Statistics The Theory And Methods Lecture[1]

Master of Water and Environmental Science Course Title Statistical Methods in water and Environmental Science.

Dr. Mohammed Abudaya

Course Outline Catalog description: Using of advanced Statistical methods in evaluation and interpretation of water and environmental data in: graphical presentation, data sources and accuracy. It also includes an interpretation of probability theory, probability distributions, mean, median, standard deviation, variance, normal distribution and binomial distribution. Other topics will be covered such as; validity of questionnaire, sampling distributions, central limit theory, hypothesis testing, analysis of variance, correlation, regression analysis and forecasting. It will cover advance statistical methods in evaluation and interpretation of Environmental data, expectation and its applications, sampling distributions and statistical inference, two sample problems, non-parametric tests, analysis of discrete data, linear regression, multiple regression, analysis of variance (ANOVA).

Required Text Books/other materials (1) Choosing and Using Statistics. A Biologist's Guide, 2n ed. Calvin Dytham (Blackwell Publishing 2003). (2) SPSS software

Recommended Text Books. (3) Statistical For Environmental Science and Management. 2nd ed. Bryan F.J.Manly (Taylor & Francis Group 2009). (4) Using Statistical Methods for Water Quality Management, Issues, Problems and Solutions. 1st ed. Graham B. McBride (A John Wiley & Sons, Ltd. 2005). (5) Environmental Statistics, Methods and Applications. 1st ed. Vic Barnett (A John Wiley & Sons, Ltd. 2007). (6) ‫ الطبعة‬.‫ نعمان شحادة‬.‫والتوزيع د‬0 .‫الساليب الكمية في الجغرافية باستخدام الحاسوب‬ ‫ دار الصفاء للنشر‬.1997 .‫الولي‬.

Statistical Methods in water and Environmental Science COURSE. Units of study (without details): Unit I Unit II Unit III Unit IV Unit V Unit VI

Statistics, Variables and Distribution Hypothesis testing, sampling and experimental design Descriptive and Presentational Techniques Tests to Look at Differences Tests to Look at Relationships Applications of SPSS

Evaluation of student learning: 30% Mid Exam 20% Case Studies 40% Final Exam 10% Class Participation

Chapter 1: Introduction ?What are Statistics Methods for organizing, summarizing, presenting, & )interpreting information (data Statistics “bring chaos to order ”—condense large amounts of information into smaller understandable units Vocabulary & symbols for communicating about data ”How to make “judgments (about data) under uncertainty ? How do you know which tool to use) 1( ?What do you want to know) 2( ?What type of data do you have) 3(

Statistics Definition is [the theory and method of analyzing quantitative data obtained from samples of observations in order to study and compare sources of variation of phenomena, to help make decisions to accept or reject hypothesized relations between phenomena, and to aid in] making [reliable] inferences from empirical observations" )](Kerlinger, 1986, p. 175

Limitations of Statistics Statistics is used from the mooring bed ???? tea to the bed at night, how •Statistics methods are best applicable to quantitative data. •Statistics decisions are subject to certain degree of error. • Statistics statements are true on an average i.e. true for a group of individuals and may not be true for an individuals.

Branches of Statistics 1. Descriptive Statistics Tools for summarizing, organizing & simplifying data • Tables & Graphs • Measures of Central Tendency • Measures of Variability Examples: Average rainfall in Gaza last year Concentration of Nitrate in ground water Percentage of seniors in this class

2. Inferential Statistics Data from sample used to draw inferences about a population Tools for generalizing beyond actual observations Generalize from a sample to a population Population • The entire collection of events of interest • E.g., collection of people you want to understand • Doesn’t necessarily mean “big” but often is

Sample •Subset of events selected from a population •Intended to represent the population ? Why not just collect data from the whole population !Sometimes impractical, often impossible If we cannot measure everyone in the population, does that mean we cannot study populations or make any ?conclusions about them !NO Data from a sample can tell us something about a population

Sample will not be identical to the population So, generalizations will have some error Generalizations will depend on how well the sample represents the population. Representative sample = Sample whose characteristics are similar to population Random sampling = each event in the population has equal chance of being selected for sample RS increases chances that sample will be representative rather than biased example: Sample of 10 students from our class Select students at random vs. select first row Random sampling does not guarantee no bias!

