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Outside learning via UVic Geography & QQS Projects Society

Geog 453 field school: Indigenous

Knowledge, Science & Resource

Management

Application deadline: extended to Feb 29

Applicants beyond UVic welcomed

 M a y 1 -  8,  2 01 6 

 Ko e y e  R i v e r   Q u e s t

 io n s ? 

d a r i mo n t @ u v ic.c

 a 

A p p l ic a t io n s o n

 

 U v ic  G eog  w e b s

 i t e 

C hr i s D ar i mo nt  –  U V i c  J e ss H o ust y  –  Q Q S  

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Very long lived (some spp>100 yrs)

Slow growing

Old age at maturity

Low r

Philopatric (don’t move)

Therefore very susceptibleto overfishing

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Rockfish Conservation Areas 

(RCAs) In Coastal British Columbia Waters

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Most surveys of rockfish are by

remote video camera or diver observation

Visibility in temperate waters not often

conducive! 

This would be an example of experimental

error   - missing fish that are present butyou cannot see them! 

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SCUBA Transect

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Baited Underwater Video

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RCA ReferenceSite

30m SCUBA & Towed Camera TransectsBUWV stations

Record every

individual fish:

• 

Species•

 

Size

• 

Immediate Habitat

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http://www.racerocks.ca/wp/administration-of-race-rocks/environmental-impacts-from-human-disturbances-to-life-at-race-rocks/illegal-fishing-in-the-rockfish-conservation-area-at-

race-rocks/

Poaching: The unknown variable

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Darienne LancasterBan Lab - ES

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RCA Efficacy

HO: Fish abundance inside and outside RCAs

is equivalent

Methodology

HO: SCUBA and BUWV yield similar estimates of

rockfish abundance

PoachingHO: RCA efficacy is independent of angler

non-compliance

Testing three hypotheses simultaneously

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High RCA Compliance

Medium RCA Compliance

Low RCA Compliance

Multiple paired sites

across compliance gradient:

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Dual Lights

Drop Line

Bait Arm(not shown)

Receptacle

Video Cable

Camera

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RCA

152020

25

3040

Reference

202025

30

3550

Total 150 180Mean 25 30

Variance 80 130StanDev 8.9 11.4

Rockfish Abundance (total # fish, all spp.)

VarianceRCA = s2RCA = (20-25)2 + (40-25)2 + (15-25)2 !. + (25-25)2 / (n-1)

= (25 + 225 + 100 + 25 + 25 + 0) / 5 = 80 individuals2 

Standard DeviationRCA = sRCA = "s2RCA = 8.9 individuals

What does this mean in English?

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LOTS MORE SURVEYS!.

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RCA

 Abundances 

25

If we assume our abundance data

to be normally distributed, we can make

some inferences! 

We expect ~2.5% of RCAsto have very large abundances(mean + (2SD)) or

(25 + 2(8.9)) = 43 fish or more

We expect ~2.5% of RCAsto have very low abundances(>mean - (2SD)) or

(>25 - 2(8.9)) = 7 fish or less

Since abundances are normally distributed wecan expect 95% of abundances to fall within

the mean +/- 2 standard deviations

7 43

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Reference

 Abundances

30

If we assume our abundance data

to be normally distributed, we can make

some inferences! 

We expect ~2.5% of non-RCAsto have very large abundances(mean + (2SD)) or

(30 + 2(11.4)) = 43 fish or more

We expect ~2.5% of non-RCAsto have very low abundances(>mean - (2SD)) or

(>25 - 2(11.4)) = 7 fish or less

We find the abundances arenormally distributed therefore we can

expect 95% of abundances to fall within

the mean +/- 2 standard deviations

7 53

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RCAs Reference Sites

25 30

There are more fish on average in the reference sites, but is the difference

of the means great enough to declare the difference statistically significant?

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 A

B

We want to know if the means are different enough to conclude a statistical difference

signal A difference between group means= = = Student’s t test

noise B variance of groups

The signal has to reach a threshold greater than the noise!this threshold for adifference to be considered significant is the p-value

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How do we determine when a difference

really is a difference?

Sir Ronald Fisher25 30

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The “p-value”

 A probability of 0.05 is just another way of sayingthe probability # 5%

Therefore if we adopt a p-value of 0.05 as the threshold

of significance, we are saying the difference we observewould occur less than 5% of the time if the populations

were really identical. We are willing to accept a 5%

chance of error.

!.or the probability that a difference as large as the one observed could haveoccurred by chance. The less likely this is, the lower the probability.

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Rockfish Abundance

SCUBA (+/- SD) BUWV (+/- SD) P-value

205 (9) 265 (4) 0.04*

RCA (+/- SD) REF (+/- SD) P-value65 (15) 70 (5) 0.01**

Poaching

RCAred (+/- SD) RCAgreen (+/- SD) P-value

180 (35) 200 (45) 0.12

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Misconception: The probability value is the probability thatthe null hypothesis is false. 

The p value is the probability of an observed result as extreme ormore so would be observed if the null hypothesis is true. Thereforeto claim a “scientific difference” exists p

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Type I errorThe error of rejecting a null hypothesis when there is no real

difference. In other words, it occurs when we observe a difference

when in truth there is none. "false positive": A false positive normally means that a test claims there to be

an effect when that is not the case.

For example, a pregnancy test with a positive result (pregnancy)

has produced a type I error if the woman is not pregnant.

Type II errorFailing to reject a null hypothesis when the alternative hypothesis

is the true state.

