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Reading Week!
This Thursday regular lectureSpring Break next week (8-12)Monday 15th – Leap Class / Drop in Q&A
Thursday 18th – Midterm in class
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The veracity of evidence is independent
of the magnitude of your belief in it
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Strongly Held Beliefs ! Facts
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Jim Inhofe (R-OK) Brings A Snowball To Te US
Senate Floor To Prove Climate Change Is A 'Hoax'
Feb 26 2015
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Gary Goodyear Secretary of State
for Science and Technology 2008-2013
When asked whether
there was a conflict
with someone with his
portfolio being a
creationist, he
responded: "Absolutely
not. How ridiculous. It's
absolutely ridiculous.
That's why I didn't
answer the question —
because it has norelevance."
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Common sense: basic ability to perceive,
understand, and judge things, common to nearly
all people and can reasonably be expected ofnearly all people without any need for debate
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The case against common sense:
“Think about how stupid
the average person is;
Now realize that half of
them are dumber thanthat ! “George Carlin
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Take a fair coin (H 50% - T 50%) —and flip it four times. How often was
heads followed by another head?
In the sequence HHHT, for example,
that happened two out of three times
— a score of about 67%.
For HHTH or HHTT, the score is 50%
" and so on ...
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There are 16 equally
possible outcomes
Calculate for eachsequence the odds of H
followed by H
Average the results
The answer is not
50-50, but 40.5% — in
favor of tails.
So much for common
sense.
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Joseph HeathPhilosophy – U of Toronto
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Evidence:Factual knowledge or data that supports or
casts doubt on a hypothesis.
Empirical Evidence:is a collective term for the knowledge orsource of knowledge acquired by means of
the senses, particularly by observation and
experimentation.
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Evidence:Factual knowledge or data that supports or
casts doubt on a hypothesis.
Empirical Evidence:is a collective term for the knowledge orsource of knowledge acquired by means of
the senses, particularly by observation and
experimentation.
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Only the
human brain
candeliberately
change
perceptions,change
patterns,
inventconcepts, and
tolerate
ambiguity .Edward de Bono
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~40% of Americans believe earthquakes, floods and
other natural events including climate chance are
god’s will "
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Funny things happen when perception is not questioned, patternsare changed and concepts are invented with willful ignorance of
ambiguity
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Aweful things happen when perception is not
questioned, patterns are changed and concepts
are invented with willful ignorance of ambiguity
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Ecology (like all thesciences) is the
search for patterns…
… their causes and
effects
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“ ! when you can measure what you are
speaking about, and express it in
numbers, you know something about it;but when you cannot measure it, when
you cannot express it in numbers,
your knowledge is of a meagre and
unsatifactory kind; it may be the begining
of knowledge, but you have scarcely in
your thoughts advanced to the stage ofscience, whatever the matter may be.”
Lord Kelvin
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Google “ecologist” and look under images".
What activity is common to most images?
MEASUREMENT
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Living off grid in the woods alone
but paying taxes exceeds youreco-footprint “share”
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Warped map of predicted
magnitude of climate change
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"(well, you might) but everyoneelse must use data "
Data analysis extracts informationfrom measurements while dealing
with uncertainty in measurements
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Organizing an [ecological] study
•
What is the aim of the study?
•
What is the main question being asked?
• What are your hypotheses?
•
Define your predictions
•
Collect data (observing the Golden Rule)
•
Summarize data in tables
•
Present data graphically•
Statistically test your predictions
•
Analyze the statistical results
•
Present a conclusion to the proposed question
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BasicTerminology
Variables
Populations
Samples
Parameters
Statistics
Nikki Heim collecting grizzly bear fur sample
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How do human
activities affect
abundance anddistribution of
cryptic predators like
wolverines?
Nikki Heim baiting camera trap line
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What is a variable?
Variable: any defined characteristic that variesfrom one biological entity to another.
Ryan Popowich – winter bull trout survey
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Examples of a variable:Plant height, bird weight, human eye colour, number of fish
species"
etc"
etc"
Samples are selected randomly from a population
If several individuals are selected, their characteristics may bevery similar or very different.
Chris Williamson collecting farm escaped Atlantic salmon in a Vancouver Island river.