Sampling .Population is an aggregate of individuals Population or the size of the population .changes with the objective of the study Sample is a fraction of the population .chosen by some sampling procedure It is not always possible to study the total population, because of (costs, (.time, requirements...etc

Methods of Sampling :Simple Random Sampling. 1 An equal chance of selection is assigned to each unit .of the population Samples less than 30 Samples above 30 Table of random numbers .Example 1: Selection of drinking water wells Example 2: Selection samples from an agricultural .field ???population and ??? sample

Methods of Sampling :Stratified Random Sampling. 2 .Dividing the population into L classes or Strata Strata are formed on the basis of .Homogeneity or similarities N=N1+N2+N3….+NL , Example 1: Population = 1000, Sample = 20 ,Strata1 = 400, Strata2 = 300, Strata3 = 200, Strata4 = 100 Answer: Number of samples Strata 1= (400/1000(x20=8 Strata 2= (300/1000(x20=6 Strata 3= (200/1000(x20=4 Strata 4= (100/1000(x20=2 20

Methods of Sampling :Systematic Sampling. 3 Divide the population units into n groups each containing an equal number of units say k Example 1: Selection of 5 drinking water wells from .50 10=50/5 Choose a random number let say 7 47 ,37 ,27 ,17 ,7

Methods of Sampling :Cluster Sampling. 4 The smallest units into which the population can be called the elements of the population, and groups of .element are called the clusters

Chapter 2: Basic concepts ?WHAT ARE DATA Collection of information, comprised of 2 parts )Individuals (also called cases or observations) 1( Variables) 2( Individuals are ANY OBJECTS described by data Do NOT have to be people Variables are characteristics recorded on/from the individuals A variable is something that varies—has at least 2 values Something that changes over time OR Something that varies across individuals

Types of Data Categorical (qualitative): records which group or category an individual/observation belongs in; it classifies; doesn’t make sense to perform arithmetic on this type of variable )E.g., gender (Female or Male Quantitative: a true numerical value; it indicates an amount; often obtained from a measuring instrument; it makes sense to perform arithmetic on these types of variables E.g., Weight in pounds ?????Other examples

Pick out the individuals and variables in these :examples 1. 100 business executives were asked their age 2. 6 water wells measured the dissolved oxygen 3. 8 farmers obtained the weight of 25 pigs 4. 4 technicians measured the sound quality of 10 stereos

:Variables can be divided into

1. Discrete (discontinuous(: a( Indivisible units( b( Restricted to whole numbers( c( Can be counted( e.g. # of children in a family # of houses in a neighborhood

:Continuous (a) Unlimited number of possible values (b) Infinite number of values can fall b/n any 2 observed values (c) No gaps between units e.g. time taken to solve a problem, height or weight Variables can be measured on four different types of scales:

1. Nominal: (a) Consists of a set of categories or labels (b) The ‘score’ does NOT indicate an amount (c) The ‘score’ is arbitrary (d) e.g. Sea Level: 1=Low, 2=Medium, 3=High (c) e.g. land use or soil classifications

(:Ordinal (Rank. 2 a) Score indicates rank order along some continuum( b) It is a relative score, not an absolute score( Might have the highest score on the exam, but we still don’t know how well you did c) There is NOT an equal distance between scores( e.g. Finish 1st ,2nd , or 3rd in a race; could be a difference of seconds b/n 1st & 2nd but a difference of 10 minutes 2 .b/n 2nd & 3rd e.g. Plants from six pots could be ranked in health order .by simple observation and assigned values from 1 to 6

Research and Gathering Data • Science attempts to “discover order in the universe” • Science searches for relationships between & among variables • Two general methods of research: • Correlation (non-experimental) • Experimental • Begin with an hypothesis, a hunch/guess/belief about how :variables might be related or influence each other Meditation can reduce stress

1. Correlational Research Measure variables as they occur naturally Questionnaires, interviews, observational or archival research Test hypotheses about association between 2 or more variables Theory may be causal, but conclusions cannot be Example: Survey 100 people Measure how often (if ever) they meditate Measure their level of life stress Look at association between meditation and stress Can we draw a causal inference?

2. Experimental Research: Manipulate one variable; examine its effect on an outcome variable Independent Variable Dependent Variable Goal is to draw causal inferences Cause

Effect

The IV presumed to cause changes in DV IV

DV

Any question Next Lecture 12/11/2009