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**1. **1 227.407 Biometrics
Alasdair Noble
a.d.noble@massey.ac.nz
AgHortA 2.72
Xt 4351 Introduce myself
Stats Group in IIS&T
Statistical Consulting part of my job
Work with Mark Stevenson, Cord Heuer, Nigel French and their students.Introduce myself
Stats Group in IIS&T
Statistical Consulting part of my job
Work with Mark Stevenson, Cord Heuer, Nigel French and their students.

**2. **2 French Veterinary Epidemiology! For the non Francophiles:-
The chicken sneezes and all of the others rush away and the farmer says:_
“No – that’s not funny – you understand“
For the non Francophiles:-
The chicken sneezes and all of the others rush away and the farmer says:_
“No – that’s not funny – you understand“

**3. **3 Office Hours 8.00am – 9.30am
Tuesdays
Or any other time that I am free.
I would encourage you to come and ask if you are having problems I am lecturing 2 papers for the first half then only 227.407
Thursdays will not be a great time to catch me as I am very likely to be in Wellington – Explain
Lunchtime is usually 12.00 – 1.00
In early - go home earlyI am lecturing 2 papers for the first half then only 227.407
Thursdays will not be a great time to catch me as I am very likely to be in Wellington – Explain
Lunchtime is usually 12.00 – 1.00
In early - go home early

**4. **4 Introduction Text Book
Aviva Petrie and Paul Watson
Good points –
Bad points –
Computing
Minitab
R (Rcmdr) Discuss Text book
Then Demonstrate Excel, Minitab, R.
Data Petrels.
Sure you can use my data. The 723 bycatch white-chinned petrels were all made available by Christopher J R Robertson and I collected all the data. The bycatch birds were caught predominantly by bottom longliners, but also by tuna longliners, squid trawlers and general fish trawlers between 2000-2003.
The main conclusions reached were that the cluster of bycatch white-chinned petrels caught close to Antipodes Island during the breeding season ('Antipodes Island cluster group') were significantly larger in most external measurements than the cluster caught close to the Auckland Islands during the breeding season ('Auckland Island cluster group'). Birds caught during the breeding season were used because the current literature suggests petrels stay closer to breeding grouds during the breeding season. Satillite tracked white-chinned petrels in the Atlantic and Indian Oceans stayed relatively close to breeding grounds during the breeding season.
Using discriminant analysis we obtained two functions (after cross validation): 1) that could discriminate between 'Auckland and Antipodes Island cluster group' males 93.5% using culmen length and tail length (a positive value = Antipodes cluster group, negative = Auckland cluster group2) a function that could discriminate between 'Auckland and Antipodes Island cluster group' females 92.0% using head and bill length, culmen depth at the base and wing length (a positive value = Antipodes cluster group, negative = Auckland cluster group. I also have a function for differentiating the 'Auckland and Antipodes Island cluster groups' if the sex is not known using head and bill length, tarsus length and tail length (after cross validation 91.4%).I could also discriminate between 'Auckland Island cluster group' males and females 95.5% using head and bill length and culmen depth at the base; and between 'Antipodes Island cluster group' males and females 91.8% using head and bill length, head width, culmen depth at the base and right MTC length.We also found that the 'Antipodes Island cluster group' related closest in size to study skins of specimens collected from the Antipodes Island, and the 'Auckland Island cluster group' related closest in size to study skins of specimens collected from the Auckland Islands. We found this by putting the study skin measurements for each skin in the functions for differentiating Auckland and Antipodes cluster group males and females. This suggested that the bycatch birds caught close to those breeding Islands were likely to be from those Islands.In the lab if we know the sex (which is easy on bycatch birds via dissection) then we can use the functions for discriminating 'Auckland and Antipodes Island cluster group' males and females to give an indication as to which breeding population the birds are from.Based on these results and the taxonomy of the species, I suggest there are two groups of different sized white-chinned petrels in NZ waters. I can only make an assumption as this process now needs to be done on breeding birds at the Auckland and Antipodes Islands to determine if there really is a difference between the two populations. If there is a real difference then there could be two (or more) sub species or species, though it is impossible to determine at this stage.More research is needed on NZ white-chinned petrels, ie measurements taken from live birds on each island during the breeding season and feathers for DNA analysis. Also some breeding biology, life history data would be necessary as well.I also found that there was only a small amount of error between two observers measuring the same sample of white-chinned petrels, and that this error was biologically insignificant. Therefore if the same measuring techniques are used data from two or more observers can be pooled.Anyway that is most of the main conclusions I reached with this research. feel free to contact me for any more information.Cheers Mark FraserDiscuss Text book
Then Demonstrate Excel, Minitab, R.
Data Petrels.
Sure you can use my data. The 723 bycatch white-chinned petrels were all made available by Christopher J R Robertson and I collected all the data. The bycatch birds were caught predominantly by bottom longliners, but also by tuna longliners, squid trawlers and general fish trawlers between 2000-2003.
The main conclusions reached were that the cluster of bycatch white-chinned petrels caught close to Antipodes Island during the breeding season ('Antipodes Island cluster group') were significantly larger in most external measurements than the cluster caught close to the Auckland Islands during the breeding season ('Auckland Island cluster group'). Birds caught during the breeding season were used because the current literature suggests petrels stay closer to breeding grouds during the breeding season. Satillite tracked white-chinned petrels in the Atlantic and Indian Oceans stayed relatively close to breeding grounds during the breeding season.
Using discriminant analysis we obtained two functions (after cross validation): 1) that could discriminate between 'Auckland and Antipodes Island cluster group' males 93.5% using culmen length and tail length (a positive value = Antipodes cluster group, negative = Auckland cluster group2) a function that could discriminate between 'Auckland and Antipodes Island cluster group' females 92.0% using head and bill length, culmen depth at the base and wing length (a positive value = Antipodes cluster group, negative = Auckland cluster group. I also have a function for differentiating the 'Auckland and Antipodes Island cluster groups' if the sex is not known using head and bill length, tarsus length and tail length (after cross validation 91.4%).