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What is apopulation?
Population:the entire
collection ofentities we
are interested
in.
Helen Ford clearing experimental oyster sets
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Corey Peet sampling lice loads on
adult Pacific salmon
Examples
Lice load on
salmon
Populationdistribution &
abundance(like your bird surveys)
Species diversity
in ocean habitats
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What is the relationship
between lice loads on
wild salmon and salmon
farms?
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Marty Krkosek sampling liceload on juvenile migratory
salmon
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What is a sample?Sample: asubsets of thepopulation
beingmeasured andused toestimate thedistribution of
the variable within the true population
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We “sampled” alot of oysters"
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What is a parameter?
Parameter :any calculated
measure used
to describe or
characterize a
population
For example, thepopulation mean is
the single, fixed
value parameter
that indicates the
average value of a
variable within the
population.
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Can we characterize the entire reef?
No, therefore must sample"
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What is a statistic?
Statistic: the estimated population parameter
Population of Interest
Sample
Population Sample
Parameter Statistic
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…this is bad… why?
PopulationSample
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…this is VERY bad…
Population
Sample
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…or this VERY good…
PopulationSample
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…or this ?
Population
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…or this ?
Population
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…or this ?
Population
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…or this ?
Population
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In an experiment we take a sample of population. From thissample we infer characteristics about the population
Random: Are your data to be selected at random from the populationyou are studying?
Independent : Has every data point available got an equal chance ofbeing selected; each is independent from all others
The Golden Rules
Error is the difference between your measurement and the true valueThis is experimental or observational error, not inherent (
real
)
variability
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In your tutorial bird survey:What is the experimental unit of the experiment?Does your bird survey follow the Golden Rule? Why?
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Example: British birds and pubs
Samples neither random or independent
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Example: Nile Perch and net meshSamples not random
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If either rule is broken, results will be biased in one form oranother and your conclusions will surely be wrong.
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We have data!!First question: What kind?
1.Continuous variables These are variables that can
take the form of decimals.
Example. Weight, length, height, GPA.
2. Discrete (or discontinuous) variable These arevariables that can’t take the form of decimals.
Example: number of students, number of trees at a site
3. Categorical variable Used when data fit intocategories or classes
Example: Age class (egg, larva, pupa, adult)
Co D Co
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Wing length data?
Current speed?
Dog holes?# of prairie dog burrows?
Gut contents (i.e. food)?Tree respiration?
Banana slug colourmorphs?
Co D Co
Ca Co Ca
Co
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After we have collectedthe data and identifiedthe variable type wegenerate descriptivestatistics
i) Central Tendency
ii)
Variation
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Measures of Central Tendency:
Describe where the data points cluster.
• Mean
• Median
• Mode
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(aka MEAN
)
Frequency distribution ofthe monthly salary of 25workers…..
X
Mean now$2,760Median & Mode
largely unchanged
“The average salary at our company isgreater than all our competitors…
What drives large differences betweenmean, mode and median?
Mean homeprice in GreaterVictoria today is$637,853
Median $589,000
M d 82 50%
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Midterm I Frequency DistributionMode: 82.50%Median: 72.5%
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Why use statistics?
•
It is almost never possible to obtain measures and calculateparameters (the “real” value) of variables for the entirepopulation of interest
• Statistics allow us to estimate these values for the entire
population based on samples
• Statistics allow us to calculate the level of confidence in ourresults. (as a rule, the larger the number of samples, the closerthe statistic is to the parameter, and therefore the higher the
confidence)
• Statistics also allow us to efficiently compare populations todetermine differences among them (in time and/or space)
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Isle Royale National Park - Wolf - Moose Dynamics
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the linear equationy = slope(x)+intercept
y = mx+by = 1/3x + 0.14
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Sources of
VariationHow To
Deal With
Them".
Scatter plot of fish abundance as a function
of pothole size
Why are all points
not on the line?
R2=0.81
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Core elements of statistics
Data qualityIndependentRandom
Descriptive StatisticsClassification of VariablesMeans, Modes, MediansVariation in your sample
Analytical Procedure(aka Comparative Statistics )SignificancePowerT-test
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