In other words, this is the error of failing to observe a differencewhen in truth there is one.

In the example of a pregnancy test, a type II error occurs if the

test reports negative when the woman is, in fact, pregnant."false negative":

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Two salmon, same age, same food, same environment.

Treatment: One is a “normal” salmon the other has been

genetically modified to increase growth rate.

Power to detect difference increases with effect size

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The power of a statistical test is the

probability that the test will [correctly]reject a false null hypothesis

In other words, if the differencebetween GM salmon and normal

salmon is real, the ability of our test to

detect that difference is its “power ”;The likelihood that Ho is correctly (in

this case) rejected.

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Statistical power is a measure of the likelihood that a researcher will findstatistical significance in a sample if the effect exists in the full population.

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 All other things being equal

which of the following increase power?

Increasing variation

Increasing sample size

Increasing acceptable error

Increasing the magnitude of

difference between means

! 

" 

! 

" 

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 Group A ("A") of five

animals given onegene and each

animal’s growth

monitored

(46,42,44,45,43)

(g / day)

Group B ("B") is given a different gene

(52,80,22,30,36) (g / day)

 A third set ("C") of five “normal” animals was used as controls;(i.e. no treatment) (20,23,24,19,24) (g / day).

The mean of the control group is 22 and the SD is 2.3Did treatment A have a significant effect? Did treatment B?

 An example – test of transgenes on growth

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95% Confidence Interval is the breadth of values needed to be sure the realparameter value (ex. population mean) is covered in 95 of 100 studies performed.

Is affected by i) sample size and ii) variation in the data

   G  r  o  w   t   h   (  g   /   d

  a  y   )

GM-A GM-B Control

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The graph shows the mean for each data set (red dots).The dark lines represent the 95% confidence limits.

 Although both experimental means (A and B) are twice as largeas the control mean, only the A diet produced significantly

different results. The probability that the real mean of B is thesame as the real mean of C is greater than 5%. Therefore we

cannot say B and C are significantly (aka “statistically” or

“scientifically”) different.

Confidence Interval:

 An estimated range of values

with a of known probability

(here 95%) of covering the

true population mean if the

experiment were run 100

times. If CIs overlap, the

populations from which

samples were drawn

are not considered different.

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rockfish)

rockfish)

rockfish)

 Are Reference sites different from RCAs? Use CIs to plot the magnitude of difference.If the CI for reference sites overlaps with “0” different (i.e. the 95% CI of the difference

between RCAs & Ref Site means includes “0”)

95CIs of mean rockfish abundance in Ref Sites relative to RCAs (0)

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rockfish)

rockfish)

rockfish)

 Are Reference sites different from RCAs? Use CIs to plot the magnitude of difference.If the CI for reference sites overlaps with “0” difference (i.e. the 95% CI of the difference

between RCAs & Ref Site means includes “0”), there is no statistical difference

95CIs of mean rockfish abundance in Ref Sites relative to RCAs (0)

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rockfish)

rockfish)

rockfish)

 Are Reference sites different from RCAs? Use CIs to plot the magnitude of difference.If the CI for reference sites overlaps with “0” different (i.e. the 95% CI of the difference

between RCAs & Ref Site means includes “0”)

95CIs of mean rockfish abundance in Ref Sites relative to RCAs (0)

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rockfish)

rockfish)

rockfish)

 Are Reference sites different from RCAs? Use CIs to plot the magnitude of difference.If the CI for reference sites overlaps with “0” different (i.e. the 95% CI of the difference

between RCAs & Ref Site means includes “0”)

95CIs of mean rockfish abundance in Ref Sites relative to RCAs (0)

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rockfish)

rockfish)

rockfish)

 Are Reference sites different from RCAs? Use CIs to plot the magnitude of difference.If the CI for reference sites overlaps with “0” difference (i.e. the 95% CI of the difference

between RCAs & Ref Site means includes “0”)

95CIs of mean rockfish abundance in Ref Sites relative to RCAs (0)

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rockfish)

rockfish)

rockfish)

 Are Reference sites different from RCAs? Use CIs to plot the magnitude of difference.If the CI for reference sites overlaps with “0” different (i.e. the 95% CI of the difference

between RCAs & Ref Site means includes “0”)

95CIs of mean rockfish abundance in Ref Sites relative to RCAs (0)

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rockfish)

rockfish)

rockfish)

 Are Reference sites different from RCAs? Use CIs to plot the magnitude of difference.If the CI for reference sites overlaps with “0” different (i.e. the 95% CI of the difference

between RCAs & Ref Site means includes “0”)

95%CIs of mean rockfish abundance in RCAs relative to Reference Sites (0)

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Download the Mathematica CDF Player at http://www.wolfram.com/cdf/ (CDF: computable document format)

Search the CDF library for “confidence level sample size margin of error”you will see this screenshot, click it.

http://demonstrations.wolfram.com/ConfidenceIntervalsConfidenceLevelSampleSizeAndMarginOfError/

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P-values are used to determine whether a null hypothesis of the study is to beaccepted or rejected, given a predetermined level of accepted error (usually 5%).

P-values enable the recognition of any statistically noteworthy findings and make explicit

the threshold for “scientific difference”.

Confidence intervals provide information about a range in which the truevalue lies with a certain degree of probability (usually 95%), as well as about the

direction and strength of the demonstrated effect. This enables conclusions to be drawnabout the statistical plausibility and biological relevance of the study findings.

BOTH measures must be reported AND UNDERSTOOD before a

conclusion can be drawn by a reader.