Topic (1) INTRODUCTIONGood Science (and Statistics) requires that we:Bird_ID Age Choice Date12 8 blue 0601016 15 purple 052801…The data might look likeSpecies Ind Cover Time BTemp GrdTempArtiod 5 bare 1730 24 16Perissod 1 bare 1732 23.6 16.2Hyraxes 3 grass 1822 25.1 14.8….The data might look likeLat Long DO Temp Time Depth N28.45 141.87 5.4 16.3 0800 10 3.628.68 141.43 8.1 18.9 0910 21 4.1…where Lat is latitude, Long is longitude, DO is dissolved ox4) Summarize and explore the dataset obtainedTopic (1) INTRODUCTION 1-1 Topic (1) INTRODUCTION STATISTICS is … “the science of gaining insight from data.” “the science of making decisions and quantifying the uncertainty in our predictions.” “a way of reasoning.” “a set of tools for displaying, summarizing, comparing, and modeling patterns in data.” “the branch of learning which deals with the processes by which knowledge is gained from observation.”Topic (1) INTRODUCTION 1-2 Vocabulary Data: systematically recorded information, whether numbers or labels, together with its context Datum: singular of data Case (respondent, subject, observational unit, experimental unit) Variable: a piece of information recorded for every case Statistic: a numerical value computed from data Statistics: (singular) the subject of this course, (plural) the plural of the word “statistic” Parameter: a population characteristic, usually we want to estimate this value with our data. Data values are useless without a context: Who, What (and in what units), When, Where, Why, HowTopic (1) INTRODUCTION 1-3 Types of variables: Quantitative: numerical values which measure the amount of something: height, weight, percent bare ground Categorical: labels which identify which of several categories applies to the case: eye color, gender, species. The labels may be numerical (0 for no, 1 for yes). Categorical variables with two categories are also called binary variables. Not all variables are inherently quantitative or categorical. For example, it is common in the social sciences to use a Likert scale variable to measure agreement or disagreement with a statement (1 = strongly disagree, 2 = mildly disagree, 3 = neither agree nor disagree, 4 = mildly agree, 5 = strongly agree). This is an ordinal variable (a categorical variable with a natural order to the categories) and one could treat this as either categorical or quantitative (there are advantages and disadvantages to both).Topic (1) INTRODUCTION 1-4 In addition, quantitative variables are sometimes transformed into categorical variables (age: < 35 years, 35-54 years, >54 years). Categorization discards information, but it may make the analysis simpler to understand, and be a useful way to deal with outliers. It may also more accurately reflect our ability to measure the quantitative variable. For example, if we are ‘eyeballing’ the percent cover of different plant species over a square meter, can we really tell the difference between 17% and 23%? Data Organization Data are generally organized in a spreadsheet, as a matrix, with rowheading being cases and columnheadings being variables. For example, suppose that I have recorded the salaries of the 150 female and 250 male faculty members.Topic (1) INTRODUCTION 1-5 I should view this as one data set with 400 cases and two variables: gender (categorical) and salary (quantitative). Thus, the data should be recorded as follows: ID# Name Gender Salary ($) 1 Jones Male 65000 2 Schmidt Female 48000 3 Lamy Female 68000 4 Shao Female 72000 5 Martinez Male 36000 6 Zuwani Female 28000 . . . . . . . . 400 Stepanauskas Male 80000Topic (1) INTRODUCTION 1-6 Problems: 1. For each of the following variables, identify the observational unit (case) and indicate whether it is quantitative or categorical: a) the number of calories in a fast food sandwich b) whether or not a newborn baby tests HIV-positive c) Florida’s rate of auto thefts per 1000 residents d) the number of birds counted by an observer in 10 minutes at each of several regularly spaced pointsTopic (1) INTRODUCTION 1-7 2. A pizza chain is conducting an experiment to find the optimal baking time (12, 16 or 20 minutes) and temp (400, 425 or 450 F◦) for its pizzas. Four pizzas will be baked under each combo of baking time and temp and the pizzas evaluated for texture and flavor. Draw a data matrix and identify the cases and variables.Topic (1) INTRODUCTION 1-8 3. Suppose that the 50 states are the cases (observational units). Indicate which of the following are variables and which are statistics. a) the number of states that have a female governor b) the percentage of a state’s residents that are over 65 years of age c) the highest speed limit in the state d) the average number of Congressional representatives per state e) the number of births per 1000 residents of the state in 2003Topic (1) INTRODUCTION 1-9 STATISTICS AND THE SCIENTIFIC METHOD Good Science (and Statistics) requires that we: 1) Understand the problem of interest 2) Decide what to measure and how to measure it 3) Collect the data 4) Summarize and explore the dataset obtained 5) Conduct formal data analysis 6) Interpret the results in the context of the original problemTopic (1) INTRODUCTION 1-10 1) Understand the problem of interest (aka construct hypotheses to be tested) Define the hypotheses that you wish to test or the quantities you wish to estimate or describe the model of interest Examples a. For decorating their bowers, male Bower Birds appear to prefer blue ornaments over any other color Hypothesis: the birds choose blue over other colors more often than by chance b. How long does it take for the temperature of a freshly dead animal to drop to the temperature of the ground on which the carcass is resting? Estimation: calculate a 95% confidence interval estimate of the average time after death until the body reaches ground temperatureTopic (1) INTRODUCTION 1-11 c. Construct a model that describes the spatial distribution of Dissolved Oxygen (DO in mg/l) in bottom waters in Chesapeake Bay Model: εηδβα++++= NitrogenDepthTempDO where Temp is water temperature at a location, Depth is the water depth where the sample is taken, and
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