Data Analysis

# Data Analysis
## in the context of wildlife ecology and management
### Joe Thorley Ph.D. R.P.Bio.
### 2018-10-29

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# Introduction

In this talk we will cover

- What Data Analysis is

- What Uncertainty is

- What Data are

- What Statistical Models are

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# What is Data Analysis?

Data analysis is about

- reducing uncertainty (question)

- using information (observations/measurements -> data)

- given assumed relationships (model)

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# Uncertainties in Wildlife Management

The main uncertainties are

- How many individuals are there?

- How are they distributed through space?

- How are they changing through time?

- What factors are responsible for the distribution/changes?

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Factors can be environmental and anthropogenic.

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# Uncertainty is measured using Probability

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# A tossed coin

- What is the probability of a heads before I toss the coin?

- What is the probability after I toss it but before I look at it?

- What is the probability after I look at it but before I tell you?

- What is the probability after I tell you its tails?

- What is the probability if I then tell you I was lying and its heads?

- What is the probability if I'm willing to bet you $10 its heads?

- Are you willing to accept odds of 10:1?

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# PROBABILITY DOES NOT EXIST

De Finetti (1970) Theory of Probability

- Probability is a measure of **your** uncertainty about the possible states of the world.

![](18-analysis_files/figure-html/unnamed-chunk-5-1.svg)

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# How many bison are there?

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![](18-analysis_files/figure-html/unnamed-chunk-6-1.svg)

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# Information reduces uncertainty

- How much information is conveyed by being shown a coin is heads?

`$$-\log_2(1/2) = 1\ \text{bit}$$`

- How much information is conveyed by being shown a two headed coin is heads?

`$$-\log_2(1/1) = 0\ \text{bits}$$`

- What about a random number generator?

It depends on the number of possible values.

If there are 256 possible values then

`$$-\log_2(1/256) = 8\ \text{bits} = 1\ \text{byte}$$`

It also depends on the generator...

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![](http://assets.amuniversal.com/321a39e06d6401301d80001dd8b71c47)

Not all generators are created equal!

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## Data is Coded Information

> At easter about an hour after midday I was walking by the river and I saw a female bison, and another female behind it and another male one behind it. I went back at sunset but didn't see anything.

"04/01/18 1:05 two female and one male bison 44.4280 N 110.5885 W"

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## Data is machine-readable

<div id="htmlwidget-118692f3c5f25affad3d" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-118692f3c5f25affad3d">{"x":{"filter":"none","fillContainer":false,"data":[["1","2"],["male","female"],[2,1],["JLT","JT"],["2018-01-04","2018-01-04"],["01:05:00","01:05:00"],[110.5885,110.5885],[44.428,44.428]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>Sex<\/th>\n      <th>Count<\/th>\n      <th>Obs<\/th>\n      <th>Date<\/th>\n      <th>Time<\/th>\n      <th>Long<\/th>\n      <th>Lat<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"pageLength":8,"columnDefs":[{"className":"dt-right","targets":[2,6,7]},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[8,10,25,50,100]}},"evals":[],"jsHooks":[]}</script>

This dataset has at least five problems!
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- Numbers are mispunched
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- Two different observers
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- 4th of January
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- Just after middnight
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- In the Gobi Desert
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- Missing zero count!
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- Didn't record whether calves!
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- I am not trained to sex bison!

*80% of data analysis is data cleansing and tidying!!*
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## Data should be stored in relational databases

<div id="htmlwidget-ce0422a812407e6617b4" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-ce0422a812407e6617b4">{"x":{"filter":"none","fillContainer":false,"data":[["1","2"],["male","female"],["adult","adult"],[1,2],[1,1]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>Sex<\/th>\n      <th>Stage<\/th>\n      <th>Count<\/th>\n      <th>Visit<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"pageLength":8,"columnDefs":[{"className":"dt-right","targets":[3,4]},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[8,10,25,50,100]}},"evals":[],"jsHooks":[]}</script>

<div id="htmlwidget-1f5413bf16de7f43d1c1" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-1f5413bf16de7f43d1c1">{"x":{"filter":"none","fillContainer":false,"data":[["1","2"],[1,2],["JT","JT"],["2018-04-01","2018-04-01"],["13:05:00","18:10:00"],[-110.5885,-110.5885],[44.428,44.428]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>Visit<\/th>\n      <th>Obs<\/th>\n      <th>Date<\/th>\n      <th>Time<\/th>\n      <th>Longitude<\/th>\n      <th>Latitude<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"pageLength":8,"columnDefs":[{"className":"dt-right","targets":[1,5,6]},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[8,10,25,50,100]}},"evals":[],"jsHooks":[]}</script>

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# What are we able/willing to assume?

- All individuals were at the river at middday on April 1st and observer efficiency is 100%?

Then there are 3 bison!

- Bison are distributed randomly/evenly throughout their range?

- Bison groups spend 50% of their time near water?

- Bison aggregate in groups of 3 to 10 individuals?

- Observer efficiency is 50%?

- Observer efficiency varies between 40% and 60%?

A model is one or more relationships.

Such relationships can be certain or uncertain.
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# All models are wrong
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# All models are wrong (but some are useful)

> The map is not the territory

Alfred Korzybski

> Everything simple is false. Everything which is complex is unusable.

Paul Valery

> There is no such thing as an absolutely True thought.

Steven Gray

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# Confidence/Credible Intervals

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Uncertainty can be summarized using confidence/credible intervals.

![](18-analysis_files/figure-html/unnamed-chunk-13-1.svg)

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Uncertainty is typically represented on the y-axis.

![](18-analysis_files/figure-html/unnamed-chunk-14-1.svg)

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# Statistical Significance

Significance is often used to test whether a factor has an effect.

![](18-analysis_files/figure-html/unnamed-chunk-15-1.svg)

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# Significance is not Importance!

![](18-analysis_files/figure-html/unnamed-chunk-16-1.svg)

With no data all effects are insignificant!

With infinite data all effects are significant!
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# Report Effect Sizes

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# Summary

- Uncertainty is personal

- Clean and tidy data is essential

- Models are inescapable

- Effect sizes are needed for decision-making

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# Thanks!

For more information see