381 QSCI Winter 2012 Introduction to Probability and Statistics

381 Basic Information Instructor: Dr André Punt (FISH 206A; Office hours: Contact directly Teaching Assistant Mr Thomas Pool Office hours: See web-site Class web-site 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

381 Class Structure BNS 117 Lectures (BNS 117): M, Tu, W, Th ( ) MGH 044 Computer laboratory sessions (MGH 044): F (9:30-10:20) Weekly homework assignments.

381 Class Evaluation Submission of homework assignments. Homework assignments (30%; based on the best 8 of 9). Mid-term examination (30%). Final examination (40%).

381 Course Overview Introduction (2 lectures) Summarizing data (4 lectures) Probability (3 lectures) Probability distributions (6 lectures) Making inferences from data (17 lectures)

381 Course Textbooks Required Elementary Statistics by Larson and Farber Optional An EXCEL manual

381 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.

381 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

381 The Statistical Cycle 1. 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.

381 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.

381 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.

381 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.

381 Samples and Populations

381 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?

381 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.

381 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).

381 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.

381 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.

381 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)

381 Data Classification-II Species # Ocean Basin Maximum Age Merluccius capensis1Atlantic7 Merluccius paradoxus2Atlantic5 Merluccius productus3Pacific20 Which fields are qualitative and which are quantitative?

381 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. Nominal 2. Ordinal 3. Interval 4. Ratio

381 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).

381 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.

381 Levels of Measurement-IV (Cheat sheet) LevelPut in categories Arrange in order Subtract values Divide values NominalYesNo OrdinalYes No IntervalYes No RatioYes