381 QSCI 381 - Winter 2012

Introduction to Probability and Statistics

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Basic Information Instructor:

Dr André Punt (FISH 206A; aepunt@u) Office hours: Contact directly

Teaching Assistant Mr Thomas Pool (tpool@uw.edu) Office hours: See web-site

Class web-site http://courses.washington.edu/qc381aep/

Prerequisites for this course MATH 120, a score of 2 on the advanced placement test, or or a score of 67% on the MATHPC placement test

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Class Structure Lectures (BNS 117BNS 117): M, Tu, W, Th

(9.30-10.20) Computer laboratory sessions

(MGH 044MGH 044): F (9:30-10:20) Weekly homework assignments.

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Class Evaluation Submission of homework

assignments. Homework assignments (30%;

based on the best 8 of 9). Mid-term examination (30%). Final examination (40%).

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Course Overview Introduction (2 lectures) Summarizing data (4 lectures) Probability (3 lectures) Probability distributions (6

lectures) Making inferences from data (17

lectures)

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Course Textbooks Required

Elementary Statistics by Larson and Farber

Optional An EXCEL manual

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The Course and the Web Page The slides for each day’s lecture

will be placed on the web-page at the start of the day.

The readings for the week are already on the web-page.

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What is Statistics About?

Statistics is the science of collecting, organizing, analyzing and interpreting

data in order to make decisions

Statistics is the science of data-based decision making in the face of

uncertainty

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The Statistical Cycle1. Identify the questions that are to be

addressed.2. Select a set of hypotheses related to

the question.3. Collect data appropriate to the

question.4. Summarize and analyze the data.5. Do the results make sense / are they

consistent with other information.6. Repeat steps 2-5.

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Statistics and the Natural Sciences

Statistics are a key part of the doing business in the natural sciences today: “Eliminating harvesting will reduce the risk

of extinction by 20%”; “50% of fish caught in the fishery are

immature”; and “80% of fish mature by age 5”.

Statistics is not just summarizing data.

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Some definitions-I - information coming from

observations, counts, measurements, or responses.

The data you will be analyzing will almost always be a sample from a population.

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Some definitions-II - the collection of all

outcomes, responses, measurements or counts that are of interest.

- a subset of a population.

We will almost always be dealing with samples and hoping to make inferences about the population.

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Samples and Populations

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Samples and Populations It is important to be able to identify: a)

the data set, b) the sample, and c) the population.

This isn’t always so easy: Data = 10 counts of predator numbers in

West coast Marine Reserves. Populations = a) West coast marine

reserves, b) U.S. marine reserves, c) World marine reserves, d) Marine reserves off the west coast that can be sampled?

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Parameters and Statistics-I - a numerical description of

a characteristic of the population. - a numerical description of a

characteristic of the sample.

We will often wish to make inferences about parameters based on statistics.

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Parameters and Statistics-II

Whether you are dealing with a parameter or a statistic depends on whether the data relate to the whole population or only a subset of it.

Examples: Average length of all fish passing a weir. Average length of a sample of the fish passing

the same weir. Note: sometimes a quantity could be both

a parameter and a statistic depending the definition of the population (and the question being addressed).

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Branches of Statistics - relate to

organizing, summarizing, and displaying data.

- relate to using a sample to draw conclusions about a population.

Inferential statistics involves drawing a conclusion from some data.

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Inferences vs Summaries This can be quite subtle. Consider:

Average length of females and males: 90cm and 100cm respectively.

Descriptive statistics: the values. Inference: males are (in general)

larger than females.

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Data Classification-I - attributes, labels, non-

numerical values. - numerical

measurements or counts.

Note: Numbers can be “qualitative” (e.g. when analyzing data from surveys, the haul number is qualitative)

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Data Classification-II

Species Species#

Ocean Basin

Maximum Age

Merluccius capensis 1 Atlantic 7

Merluccius paradoxus 2 Atlantic 5

Merluccius productus 3 Pacific 20

Which fields are qualitative and which are quantitative?

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Levels of Measurement-I A data set can be classified according

to the highest level of measurement that applies. The four levels of measurement, listed from lowest to highest are:

1. Nominal2. Ordinal3. Interval4. Ratio

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Levels of Measurement-II - Categories, names, labels,

or qualities. Species name, maturity state, river sampled

- The data can be arranged

in order, but there is no way to assign numerical values to the differences among levels. Condition of a released fish (live, dubious,

dead).

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Levels of Measurement-III - Data can be ordered and

values subtracted, but ratios make little sense / zero is simply a “reference” level. Year, Month, Temperature

- As for interval data, but zero and ratios of values have meaning. Height, length, weight, speed, number of

recaptures.

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Levels of Measurement-IV(Cheat sheet)

Level Put in categorie

s

Arrange in order

Subtract values

Divide values

Nominal Yes No No No

Ordinal Yes Yes No No

Interval Yes Yes Yes No

Ratio Yes Yes Yes Yes