one is a girl?
The if clause makes all the difference
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Not con - A mum gives birth to twins (not identical).
It provides extra information that alters the odds
The influence of additional info on odds was
developed by Thomas Bayes (b 1702)
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Bayesian odds
Prior prob (1 in 4) and posterior prob (1 in 3)
Three variations on a theme…
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A family has two children; what are the
chances that both children are girls?
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A family has two children; what are the
chances that both children are girls if one is a
girl?
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1 in 4, 1 in 3, 1 in 2?
1 in 4, 1 in 3, 1 in 2?
A family has two children; what are the
chances that both children are girls, if one is a
girl (called Florida, btw)?
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1 in 4, 1 in 3, 1 in 2?
Three variations on a theme…
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2 children; P that both children are girls?
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2 children; P both girls if one is a girl?
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GB, BG, BB, GG
1 in 4
GB, BG, BB, GG
1 in 3
2 children; P both girls if 1 girl named Florida?
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BB,BGF,BGNF,GFB,GNFB,GFGNF,GNFGF,GNFGNF,GFGF
BB,BGF,BGNF,GFB,GNFB,GFGNF,GNFGF,GNFGNF,GFGF
1 in 2
Conspiracy Theories and Probability
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Are these equivalent?
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1) The P of a series of events happening if due to a
huge conspiracy
2) The P of a huge conspiracy existing if a series of
events happened
P of 1) > P of 2)
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a ‘single’ explanation vs ‘many’ other explanations
think 9/11, moon landings, paranoia, confabulation
Bayes’ theory supports this noncorrespondence
Conditional Probability and Testing
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A test for disease ‘X’ comes back positive
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But. Is…
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the chance of not having the disease if I tested
positive
…the same as…
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And the false-positive rate is low at only 1 in 1000
Only a 0.1% chance of not having the disease?! 
the chance of testing positive if I didn’t have the
disease? (1 in 1000)
No. Think of the ‘sample space’
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‘categories’ of people tested
The Test’s Sample Space
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1) tested +ve and have ‘X’ (true positives)
2) tested +ve put don’t have ‘X’ (false positive)
3) tested –ve and don’t have ‘X’ (true negative)
4) tested –ve and have ‘X’ (false negatives)
Reported false positive rate is 1 in 1000
Incidence rate: say 1 in 10,000 tested have the
disease (and false neg effectively 0)
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incidence rate not usually mentioned/considered
For 10,000 tested, there will be 10 false
positives and only 1 true positive
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so 10/11 chance of not having the disease!
Summary
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Probability estimates the odds of future events based
on theory or observation
Probability cannot predict an individual event
Probability can predict pattern of events
Probability, P, 0  1 or 0%  100%
Probability is often not ‘intuitive’, it fools us
Combining probabilities
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Independent events: p(A and B) = p(A) x p(B)
Incompatible events: p(A or B) = p(A) + p(B)
Conditional probabilities (prob of A if B)
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Baysian probability
Prior probability + extra info  posterior probabilities
prob of A if B often different to prob of B if A