Topic (1) INTRODUCTIONGood Science (and Statistics) requires the following: Bird_ID Age Choice Date12 8 blue 060101 6 15 purple 052801…The data might look likeSpecies Bird Cover Time BTemp GrdTempMallard 5 bare 1730 24 16Quail 1 bare 1732 23.6 16.2Teal 3 grass 1822 25.1 14.8….where Lat is latitude, Long is longitude, DO is dissolved oxygen (mg/l), temp is water temperature, time is sampling time, Depth is water depth of the sample, and N is total dissolved Nitrogen (mg/l). 4) Summarize and explore the dataset obtainedTopic (1) INTRODUCTION 1-1 Topic (1) INTRODUCTION Defn: STATISTICS is the science of collecting and analyzing data and making decisions in the face of uncertainty and variability. Good Science (and Statistics) requires the following: 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 1-2 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 prefer blue ornaments over any other color Hypothesis: birds choose blue over other colors more often than by chance b. How long does it take for the body temperature of a freshly dead animal to drop to the ground temperature where 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 1-3 c. Describe the relationship between Dissolved Oxygen (DO in mg/l) in bottom waters in the Chesapeake Bay and a set of environmental covariates Model: εηδβα++++= NitrogenDepthTempDO where Temp is bottom water temperature at a location, Depth is the water depth where the sample is taken, and Nitrogen is the total dissolved nitrogen level in the water sample. 2) Decide what to measure and how to measure it (aka design your experiment or observational study) OBSERVATIONAL STUDIES are those in which data are observed on a sample of the population. Here the usual interest is either describing the population or comparing two or more populations. No manipulations of the elements under study are done.Topic (1) INTRODUCTION 1-4 EXPERIMENTAL STUDIES are planned and are studies in which units are manipulated or treated in order to observe the responses to the treatment. Examples a. Bower birds Construct an experiment in which male bower birds are given a range of color choices in ornaments and observe the percentage of birds which choose blue first. b. Body temperature of a carcass Decide to study the phenomenon in three species of birds on two different ground covers. This is a planned experiment in which we need to decide how many birds of each species, how to arrange the birds over the area available, how to measure the body temperature, how often to measure, how to measure the ground temperature, how long to measure, how many nights should the experiment be done on, and how to analyze the data once we have it!Topic (1) INTRODUCTION 1-5 c. Bottom dissolved oxygen in the Chesapeake Bay Observational study and need to decide where to collect water samples, when to collect them (time of day? Season?), method of measuring the water DO, and the model used to construct a prediction map for DO. 3) Collect the data Once the logistics have been worked out and the statistical analysis methods have been identified, perform the experiment and collect the data. This step includes the data management aspect, i.e. making sure the data are entered correctly, there are no miscoded values, and the data are in a form that makes it easy to analyze later. Examples a. Bower Birds Here the data might look likeTopic (1) INTRODUCTION 1-6 Bird_ID Age Choice Date 12 8 blue 060101 6 15 purple 052801 … b. body temperature of a carcass The data might look like Species Bird Cover Time BTemp GrdTemp Mallard 5 bare 1730 24 16 Quail 1 bare 1732 23.6 16.2 Teal 3 grass 1822 25.1 14.8 …. where Bird is a unique identifier, BTemp is the body temperature, and GrdTemp is the ground temperature next to the bird carcass. c. bottom dissolved oxygen The data might look like Lat Long DO Temp Time Depth N 28.45 141.87 5.4 16.3 0800 10 3.6 …Topic (1) INTRODUCTION 1-7 where Lat is latitude, Long is longitude, DO is dissolved oxygen (mg/l), temp is water temperature, time is sampling time, Depth is water depth of the sample, and N is total dissolved Nitrogen (mg/l). 4) Summarize and explore the dataset obtained Looking for patterns in the data and summaries including the minimum value, the maximum value, the middle or average value, the spread of the data, how common are different values, are there unusual values. Use graphs and summary statistics to describe the patterns in the data. Examples a. Bower Birds Use a bar chart to show the proportions of tested birds who first selected the proffered color chips 2.55.07.510.0Count Axisblue green purple red yellowTopic (1) INTRODUCTION 1-8 b. Body temperature of a carcass First, for each sampling time, calculate the temperature difference TDiff = BodyTemp – GroundTemp. Then plot the TDiff against time of night. -20246810TDiff1500 1750 2000 2250 2500 2750 3000Time b. bottom dissolved oxygen An exploratory method would include a map of the spatial distribution. Use an non-statistical interpolator to map DO over the study regionTopic (1) INTRODUCTION 1-9 22222444444444666observed values 0224466piecewise regr.fitted values-1-1-1-1-1-1-1 0 0 0 0 0 0 0 0 0 0 0 0 0111111111122223piecewise regr.residuals 5) Conduct formal data analysis Here’s where the actual statistical analysis is done. At this point you should know exactly how you will analyze the data – Analysis of Variance?, Regression Model?, T-test?, Chi-square goodness of fit test? Or some other method.Topic (1) INTRODUCTION 1-10 Examples a. Bower Birds Here you might use a
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