**5. **5 Data Analysis Exploratory
Looking for features of the data, some may be expected, some may not.
Inferential (we will look at this later)
Confirming hypotheses previously posited

**6. **6 EDA We may have some preconceived ideas which may be investigated or we may have little idea.
Graphical displays and simple statistics are all that are needed.
Conclusions drawn are tentative.

**7. **7 Graphs Univariate:
Dotplot
Boxplot
Stem and Leaf Plot
Histogram
Frequency/Relative Frequency Distributions
Bargraph
Pie Chart
Time Series Plot
Bivariate
Scatter Plot

**8. **8

**9. **9

**10. **10

**11. **11

**12. **12

**13. **13

**14. **14

**15. **15

**16. **16

**17. **17

**18. **18 Numerical Statistics Numbers calculated from the data to summarise it.
Location
Mean
Median
Geometric mean
Mode
Spread
Standard deviation (Variance)
Interquartile Range

**19. **19 Numerical Statistics These are only summaries.
Do not focus on means.

**20. **20 Tables Can be very powerful if used carefully
Useful for categorical variables
Often contain “Counts”

**21. **21

**22. **22

**23. **23 Definitions of Probability Long Run Relative Frequency
Repeated experiments or observation
“Equally Likely Outcomes”
Dice, Grecian urns, packs of cards
Subjective Probability
Your degree of belief

**24. **24 Notation Probability of an Event A is written

**25. **25 Simple Rules

**26. **26

**27. **27 Conditional Probability

**28. **28 More Conditional ProbabilityandBayes Theorem

**29. **29 Conditional Probability

**30. **30 The Monte Hall Problem(aka Teaching Statistics by Chocolate)

**31. **31 Avoiding the Theory!! Two points:-
There is mathematical theory supporting the statistics that we use.
You may find in the future that you can no longer avoid it and have to bite the bullet. Some vets are very mathematical!!!

**32. **32 Continuous Distributions The Normal Distribution
Characterised by the mean and Standard deviation
Unimodal and symmetric
Mean median and mode are equal
Changing the mean shifts the curve horizontally
Changing the standard deviation alters the width/height of the curve

**33. **33

**34. **34

**35. **35 Normal Distribution Probability Calculations Total Area under the curve is 1
Different tables give different probabilities as they refer to different areas.
Petrie and Watson p.199 (unnumbered!) give “ 2 tailed probabilities” which is a little unusual.
Check carefully any tables that you use.

**36. **36 The Normal Curve Areas under the normal curve give us the probability of an event happening.
How likely is it that we will get a result between 25 and 28?

**37. **Areas Under Normal Curves Draw a rough diagram and guess the answer
Find the number of standard deviations that the end of each interval is from the mean
Look up the areas for these numbers in the tables and write them on the diagram
Add or subtract areas to give the required answer

**38. **38 Using Standard Normal Tables Z values are plotted on the horizontal axis.
Areas under the normal curve are given in the table from the z value back to -infinity.
Find the area for :-
z < 1.30
z < -0.75
z > 1.23
Find the z value if the area is 0.6734

**39. **39 Calculations for “Real” Data Most data does not have a mean of 0 and a standard deviation of 1.
To convert to z values subtract the mean and divide by the standard deviation.
Then look up z values in the table as before.

**40. **Examples Mean is 15, standard deviation is 3 what is the proportion :-
Less than 10
Less than 19
Greater than 14
Greater than 22
Between 13 and 20

**41. **Solution:- Step 2______is _____ above/below the mean. _____is____SD above/below the mean
step 3 From table z=_____gives an area of _____Proportion is ______

**42. **42 Approximate Normal Probabilities

**43. **43 Approximate Normal Probabilities

**44. **44 Approximate Normal Probabilities

**45. **45 Assessing Normality Look at a graph
Symmetry
Single Mode
“Bell shape”

**46. **46 Assessing Normality Find proportions
68% within 1 standard deviation
95% within 2 standard deviations
99% within 3 standard deviations

**47. **47 Assessing Normality Normal probability Plot

**48. **48 Discrete Probability Distributions A discrete set of possible outcomes with a probability attached to each possible outcome.
Two will be considered:-
Binomial Distribution
Commonly for events which happen with a fixed probability
Poisson Distribution
Commonly for “Count” data

**49. **49 Binomial Distribution Four assumptions
Fixed number of trials n
Only two outcomes
Fixed probability of “success” p
Events are independent
Eg
Proportion of cows in a herd with a disease
Associated with each event is a probability of success

**50. **50 Binomial Distribution Mean = np
Variance = np(1-p)
Standard deviation =
For large sample sizes the binomial can be approximated with a Normal distribution
Large means np or n(1-p) is greater than 30

**51. **51 Example The prevalence of Leptospira in the cattle population is approximately 30%
What is the probability that 5 or more of the next 10 cows tested will be positive?

**52. **52 Poisson Distribution A count of the number of independent events occurring randomly over time or space
The mean and variance are equal
Often
“The number of something per something else.”
Again as sample sizes increase the Poisson can be approximated by a Normal distribution

**53. **53 Example If cases of a disease are independent new cases found per day should follow a Poisson distribution. Given a mean number of new cases per day of 4 what is the probability of finding 10 new cases on a particular day?