Introduction to statistics, Exercises of Environmental Science

Download Introduction to statistics and more Exercises Environmental Science in PDF only on Docsity! EES 2202 Statistics for Environmental Sciences What is statistics? • The word statistics has two meanings. In the more common usage, statistics refers to numerical facts. • The second meaning of statistics refers to the field or discipline of study. • The second meaning of statistics refers to the field or discipline of study. In this sense of the word, statistics is defined as follows. • Descriptive statistics consists of methods for organizing, displaying, and describing data by using tables, graphs, and summary measures. • Inferential statistics consists of methods that use sample results to help make decisions or predictions about a population. • A variable whose values are countable is called a discrete variable. In other words, a discrete variable can assume only certain values with no intermediate values. • Continuous Variable can assume any numerical value over a certain interval or intervals Statistics for environmental sciences • Once we have identified our environmental question, the first thing we need to do is determine what data to collect. • This is one of the most important steps because if we collect the wrong type of data, no statistical model of any kind will allow us to answer our environmental question. • While there are many important considerations to this step, we need to carefully consider the “type” of data and the relationships among variable. • The major types of data in environmental studies are: 1) continuous data, 2) counts, 3) proportions, 4) binary data, 5) time at death, 6) time series, and 7) circular data. • And there are at least three major types of variables based on their relationships to each other: 1) independent variables, 2) dependent variables, and 3) interdependent variables. • The data is measured in any of the four scales 1) Nominal, 2) Ordinal, 3)Interval and 4) ratio • Nominal - Categorical variables with no inherent order or ranking sequence such as names or classes (e.g., gender). Value may be a numerical, but without numerical value (e.g., I, II, III). The only operation that can be applied to Nominal variables is enumeration. • Ordinal - Variables with an inherent rank or order, e.g. mild, moderate, severe. Can be compared for equality, or greater or less, but not how much greater or less. • Interval - Values of the variable are ordered as in Ordinal, and additionally, differences between values are meaningful, however, the scale is not absolutely anchored. Calendar dates and temperatures on the Fahrenheit scale are examples. Addition and subtraction, but not multiplication and division are meaningful operations. • Ratio - Variables with all properties of Interval plus an absolute, non-arbitrary zero point, e.g. age, weight, temperature (Kelvin). Addition, subtraction, multiplication, and division are all meaningful operations. Scales of measurements 5. Time to death/failure data • Is data that take the form of measurements of the time to death, or the time to failure of a component; each individual is followed until it dies (or fails), then the time of death (or failure) is recorded. • Time to death/failure data is not limited to plant and animal longevity studies, however, it applies to any situation in which the time to completion of a process is relevant.; for example, the time it takes juveniles to disperse out of the study area, or the time it takes a snag to fall. 6. Time series data • Involves a sequence (vector) of data points, measured typically at successive times (or locations), spaced at (often uniform) time (or space) intervals. • Usually time series data contains repeated patterns of variation, and identifying and quantifying the scale(s) of the repeated pattern is often the focus of the analysis. • There are many examples of time series data in environmental science: population size measured annually, temperature data measured at fixed intervals, river discharge measured over time, etc. • Time series data also includes spatial data that is serially correlated in space rather than time, such as variables measured at intervals along transects, e.g., plant cover, soil chemistry, water depth, etc.. 7. Circular data • data in which the observations are circular in nature; where the beginning and end of the sequence is the same. • Classic examples of circular data are topographic aspect, day of the year, and orientation of movement. Type of variable • Independent variable... typically the variable(s) being manipulated or changed, or the variable(s) controlled or selected by the experimenter to determine its relationship to an observed phenomenon (i.e., the dependent variable). – In observational studies, the independent variable(s) is not explicitly manipulated or controlled through experimentation, but rather observed in its naturally occurring variation, yet it is presumed determine or influence the value of the dependent variable. – The independent variable is also known as "x ", "explanatory," "predictor," "regressor," "controlled," "manipulated," "exposure," and/or "input” variable. • Dependent variable... the observed result of the independent variable(s) being manipulated, and it usually cannot be directly controlled. – The dependent variable is generally the phenomenon whose behavior we are interested in understanding. – The dependent variable is also known as "y", "response," "regressand," "measured," "observed," "responding," "explained," "outcome," "experimental," and/or "output" variable.