240 8 Logic, Reason Central Tendency

8/19/2019 240 8 Logic, Reason Central Tendency

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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

240 8 Logic, Reason Central Tendency

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